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This paper investigates the Gaussian state-dependent interference channel (IC) and Z-IC, in which two receivers are corrupted respectively by two different but correlated states that are noncausally known to two transmitters but are unknown to the receivers. Three interference regimes are studied, and the capacity region boundary or the sum capacity boundary is characterized either fully or partially under various channel parameters. In particular, the impact of the correlation between states on cancellation of state and interference as well as achievability of capacity is explored with numerical illustrations. For the very strong interference regime, the capacity region is achieved by the scheme where the two transmitters implement a cooperative dirty paper coding. For the strong but not very strong interference regime, the sum-rate capacity is characterized by rate splitting, layered dirty paper coding, and successive cancellation. For the weak interference regime, the sum-rate capacity is achieved via dirty paper coding individually at two receivers as well as treating interference as noise. This paper also provides the achievable region for the state-dependent IC with each state known at its corresponding transmitter. [ABSTRACT FROM AUTHOR]

This paper studies a two-user state-dependent Gaussian multiple-access channel (MAC) with state noncausally known at one encoder. Two scenarios are considered: 1) each user wishes to communicate an independent message to the common receiver; and 2) the two encoders send a common message to the receiver and the non-cognitive encoder (i.e., the encoder that does not know the state) sends an independent individual message (this model is also known as the MAC with degraded message sets). For both scenarios, new outer bounds on the capacity region are derived, which improve uniformly over the best known outer bounds. In the first scenario, the two corner points of the capacity region as well as the sum rate capacity are established, and it is shown that a single-letter solution is adequate to achieve both the corner points and the sum rate capacity. Furthermore, the full capacity region is characterized in situations in which the sum rate capacity is equal to the capacity of the helper problem. The proof exploits the optimal-transportation idea of Polyanskiy and Wu (which was used previously to establish an outer bound on the capacity region of the interference channel) and the worst case Gaussian noise result for the case in which the input and the noise are dependent. [ABSTRACT FROM AUTHOR]

This paper is about deriving lower bounds on the error exponents for the two-user interference channel under the random coding regime for several ensembles. Specifically, we first analyze the standard random coding ensemble, where the codebooks are comprised of independently and identically distributed (i.i.d.) codewords. For this ensemble, we focus on optimum decoding, which is in contrast to other, suboptimal decoding rules that have been used in the literature (e.g., joint typicality decoding, treating interference as noise, and so on). The fact that the interfering signal is a codeword, rather than an i.i.d. noise process, complicates the application of conventional techniques of performance analysis of the optimum decoder. In addition, unfortunately, these conventional techniques result in loose bounds. Using analytical tools rooted in statistical physics, as well as advanced union bounds, we derive single-letter formulas for the random coding error exponents. We compare our results with the best known lower bound on the error exponent, and show that our exponents can be strictly better. Then, in the second part of this paper, we consider more complicated coding ensembles and find a lower bound on the error exponent associated with the celebrated Han–Kobayashi random coding ensemble, which is based on superposition coding. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of coordinating several agents through their actions, focusing on an asymmetric observation structure with two agents. Specifically, one agent knows the past, present, and future realizations of a state that affects a common payoff function, while the other agent either knows the past realizations of nothing about the state. In both cases, the second agent is assumed to have strictly causal observations of the first agent’s actions, which enables the two agents to coordinate. These scenarios are applied to distributed power control; the key idea is that a transmitter may embed information about the wireless channel state into its transmit power levels so that an observation of these levels, e.g., the signal-to-interference-plus-noise ratio, allows the other transmitter to coordinate its power levels. The main contributions of this paper are twofold. First, we provide a characterization of the set of feasible average payoffs when the agents repeatedly take long sequences of actions and the realizations of the system state are i.i.d.. Second, we exploit these results in the context of distributed power control and introduce the concept of coded power-control. We carry out an extensive numerical analysis of the benefits of coded power control over alternative power-control policies, and highlight a simple yet non-trivial example of a power control code. [ABSTRACT FROM PUBLISHER]

Over the past decade, the bulk of wireless traffic has shifted from speech to content. This shift creates the opportunity to cache part of the content in memories closer to the end users, for example in base stations. Most previous paper focuses on the reduction of load in the backhaul and core networks due to caching, i.e., on the benefits caching offers for the wireline communication link between the origin servers and the caches. In this paper, we are instead interested in the benefits caching can offer for the wireless communication link between the caches and the end users. To quantify the gains of caching for this wireless link, we consider an interference channel in which each transmitter is equipped with an isolated cache memory. Communication takes place in two phases, a content placement phase followed by a content delivery phase. The objective is to design both the placement and the delivery phases to maximize the rate in the delivery phase in response to any possible user demands. Focusing on the three-user case, we show that through careful joint design of these phases, we can reap three distinct benefits from caching: a load balancing gain, an interference cancellation gain, and an interference alignment gain. In our proposed scheme, load balancing is achieved through a specific file splitting and placement, producing a particular pattern of content overlap at the caches. This overlap allows to implement interference cancellation. Furthermore, it allows us to create several virtual transmitters, each transmitting a part of the requested content, which increases interference-alignment possibilities. [ABSTRACT FROM AUTHOR]

This paper investigates the symmetric degrees of freedom (DoF) of multiple-input multiple-output (MIMO) cellular networks with $G$ cells and $K$ users per cell, having $N$ antennas at each base station and $M$ antennas at each user. In particular, we investigate techniques for achievability that are based on either decomposition with asymptotic interference alignment or linear beamforming schemes and show that there are distinct regimes of $(G,K,M,N)$ , where one outperforms the other. We first note that both one-sided and two-sided decomposition with asymptotic interference alignment achieve the same DoF. We then establish specific antenna configurations under which the DoF achieved using decomposition-based schemes is optimal by deriving a set of outer bounds on the symmetric DoF. Using these results, we completely characterize the optimal DoF of any $G$ -cell network with single-antenna users. For linear beamforming schemes, we first focus on small networks and propose a structured approach to linear beamforming based on a notion called packing ratios. Packing ratio describes the interference footprint or shadow cast by a set of transmit beamformers and enables us to identify the underlying structures for aligning interference. Such a structured beamforming design can be shown to achieve the optimal spatially normalized DoF (sDoF) of two-cell two-user/cell network and the two-cell three-user/cell network. For larger networks, we develop an unstructured approach to linear interference alignment, where transmit beamformers are designed to satisfy conditions for interference alignment without explicitly identifying the underlying structures for interference alignment. The main numerical insight of this paper is that such an approach appears to be capable of achieving the optimal sDoF for MIMO cellular networks in regimes where linear beamforming dominates asymptotic decomposition, and a significant portion of sDoF elsewhere. Remarkably, polynomial identity test appears to play a key role in identifying the boundary of the achievable sDoF region in the former case. [ABSTRACT FROM AUTHOR]

This paper shows that for the two-user Gaussian interference channel (G-IC) treating interference as noise without time sharing (TINnoTS) achieves the closure of the capacity region to within either a constant gap, or to within a gap of the order O(\log (\ln (\min ( \mathsf S, \mathsf I))/\gamma )) up to a set of Lebesgue measure \gamma \in (0,1] , where {\mathsf {S}} is the largest signal to noise ratio on the direct links and {\mathsf {I}}$ is the largest interference to noise ratio on the cross links. As a consequence, TINnoTS is optimal from a generalized degrees of freedom (gDoF) perspective for all channel gains except for a subset of zero measure. TINnoTS with Gaussian inputs is known to be optimal within 1/2 bit for a subset of the weak interference regime. Rather surprisingly, this paper shows that TINnoTS is gDoF optimal in all parameter regimes, even in the strong and very strong interference regimes where joint decoding of Gaussian inputs is optimal. For approximate optimality of TINnoTS in all parameter regimes, it is critical to use non-Gaussian inputs. This paper thus proposes to use mixed inputs as channel inputs for the G-IC, where a mixed input is the sum of a discrete and a Gaussian random variable. Interestingly, with reference to the Han–Kobayashi achievable scheme, the discrete part of a mixed input is shown to effectively behave as a common message in the sense that, although treated as noise, its effect on the achievable rate region is as if it were jointly decoded together with the desired messages at a non-intended receiver. The practical implication is that a discrete interfering input is a friend, while an Gaussian interfering input is in general a foe. This paper also discusses other practical implications of the proposed TINnoTS scheme with mixed inputs. Since TINnoTS requires neither explicit joint decoding nor time sharing, the results of this paper are applicable to a variety of oblivious or asynchronous channels, such as the block asynchronous G-IC (which is not an information stable channel) and the G-IC with partial codebook knowledge at one or more receivers. [ABSTRACT FROM AUTHOR]

In this paper, we determine the entire secure degrees of freedom (s.d.o.f.) regions of the $K$ -user Gaussian multiple access (MAC) wiretap channel and the $K$ -user interference channel (IC) with secrecy constraints. For the IC, we consider three secrecy constraints: K-user IC with an external eavesdropper (IC-EE), K-user IC with confidential messages (IC-CM), and their combination Kuser IC with confidential messages and external eavesdropper (IC-CM-EE). The converse for the IC includes constraints both due to secrecy as well as due to interference. For the IC, although the portion of the region close to the optimum sum s.d.o.f. point is governed by the upper bounds due to secrecy constraints, the other portions of the region are governed by the upper bounds due to interference constraints. Different from the existing literature, in order to fully understand the characterization of the s.d.o.f. region of the IC, one has to study the four-user case, i.e., the two- or three-user cases do not illustrate the full generality of the problem. In order to prove the achievability, we use the polytope structure of the converse region. In both MAC and IC cases, we develop explicit schemes that achieve the extreme points of the polytope region given by the converse. In particular, the extreme points of the MAC region are achieved by an $m$ -user MAC wiretap channel with $K-m$ helpers, i.e., by setting $K-m$ users’ secure rates to zero and utilizing them as pure (structured) cooperative jammers. The extreme points of the IC region are achieved by a $(K-m)$ -user IC with confidential messages, $m$ helpers, and $N$ external eavesdroppers, for $m\ge 1$ and a finite $N$ . A byproduct of our results in this paper is that the sum s.d.o.f. is achieved only at one extreme point of the s.d.o.f. region, which is the symmetric-rate extreme point, for both MAC and IC channel models. [ABSTRACT FROM AUTHOR]

In this paper, we study the number of different interference alignment (IA) solutions in a $K$ -user multiple-input multiple-output (MIMO) interference channel, when the alignment is performed via beamforming and no symbol extensions are allowed. We focus on the case where the number of IA equations matches the number of variables. In this situation, the number of IA solutions is finite and constant for any channel realization out of a zero-measure set and, as we prove in this paper, it is given by an integral formula that can be numerically approximated using Monte Carlo integration methods. More precisely, the number of alignment solutions is the scaled average of the determinant of a certain Hermitian matrix related to the geometry of the problem. Interestingly, while the value of this determinant at an arbitrary point can be used to check the feasibility of the IA problem, its average (properly scaled) gives the number of solutions. For single-beam systems, the asymptotic growth rate of the number of solutions is analyzed and some connections with classical combinatorial problems are presented. Nonetheless, our results can be applied to arbitrary interference MIMO networks, with any number of users, antennas, and streams per user. [ABSTRACT FROM PUBLISHER]

The degrees of freedom (DoFs) of the $K$ -user Gaussian interference channel determine the asymptotic growth of the maximal sum rate as a function of the signal-to-noise ratio. Subject to a very general sufficient condition on the cross-channel gains, we give a formula for the DoFs of the scalar interference channel as a function of the deterministic channel matrix, which involves maximization of a sum of information dimensions over $K$ scalar input distributions. Known special cases are recovered, and even generalized in certain cases with unified proofs. [ABSTRACT FROM PUBLISHER]

This paper studies the interference channel with a cognitive relay under delayed feedback. Three types of delayed feedback are studied: delayed channel state information at the transmitter, delayed output feedback, and delayed Shannon feedback. Outer bounds are derived for the degrees of freedom (DoF) region of the two-user multiple-input multiple-output interference channel with a cognitive relay with delayed feedback as well as without feedback. For the single-input single-output scenario, optimal schemes are proposed based on retrospective interference alignment. It is shown that while a cognitive relay without feedback cannot improve the sum-DoF in the two-user single-input single-output interference channel, delayed feedback in the same scenario can increase the sum-DoF to $4/3$ . For the multiple-input multiple-output case, achievable schemes are obtained via extensions of retrospective interference alignment, leading to the DoF regions that meet the respective upper bounds. [ABSTRACT FROM AUTHOR]

Consider a multi-user channel, where each user has a large but non-replenishable bit pool to transmit. Completion time refers to the number of channel uses spent by each user to complete its transmission. In this paper, an information-theoretic formulation of completion time is based on the concept of constrained rates, which are defined over possibly different number of channel uses. Analogous to the capacity region, the completion time region characterizes all possible trade-offs among users’ completion times. For a two-user multi-access channel, it is shown that the completion time region is achieved by operating the channel in two independent phases: a multi-access phase when both users are transmitting, and a point-to-point phase when one user has finished and the other is still transmitting. Using a similar two-phase approach, the completion time regions (or inner and outer bounds) are established for a two-user Gaussian broadcast channel and a two-user Gaussian interference channel. It is observed that although consisting of two convex subregions, the completion time region may not be convex in general. Finally, optimization problems of minimizing the weighted sum completion time for a Gaussian multi-access channel and a Gaussian broadcast channel are solved, demonstrating the utility of the completion time approach. [ABSTRACT FROM PUBLISHER]

We establish the degrees of freedom (DoF) region for the multiple-input multiple-output (MIMO) two-transmitter, and two-receiver ( $2 \times 2$ ) interference network with a general message set consisting of nine messages, one for each pair of a subset of transmitters at which that message is known and a subset of receivers where that message is desired. An outer bound on the general nine-message $2 \times 2$ interference network is obtained and it is shown to be tight, thereby establishing the DoF region for the most general antenna setting wherein the four nodes have an arbitrary number of antennas each. The DoF-optimal scheme is applicable to the MIMO $2 \times 2$ interference network with constant channel coefficients, and hence, a fortiori, to time/frequency varying channel scenarios. In particular, a linear precoding scheme is proposed that can achieve all the DoF tuples in the DoF region. In it, the precise roles played by transmit zero-forcing, interference alignment, random beamforming, symbol extensions, and asymmetric complex signaling (ACS) are delineated. For instance, we identify a class of antenna settings, in which ACS is required to achieve the fractional-valued corner points. Evidently, the DoF regions of all previously unknown cases of the $2 \times 2$ interference network with a subset of the nine-messages are newly established as special cases of the general result of this paper. For instance, the DoF region of the well-known four-message (and even three-message) MIMO $X$ channel is newly established. This problem had remained open despite previous studies, which had found inner and outer bounds that were not tight in general. Hence, the DoF regions of all special cases obtained from the general DoF region of the nine-message $2\times 2$ interference network of this paper that include at least three of the four $X$ channel messages are new, among many others. This paper sheds light on how the same physical $2 \times 2$ interference network could be used by a suitable choice of message sets to take most advantage of the channel resource in a flexible and efficient manner. [ABSTRACT FROM PUBLISHER]

In this paper, the $\eta $ -Nash equilibrium ( $\eta $ -NE) region of the two-user Gaussian interference channel (IC) with perfect output feedback is approximated to within 1 bit/s/Hz and $\eta $ arbitrarily close to 1 bit/s/Hz. The relevance of the $\eta $ -NE region is that it provides the set of rate pairs that are achievable and stable in the IC when both transmitter–receiver pairs autonomously tune their own transmit–receive configurations seeking an $\eta $ -optimal individual transmission rate. Therefore, any rate tuple outside the $\eta $ -NE region is not stable as there always exists one link able to increase by at least $\eta $ bits/s/Hz its own transmission rate by updating its own transmit–receive configuration. The main insights that arise from this paper are as follows. First, the $\eta $ -NE region achieved with feedback is larger than or equal to the $\eta $ -NE region without feedback. More importantly, for each rate pair achievable at an $\eta $ -NE without feedback, there exists at least one rate pair achievable at an $\eta $ -NE with feedback that is weakly Pareto superior. Second, there always exists an $\eta $ -NE transmit–receive configuration that achieves a rate pair that is at most 1 bit/s/Hz per user away from the outer bound of the capacity region. [ABSTRACT FROM PUBLISHER]

We investigate the benefits of incorporating relays in future multi-user wireless networks that seek to exploit unexplored bands of very high frequency spectrum, where transmitted signals are known to be highly susceptible to outages. To this end, we examine a two-user bursty MIMO Gaussian interference channel with an in-band relay, where Bernoulli random states conceptually capture signal outages. As our main result, we show that an in-band relay can provide a degrees of freedom (DoF) gain in this bursty channel. This beneficial role of in-band relays in the bursty channel is in direct contrast to their role in the non-bursty channel which is not as significant to provide a DoF gain. More importantly, we demonstrate that in certain antenna configurations, an in-band relay can help achieve interference-free performances with increased DoF. We find the benefits particularly substantial in high-outage circumstances, as the DoF gain can grow linearly with the number of antennas at the relay. In this paper, first we derive an outer bound from which we obtain a necessary condition for interference-free DoF performances. Then we develop a novel scheme that exploits information of the bursty channel states to achieve them. [ABSTRACT FROM AUTHOR]

In order to gain new insights into multiple-input–multiple-output (MIMO) interference networks, the optimality of \sum k=1^{K} Mk/2 (half the cake per user) degrees of freedom is explored for a K -user MIMO interference channel where the cross-channels have arbitrary rank constraints, and the k th transmitter and receiver are equipped with Mk antennas each. The result consolidates and significantly generalizes results from prior studies by Krishnamurthy et al., of rank-deficient interference channels where all users have M antennas; and by Tang et al., of full rank interference channels where the $k$ th user pair has M_{k} antennas. The broader outcome of this paper is a novel class of replication-based outer bounds for arbitrary rank-constrained MIMO interference networks where replicas of existing users are added as auxiliary users and the network connectivity is chosen to ensure that any achievable scheme for the original network also works in the new network. The replicated network creates a new perspective of the problem, so that even simple arguments such as user cooperation become quite powerful when applied in the replicated network, giving rise to stronger outer bounds, than when applied directly in the original network. Remarkably, the replication-based bounds are broadly applicable not only to MIMO interference channels with arbitrary rank-constraints, but much more broadly, even beyond Gaussian settings. [ABSTRACT FROM PUBLISHER]

Recent results have shown that feedback can significantly increase the capacity of interference networks. This paper considers the impact of noise on such gains due to feedback. In particular, this paper considers the two-user linear deterministic interference channel with noisy feedback, as a stepping stone to characterize the approximate capacity region for the two-user Gaussian interference channel with noisy feedback. First, the capacity region for the symmetric linear deterministic interference channel with noisy feedback is obtained. It is shown that noisy feedback enlarges the capacity region if and only if the number of feedback bits l is greater than a certain threshold l^{*} . It is found that, excluding the regime ({1}/{2}) \leq \alpha \leq 2 , where \alpha is the normalized interference level, in which even full feedback does not increase symmetric capacity, this threshold l^{*} is equal to the per-user symmetric capacity without feedback. One of the key ideas is a novel converse outer bounding technique for the weighted sum rates 2R_{1} + R_{2}$ and R_{1} + 2R_{2} . These results and the techniques developed for the linear deterministic model are then applied to characterize inner bounds and outer bounds for the symmetric Gaussian interference channel with noisy feedback. The outer bounds are shown to be at most 4.7 b/s/Hz away from the achievable rate region. As a corollary, the generalized-degrees-of-freedom region, which approximates the capacity region of the symmetric Gaussian interference channel at high SNR, is found. [ABSTRACT FROM PUBLISHER]

This paper studies and derives new results for the interference channel with a relay (ICR). Three inner bounds for the discrete memoryless ICR are proposed, based on three coding strategies that employ layered code at the relay. The first scheme is inspired by layered noisy network coding, proposed by Lim et al. for the two-way relay channel, the second and the third schemes rely on simpler encoding and decoding processes, dubbed layered quantize-forward. Performance of the proposed schemes is investigated for two classes of channels with Gaussian noise: the interference channel with in-band relay reception/out-of-band relay transmission and the interference with in-band relay reception/in-band relay transmission. For the former class of channels, it is shown that the first proposed scheme achieves the same inner bound as the generalized hash-forward scheme with incremental binning. In addition, the inner bound is within 0.5 bit of the capacity region under certain conditions on the channel parameters. For the latter class of channels, new upper bounds on sum-rate are established by extending known upper bounds for symmetric channels. The first inner bound is shown to be within 0.5 bit of the capacity region if the relay’s power exceeds a certain threshold, which depends on channel parameters. Numerical examples show that the proposed schemes can achieve significantly higher sum-rates when compared with other compress-forward schemes. Analysis also reveals a tradeoff between achievable rates, coding delay, and complexity of the proposed schemes. Results in this paper provide a better understanding of coding for the ICR, in particular, they show that layered coding is a beneficial element in multiuser networks with relays. [ABSTRACT FROM AUTHOR]

In this paper, capacity bounds for the two-user interference channels with cooperative receivers via conferencing links of finite capacities are investigated. Capacity results known for these communication scenarios are limited to a very few special cases of the one-sided channels. One of the challenges in obtaining capacity limits of such cooperative networks is how to establish efficient capacity outer bounds for them. In this paper, by applying new techniques, novel capacity outer bounds are established for the interference channels with conferencing receivers. Using the outer bounds, several new capacity results are proved for interesting channels with unidirectional cooperation in strong and mixed interference regimes. A conferencing link (between receivers) may be utilized to provide a receiver with “information about its desired signal” or “information about its interfering signal”. It is demonstrated that both strategies can be helpful to achieve capacity. Finally, for the case of Gaussian interference channel with conferencing receivers, it is argued that our outer bound is strictly tighter than the previous one derived by Wang and Tse. [ABSTRACT FROM AUTHOR]

So-called improper complex signals have been shown to be beneficial in the single-antenna two-user Gaussian interference channel under the assumptions that all input signals are Gaussian and that we treat interference as noise (TIN). This result has been obtained under a restriction to pure strategies without time-sharing, and it was extended to the case where the rates, but not the transmit powers, may be averaged over several transmit strategies. In this paper, we drop such restrictions and discuss the most general case of coded time-sharing, where both the rates and the powers may be averaged. Since coded time-sharing can in general not be expressed by means of a convex hull of the rate region, we have to account for the possibility of time-sharing already during the optimization of the transmit strategy. By means of a novel channel enhancement argument, we prove a surprising result: proper signals are optimal if coded time-sharing is allowed. In addition to establishing this result, we present an algorithm to compute the corresponding achievable rate region. [ABSTRACT FROM AUTHOR]

In this paper, we consider $K$ –user interference channels with $M$ antennas per node and with backhaul collaboration in one side (among the transmitters or among the receivers), for $M,K\in \mathbb {N}$ , and investigate the tradeoff between the rate in the channel versus the communication load in the backhaul. In this investigation, each node is equipped with $M$ antennas and we focus on a first order approximation result, where the rate of the wireless channel is measured by the degrees of freedom (DoF) per user, and the load of the backhaul is measured by the entropy of backhaul messages per user normalized by $\log $ of transmit power, at high power regimes. This tradeoff is fully characterized for the case of even values of $K$ and approximately characterized for the case of odd values of $K$ , with vanishing approximation gap as $K$ grows. To achieve DoF of $M$ per user, this result establishes the asymptotic optimality of the most straightforward scheme, called central processing, in which the messages are collected at one of the nodes, centrally processed, and forwarded back to each node. In addition, this result shows that the gain of the schemes, relying on distributed processing, through pairwise communication among the nodes (e.g., cooperative alignment) does not scale with the size of the network. For the converse, we develop a new outer-bound on the tradeoff based on splitting the set of collaborative nodes (transmitters or receivers) into two subsets and assuming full cooperation within each group. We further present a sufficient condition on the wireless channel connectivity, which although more relaxed, guarantees the validity of the above tradeoff. Finally, we show that verifying this condition takes a polynomial time in the network size. [ABSTRACT FROM AUTHOR]

We consider the $K$ -user Multiple Input Multiple Output (MIMO) Gaussian interference channel with $M$ antennas at each transmitter and $N$ antennas at each receiver. It is assumed that channel coefficients are constant real numbers and are available at all transmitters and at all receivers. The main objective of this paper is to characterize the number of Degrees of Freedom (DoF) of this channel. Using the real interference alignment technique introduced in Motahari et al., 2014, we show that $\frac {MN}{M+N} K$ degrees of freedom can be achieved for almost all channel realizations. Also, a new upper-bound on the DoF of this channel is provided. This upper-bound coincides with our achievable DoF for $K\geq K_{u} \triangleq \frac {M+N}{\gcd (M,N)}$ , where $\gcd (M,N)$ denotes the greatest common divisor of $M$ and $N$. This gives an exact characterization of DoF for $M\times N$ MIMO Gaussian interference channel in the case of $K\geq K_{u}$. Since there is no cooperation between transmit (or receive) antennas of each user in our transmission scheme, this result shows that the DoF benefit of joint processing in collocated antennas vanishes when the number of users is greater than a certain threshold. [ABSTRACT FROM AUTHOR]

We consider three channel models: the wiretap channel with M helpers, the K -user multiple access wiretap channel, and the K -user interference channel with an external eavesdropper, when no eavesdropper’s channel state information (CSI) is available at the transmitters. In each case, we establish the optimal sum secure degrees of freedom (s.d.o.f.) by providing achievable schemes and matching converses. We show that the unavailability of the eavesdropper’s channel state information at the transmitter (CSIT) does not reduce the s.d.o.f. of the wiretap channel with helpers. However, there is loss in s.d.o.f. for both the multiple access wiretap channel and the interference channel with an external eavesdropper. In particular, we show that in the absence of eavesdropper’s CSIT, the K -user multiple access wiretap channel reduces to a wiretap channel with (K-1) to \frac K-1K . For the interference channel with an external eavesdropper, the optimal sum s.d.o.f. decreases from \frac K(K-1)2K-1 to \frac K-12 in the absence of the eavesdropper’s CSIT. Our results show that the lack of eavesdropper’s CSIT does not have a significant impact on the optimal s.d.o.f. for any of the three channel models, especially when the number of users is large. This implies that physical layer security can be made robust to the unavailability of eavesdropper CSIT at high signal-to-noise ratio regimes by the careful modification of the achievable schemes as demonstrated in this paper. [ABSTRACT FROM PUBLISHER]

This paper studies the value of limited rate cooperation between the transmitters for managing interference and simultaneously ensuring secrecy, in the two-user Gaussian symmetric interference channel (IC). First, the problem is studied in the symmetric linear deterministic IC (SLDIC) setting, and achievable schemes are proposed, based on interference cancelation, relaying of the other user’s data bits, and transmission of random bits. In the proposed achievable scheme, the limited rate cooperative link is used to share a combination of data bits and random bits depending on the model parameters. Outer bounds on the secrecy rate are also derived, using a novel partitioning of the encoded messages and outputs depending on the relative strength of the signal and the interference. The partitioning helps to bound certain negative entropy terms, leading to a tractable outer bound. The inner and outer bounds are derived under all possible parameter settings. It is found that, for some parameter settings, the inner and outer bounds match, yielding the capacity of the SLDIC under transmitter cooperation and secrecy constraints. In some other scenarios, the achievable rate matches with the capacity region of the two-user SLDIC without secrecy constraints derived by Wang and Tse; thus, the proposed scheme offers secrecy for free, in these cases. Inspired by the achievable schemes and outer bounds in the deterministic case, achievable schemes and outer bounds are derived in the Gaussian case. The proposed achievable scheme for the Gaussian case is based on Marton’s coding scheme and stochastic encoding along with dummy message transmission. One of the key techniques used in the achievable scheme for both the models is interference cancelation, which simultaneously offers two seemingly conflicting benefits: it cancels interference and ensures secrecy. Many of the results derived in this paper extend to the asymmetric case also. The results show that limited transmitter cooperation can greatly facilitate secure communications over two-user ICs. [ABSTRACT FROM AUTHOR]

In this paper, a class of broadcast interference channels (BIC) is investigated, where one of the two broadcast receivers is subject to interference coming from a point-to-point transmission. For a general discrete memoryless broadcast interference channel (DM-BIC), an achievable scheme based on message splitting, superposition, and binning is proposed and a concise representation of the corresponding achievable rate region \mathcal R is obtained. Two partial-order broadcast conditions interference-oblivious less noisy and interference-cognizant less noisy are defined, thereby extending the usual less noisy condition for a regular broadcast channel by taking interference into account. Under these conditions, a reduced form of \mathcal R is shown to be equivalent to a rate region based on a simpler scheme, where the broadcast transmitter uses only superposition. Furthermore, if interference is strong for the interference-oblivious less noisy DM-BIC, the capacity region is given by the aforementioned two equivalent rate regions. For the interference-cognizant less noisy DM-BIC, it is argued that the strong but not very strong interference condition does not exist, and in this case, the capacity region for the very strong interference is obtained. For a Gaussian broadcast interference channel, channel parameters are categorized into three regimes. For the first two regimes, which are closely related to the two partial-order broadcast conditions, achievable rate regions are derived by specializing the corresponding achievable schemes of DM-BICs with Gaussian input distributions. The entropy power inequality-based outer bounds are obtained by combining bounding techniques for a Gaussian broadcast channel and a Gaussian interference channel. These inner and outer bounds lead to either exact or approximate characterizations of capacity regions and sum capacity under various conditions. For the remaining complementing regime, inner and outer bounds are also provided. [ABSTRACT FROM AUTHOR]

This paper explores the relationship between two ideas in the network information theory: edge removal and strong converses. Edge removal properties state that if an edge of small capacity is removed from a network, the capacity region does not change too much. Strong converses state that, for rates outside the capacity region, the probability of error converges to 1 as the blocklength goes to infinity. Various notions of edge removal and strong converse are defined, depending on how edge capacity and error probability scale with blocklength, and relations between them are proved. Each class of strong converse implies a specific class of edge removal. The opposite directions are proved for deterministic networks. Furthermore, a technique based on a novel, causal version of the blowing-up lemma is used to prove that for discrete memoryless networks, the weak edge removal property—that the capacity region changes continuously as the capacity of an edge vanishes—is equivalent to the exponentially strong converse—that outside the capacity region, the probability of error goes to 1 exponentially fast. This result is used to prove exponentially strong converses for several examples, including the discrete two-user interference channel with strong interference, with only a small variation from traditional weak converse proofs. [ABSTRACT FROM AUTHOR]

Existing polar coding schemes for the two-user interference channel follow the original idea of Han and Kobayashi, in which component messages are encoded independently and then mapped by some deterministic functions (i.e., homogeneous superposition coding). In this paper, we propose a new polar coding scheme for the interference channel based on the heterogeneous superposition coding approach of Chong, Motani, and Garg. We prove that fully joint decoding (the receivers simultaneously decode both senders’ common messages and the intended sender’s private message) in the Han–Kobayashi strategy can be simplified to two types of partial-joint decoding, which are friendly to polar coding with practical decoding algorithms. The proposed coding scheme requires less auxiliary random variables and no deterministic functions and can be efficiently constructed. Furthermore, we extend this result to interference networks and show that partial-joint decoding is a general method for designing heterogeneous superposition polar coding schemes in interference networks. [ABSTRACT FROM AUTHOR]

In multi-user wireless packet networks, interference, typically modeled as packet collision, is the throughput bottleneck. Users become aware of the interference pattern via feedback and use this information for contention resolution and packet retransmission. Conventional random access protocols interrupt communication to resolve contention, which reduces network throughput and increases latency and power consumption. In this paper, we take a different approach, and we develop opportunistic random access protocols rather than pursuing conventional methods. We allow wireless nodes to communicate without interruption and to observe the interference pattern. We then use this interference pattern knowledge and channel statistics to counter the negative impact of interference. We prove the optimality of our protocols using an extremal rank-ratio inequality. An important part of our contributions is the integration of spatial correlation in our assumptions and results. We identify spatial correlation regimes in which inherently outdated feedback becomes as good as idealized instantaneous feedback and correlation regimes in which feedback does not provide any throughput gain. To better illustrate the results, and as an intermediate step, we characterize the capacity region of finite-field spatially correlated interference channels with delayed channel state information at the transmitters. [ABSTRACT FROM AUTHOR]

Polar coding is a method for communication over noisy classical channels, which is provably capacity achieving and has an efficient encoding and decoding. Recently, this method has been generalized to the realm of quantum information processing, for tasks such as classical communication, private classical communication, and quantum communication. In this paper, we apply the polar coding method to network classical-quantum information theory, by making use of recent advances for related classical tasks. In particular, we consider problems such as the compound multiple access channel and the quantum interference channel. The main result of our work is that it is possible to achieve the best known inner bounds on the achievable rate regions for these tasks, without requiring a so-called quantum simultaneous decoder. Thus, this paper paves the way for developing network classical-quantum information theory further without requiring a quantum simultaneous decoder. [ABSTRACT FROM AUTHOR]

This paper considers the corner points of the capacity region of a two-user Gaussian interference channel (GIC). In a two-user GIC, the rate pairs where one user transmits its data at the single-user capacity (without interference), and the other at the largest rate for which reliable communication is still possible are called corner points. This paper relies on existing outer bounds on the capacity region of a two-user GIC that are used to derive informative bounds on the corner points of the capacity region. The new bounds refer to a weak two-user GIC (i.e., when both crosslink gains in standard form are positive and below 1), and a refinement of these bounds is obtained for the case where the transmission rate of one user is within \varepsilon > 0 of the single-user capacity. The bounds on the corner points are asymptotically tight as the transmitted powers tend to infinity, and they are also useful for the case of moderate SNR and INR. Upper and lower bounds on the gap (denoted by \Delta ) between the sum-rate and the maximal achievable total rate at the two corner points are derived. This is followed by an asymptotic analysis analogous to the study of the generalized degrees of freedom [where the SNR and INR scalings are coupled such that (\log (\text INR)/\log (\text SNR)) = \alpha \geq 0 ], leading to an asymptotic characterization of this gap which is exact for the whole range of \alpha . The upper and lower bounds on $\Delta $ are asymptotically tight in the sense that they achieve the exact asymptotic characterization. Improved bounds on $\Delta $ are derived for finite SNR and INR, and their improved tightness is exemplified numerically. [ABSTRACT FROM PUBLISHER]

In a $K$ -user Gaussian interference channel, it has been shown that if for each user the desired signal strength is no less than the sum of the strengths of the strongest interference from this user and the strongest interference to this user (all values in decibel scale), then treating interference as noise (TIN) is optimal from the perspective of generalized degrees of freedom (GDoF) and achieves the entire channel capacity region to within a constant gap. In this paper, we show that for such TIN-optimal interference channels, even if the message set is expanded to include an independent message from each transmitter to each receiver, operating the new channel as the original interference channel and treating interference as noise is still optimal for the sum capacity up to a constant gap. Furthermore, we extend the result to the sum-GDoF optimality of TIN in the general setting of $X$ channels with arbitrary numbers of transmitters and receivers. [ABSTRACT FROM PUBLISHER]

As the main basic building blocks of the interference networks, in this paper the broadcast channel, the classical interference channel (CIC), and the cognitive radio channel (CRC) are considered. New capacity outer bounds are established for these channels. These outer bounds are all derived based on a novel unified framework. Using the derived outer bounds, some new capacity results are proved for the CIC and the CRC; a mixed interference regime is identified for the two-user CIC, where decoding interference at one receiver and treating interference as noise at the other one is sum-rate optimal. In addition, a noisy interference regime is derived for the one-sided CIC. Our new capacity theorems for the CIC contain the previously obtained results regarding the Gaussian channel as special cases. For the CRC, a full characterization of the capacity region for a class of more-capable channels is derived. Moreover, it is shown that the derived outer bounds are useful to study channels with one-sided receiver side information wherein one of the receivers has access to the nonintended message; capacity bounds are also discussed in details for such scenarios. Our results lead to new insights regarding the nature of information flow in the basic interference networks. [ABSTRACT FROM AUTHOR]

Two-way communication is prevalent and its fundamental limits are first studied in the point-to-point setting by Shannon. One natural extension is a two-way interference channel (IC) with four independent messages: two associated with each direction of communication. In this paper, we explore a deterministic two-way IC, which captures the key properties of the wireless Gaussian channel. Our main contribution lies in the complete capacity region characterization of the two-way IC (with respect to the forward and backward sum-rate pair) via a new achievable scheme and a new converse. One surprising consequence of this result is that not only we can get an interaction gain over the one-way non-feedback capacities, we can sometimes get all the way to perfect feedback capacities in both directions simultaneously. In addition, our novel outer bound characterizes channel regimes in which interaction has no bearing on capacity. [ABSTRACT FROM AUTHOR]

This paper studies channel coding for the discrete memoryless multiple-access channel with a given (possibly suboptimal) decoding rule. A multi-letter successive decoding rule depending on an arbitrary non-negative decoding metric is considered, and achievable rate regions and error exponents are derived both for the standard MAC (independent codebooks), and for the cognitive MAC (one user knows both messages) with superposition coding. In the cognitive case, the rate region and error exponent are shown to be tight with respect to the ensemble average. The rate regions are compared with those of the commonly considered decoder that chooses the message pair maximizing the decoding metric, and numerical examples are given for which successive decoding yields a strictly higher sum rate for a given pair of input distributions. [ABSTRACT FROM AUTHOR]

The best-known achievable rate region for the two-user Gaussian interference channel corresponds to the Han-Kobayashi scheme. However, mathematical expressions that characterize the Han-Kobayashi rate region are complicated. This complexity hinders a comprehensive understanding of the rate region. For instance, when interference is weak, the maximum achievable sum-rate of the Han-Kobayashi scheme has been unknown. This paper studies the sum-rate of the Han-Kobayashi scheme with Gaussian inputs and fully characterizes the maximum achievable sum-rate, when no time sharing is used. The optimal power-splitting variables and the corresponding maximum achievable sum-rate are explicitly expressed in closed forms. With the same approach, the maximum weighted sum-rate is expressed that characterizes the boundary of the Han-Kobayashi region without time sharing. Moreover, when time sharing is used, the boundary is expressed in terms of the upper concave envelope of a function of transmitters’ powers. [ABSTRACT FROM AUTHOR]

Most coding schemes proposed for the interference channel take advantage of joint decoding to enlarge rate region. However, decoding complexity escalates considerably when joint decoding is used. This paper studies the achievable sum-rate of the two-user Gaussian interference channel when joint decoding is replaced by successive decoding. First, the strong interference class is examined, and it is proved that if transmitters’ powers satisfy certain conditions, successive decoding is optimal and achieves the sum-capacity. The number of the required splits, the amount of power allocated to each split, and the order of decoding at receivers are explicitly determined. Second, the weak interference class is examined. A novel rate-splitting scheme is proposed that does not use joint decoding. The number of required splits and the amount of power allocated to each split are expressed in closed forms. It is shown that, for a wide range of transmitters’ powers, this scheme achieves the sum-rate of the Gaussian Han-Kobayashi scheme. Moreover, it is proved that the difference between the sum-rate of this scheme and that of the Gaussian Han-Kobayashi scheme is bounded, for all values of transmitters’ powers. [ABSTRACT FROM AUTHOR]

The capacity region of the $K$ -user Gaussian interference channel (GIC) is a long-standing open problem and even capacity outer bounds are little known in general. A significant progress on degrees-of-freedom (DoF) analysis, a first-order capacity approximation, for the $K$ -user GIC has provided new important insights into the problem of interest in the high signal-to-noise ratio (SNR) limit. However, such capacity approximation has been observed to have some limitations in predicting the capacity at finite SNR. In this paper, we develop a new upper-bounding technique that utilizes a new type of genie signal and applies time sharing to genie signals at $K$ receivers. Based on this technique, we derive new upper bounds on the sum capacity of the three-user GIC with constant, complex channel coefficients and then generalize to the $K$ -user case to better understand sum-rate behavior at finite SNR. We also provide closed-form expressions of our upper bounds on the capacity of the $K$ -user symmetric GIC easily computable for any $K$ . From the perspectives of our results, some sum-rate behavior at finite SNR is in line with the insights given by the known DoF results, while some others are not. In particular, the well-known $K/2$ DoF achievable for almost all constant real channel coefficients turns out to be not embodied as a substantial performance gain over a certain range of the cross-channel coefficient in the $K$ -user symmetric real case especially for large $K$ . We further investigate the impact of phase offset between the direct-channel coefficient and the cross-channel coefficients on the sum-rate upper bound for the three-user complex GIC. As a consequence, we aim to provide new findings that could not be predicted by the prior works on DoF of GICs. [ABSTRACT FROM PUBLISHER]

The best outer bound on the capacity region of the two-user Gaussian interference channel (GIC) is known to be the intersection of regions of various bounds, including genie-aided outer bounds, in which a genie provides noisy input signals to the intended receiver. The Han and Kobayashi (HK) scheme provides the best known inner bound. The rate difference between the best known lower and upper bounds on the sum capacity remains as large as 1 b/channel use, especially around g^2=P^-1/3 , where P is the symmetric power constraint and g is the symmetric real cross-channel coefficient. In this paper, we pay attention to the moderate interference regime where g^2\in ~(\max (0.086, P^-1/3),1) . We propose a new upper-bounding technique that utilizes noisy observation of interfering signals as genie signals and applies time sharing to the genie signals at the receivers. A conditional version of the worst additive noise lemma is also introduced to derive new capacity bounds. The resulting upper (outer) bounds on the sum capacity (capacity region) are shown to be tighter than the existing bounds in a certain range of the moderate interference regime. Using the new upper bounds and the HK lower bound, we show that R\text {sym}^{ }=\frac {1}2\log \big (|g|P+|g|^{-1}(P+1)\big ) characterizes the capacity of the symmetric real GIC to within 0.104 b/channel use in the moderate interference regime at any signal-to-noise ratio (SNR). We further establish a high-SNR characterization of the symmetric real GIC, where the proposed upper bound is at most 0.1 b far from a certain HK achievable scheme with Gaussian signalling and time sharing for g^2\in ~(0,1] . In particular, R\text {sym}^{ } is achievable at high SNR by the proposed HK scheme and turns out to be the high-SNR capacity at least at g^2=0.25, 0.5 . We finally point out that there are two subregimes at high SNR in the weak interference regime, where g^2\in (0,1] . [ABSTRACT FROM AUTHOR]

The capacity region of the multicast Cognitive Inter-Ference Channel (CIFC) is investigated. This channel consists of two independent transmitters that wish to multicast two different messages, each to a different set of users. In addition, one of the transmitters—commonly referred to as the cognitive transmitter—has prior non-causal knowledge of both messages to be transmitted. This scenario subsumes some long-standing open problems, such as the interference channel, the broadcast channel, and multicast communications. The aim of this paper is the derivation of optimal interference mitigation techniques under different interference regimes. To this end, two settings, namely the multi-primary CIFC, i.e., $M=1$ and $N \geq 1$ , and its complementary, the multi-secondary CIFC, i.e., $N=1$ and $M \geq 1$ , are investigated as an attempt to build a thorough understanding for the more general multicast CIFC setting. It is shown that, for some interference regimes, well-known coding techniques for the standard CIFC remain still optimal under the constraint of multicasting to multiple users. However, in other interference regimes, capacity achieving coding and decoding schemes prove to be more involved. A careful combination of these coding schemes and new outer bounding techniques allows to characterize the capacity region for several classes of discrete memoryless and Gaussian multicast CIFC under different interference regimes. [ABSTRACT FROM PUBLISHER]

In this paper, we consider the K -user single-input single-output interference channel with delayed channel state information at the transmitters (CSIT). Our main contribution is to show that even with delayed CSIT and distributed transmitters, the achievable degrees of freedom (DoFs) still scale with the number of users. More specifically, we propose a method that achieves K/(2\sqrt {K} - 1) \geq \sqrt {K}/2 DoF. The main idea behind the proposed method is to use interference alignment (IA) at the receiver side in conjunction with repetition coding at the transmitters. Repetition coding repeats the data R$ times while IA makes the interference generated by a given transmitter identical: 1) at all non-intended receivers and 2) all transmission repetitions. Therefore, one retransmission per transmitter is sufficient to cancel all the interference. This reduces significantly the overhead required for interference removal since the number of interference terms is reduced from $RK(K-1)$ to $K$ . [ABSTRACT FROM PUBLISHER]

The impact of cooperation on interference management is investigated by studying an elemental wireless network, the so-called symmetric interference relay channel (IRC), from a generalized degrees of freedom (GDoF) perspective. This is motivated by the fact that the deployment of relays is considered as a remedy to overcome the bottleneck of current systems in terms of achievable rates. The focus of this paper is on the regime in which the interference link is weaker than the source-relay link in the IRC. Our approach toward studying the GDoF goes through the capacity analysis of the linear deterministic IRC (LD-IRC). New upper bounds on the sum capacity of the LD-IRC based on genie-aided approaches are established. These upper bounds together with some existing upper bounds are achieved by using four novel transmission schemes. Extending the upper bounds and the transmission schemes to the Gaussian case, the GDoF of the Gaussian IRC is characterized for the aforementioned regime. This completes the GDoF results available in the literature for the symmetric GDoF. It turns out that even if the incoming and outgoing links of the relay are both weaker than the desired channel, involving a relay can increase the GDoF. Interestingly, utilizing the relay in this case can increase the slope of the GDoF from −2 [in the interference channel (IC)] to −1 or 0. This shrinks the regime where ignoring the interference by treating it as noise is optimal. Furthermore, the analysis shows that if the relay ingoing and outgoing links are sufficiently strong, the relay is able to neutralize the interference completely. In this case, the bottleneck of the transmission will be the interference links, and hence, the GDoF increases if the interference link gets stronger. It is shown that in the strong interference regime, in contrast to the IC, the GDoF can be a monotonically decreasing function of the interference level. [ABSTRACT FROM PUBLISHER]

In this paper, we propose a novel “genie chains” approach to obtain information theoretic degrees of freedom (DoF) outer bounds for MIMO wireless interference networks. This new approach creates a chain of mappings from genie signals provided to a receiver to the exposed signal spaces at that receiver, and then the exposed signal spaces serve as the genie signals for the next receiver in the chain subject to certain linear independence requirements. Our approach essentially converts an information theoretic DoF outer bound problem into a linear algebra problem. Several applications of the genie chains approach are presented. [ABSTRACT FROM AUTHOR]

Effective interference management in the multiuser interference channel necessitates that the users form their transmission and interference management decisions in coordination, and adapt them to the state of the channel. Establishing such coordination, often facilitated through information exchange, is prohibitive in fast-varying channels, especially when the network size grows. This paper focuses on the multiuser Gaussian interference channel and offers a receiver-centric approach to interference management. In this approach, the transmitters deploy rate-splitting and superposition coding to generate their messages according to independent Gaussian codebooks. The receivers can freely decode any arbitrary set of interfering messages along with their designated messages in any desired joint or ordered fashion, and treat the rest of the interferers as Gaussian noise. The proposed receiver-centric interference management approach is applied to two class of problems (outage optimization and fairness-constrained rate allocation), and constructive proofs are provided to establish the following properties for the proposed approach: 1) the optimal set of codebooks to be decoded by each receiver is a local decision made by each receiver based on its local channel state information (CSI); 2) the globally optimal transmission rates are related to locally optimal rates computed by the receivers based on their local information, which implies that the transmitters do not require explicit knowledge of the CSI and can determine their rates via limited feedback from the receivers; and 3) obtaining the optimal interference management strategy at each receiver has controlled complexity. [ABSTRACT FROM AUTHOR]

The best known inner bound for the two-user discrete memoryless interference channel is the Han–Kobayashi rate region. The coding schemes that achieve this region are based on rate-splitting and superposition coding. In this paper, we develop a multicoding scheme to achieve the same rate region. A key advantage of the multicoding nature of the proposed coding scheme is that it can be naturally extended to more general settings, such as when encoders have state information or can overhear each other. In particular, we extend our coding scheme to characterize the capacity region of the state-dependent deterministic Z-interference channel when noncausal state information is available at the interfering transmitter. We specialize our results to the case of the linear deterministic model with ON/OFF interference, which models a wireless system where a cognitive transmitter is noncausally aware of the times it interferes with a primary transmission. For this special case, we provide an explicit expression for the capacity region and discuss some interesting properties of the optimal strategy. We also extend our multicoding scheme to find the capacity region of the deterministic Z-interference channel when the signal of the interfering transmitter can be overheard at the other transmitter (also known as unidirectional partial cribbing). [ABSTRACT FROM PUBLISHER]

Building on recent development by Padakandla and Pradhan, and by Lim, Feng, Pastore, Nazer, and Gastpar, this paper studies the potential of structured coset coding as a complete replacement for random coding in network information theory. The roles of two techniques used in coset coding to generate nonuniform codewords, namely, shaping and channel transformation, are clarified and illustrated via the simple example of the two-sender multiple access channel. While individually deficient, the optimal combination of shaping via nested coset codes of the same generator matrix (which we refer to as homologous codes) and channel transformation is shown to achieve the same performance as traditional random codes for the general two-sender multiple access channel. The achievability proof of the capacity region is extended to multiple access channels with more than two senders, and with one or more receivers. A quantization argument adapted to the proposed combination of two techniques is presented to establish the achievability proof for their Gaussian counterparts. It is illustrated by an example that combining shaping and channel transformation is useful even when the goal of transmission for a subset of the receivers is to recover a linear combination of messages. These results open up new possibilities of utilizing homologous codes for a broader class of applications. [ABSTRACT FROM AUTHOR]

A general time-varying feedback coding scheme is proposed for $M$ -user fully connected symmetric Gaussian interference channels. Based on the analysis of the general coding scheme, we prove a theorem which gives a criterion for designing good time-varying feedback codes for Gaussian interference channels. The proposed scheme improves the Suh-Tse and Kramer inner bounds of the channel capacity for the cases of weak and not very strong interference when $M=2$. This capacity improvement is more significant when the signal-to-noise ratio (SNR) is not very high. In addition, our coding scheme can be proved mathematically and numerically to outperform the Kramer code for $M\geq 2$ when the SNR is equal to the interference-to-noise ratio (INR). Besides, the generalized degrees-of-freedom (GDoF) of our proposed coding scheme can be proved to be optimal in the all network situations (very weak, weak, strong, very strong) for any $M$. The numerical results show that our coding scheme can attain better performance than the Suh-Tse coding scheme for $M=2$ or the Mohajer-Tandon-Poor lattice coding scheme for $M > 2$. Furthermore, the simplicity of the encoding/decoding algorithms is another strong point of our proposed coding scheme compared with the Suh-Tse coding scheme when $M=2$ and the Mohajer-Tandon-Poor lattice coding scheme when $M > 2$. More importantly, our results show that an optimal coding scheme for the symmetric Gaussian interference channels with feedback can be achieved by only using marginal posterior distributions under a better cooperation strategy between transmitters. [ABSTRACT FROM AUTHOR]

In 1959, Rényi proposed the information dimension and the $d$ -dimensional entropy to measure the information content of general random variables. This paper proposes a generalization of information dimension to stochastic processes by defining the information dimension rate as the entropy rate of the uniformly quantized stochastic process divided by minus the logarithm of the quantizer step size $1/m$ in the limit as $m\to \infty $. It is demonstrated that the information dimension rate coincides with the rate-distortion dimension, defined as twice the rate-distortion function $R(D)$ of the stochastic process divided by $-\log (D)$ in the limit as $D\downarrow 0$. It is further shown that among all multivariate stationary processes with a given (matrix-valued) spectral distribution function (SDF), the Gaussian process has the largest information dimension rate and the information dimension rate of multivariate stationary Gaussian processes is given by the average rank of the derivative of the SDF. The presented results reveal that the fundamental limits of almost zero-distortion recovery via compressible signal pursuit and almost lossless analog compression are different in general. [ABSTRACT FROM AUTHOR]

In a $K$ -user Gaussian interference channel, it has been shown by Geng et al. that if for each user, the desired signal strength is no less than the sum of the strengths of the strongest interference from this user and the strongest interference to this user (all values in decibel scale), then power control and treating interference as noise (TIN) is optimal from the perspective of generalized degrees of freedom (GDoF) and achieves the entire channel capacity region to within a constant gap. In this paper, we generalize the optimality of TIN to compound networks. We show that for a $K$ -user compound Gaussian interference channel, if in every possible state for each receiver, the channel always satisfies the TIN-optimality condition identified by Geng et al., then the GDoF region of the compound channel is the intersection of the GDoF regions of all possible network realizations, which is achievable by power control and TIN. Furthermore, we demonstrate that for a general $K$ -user compound interference channel, regardless of the number of states of each receiver, we can always construct a counterpart $K$ -user regular interference channel that has the same TIN region as the original compound channel. The regular interference channel has only one state for each receiver, which may be different from all of the original states. Solving the GDoF-based power control problem for the compound channel is equivalent to solving the same problem in its regular counterpart. Exploring the power control problem further we develop a centralized power control scheme for $K$ -user compound interference channels, to achieve all the Pareto optimal GDoF tuples. Finally, based on this scheme, we devise an iterative power control algorithm which requires at most $K$ updates to obtain the globally optimal power allocation for any feasible GDoF tuple. [ABSTRACT FROM PUBLISHER]

In this paper, the Gaussian many-to-one X channel (XC), which is a special case of general multiuser XC, is studied. In the Gaussian many-to-one XC, communication links exist between all transmitters and one of the receivers, along with a communication link between each transmitter and its corresponding receiver. As per the XC assumption, transmission of messages is allowed on all the links of the channel. This communication model is different from the corresponding many-to-one interference channel (IC). Transmission strategies, which involve using Gaussian codebooks and treating interference from a subset of transmitters as noise, are formulated for the above channel. Sum-rate is used as the criterion of optimality for evaluating the strategies. Initially, a $3 \times 3$ many-to-one XC is considered and three transmission strategies are analyzed. The first two strategies are shown to achieve sum-rate capacity under certain channel conditions. For the third strategy, a sum-rate outer bound is derived and the gap between the outer bound and the achieved rate is characterized. These results are later extended to the $K \times K$ case. Next, a region in which the many-to-one XC can be operated as a many-to-one IC without the loss of sum-rate is identified. Furthermore, in the above region, it is shown that using Gaussian codebooks and treating interference as noise achieve a rate point that is within $K/2 -1$ bits from the sum-rate capacity. Subsequently, some implications of the above results to the Gaussian many-to-one IC are discussed. Transmission strategies for the many-to-one IC are formulated, and channel conditions under which the strategies achieve sum-rate capacity are obtained. A region where the sum-rate capacity can be characterized to within $K/2-1$ bits is also identified. Finally, the regions where the derived channel conditions are satisfied for each strategy are illustrated for a $3 \times 3$ many-to-one XC and the corresponding many-to-one IC. [ABSTRACT FROM PUBLISHER]

Approximate capacity regions are established for a class of interfering multiple access channels consisting of two multiple-access channels (MACs), each with an arbitrary number of transmitters, with one transmitter in each MAC causing interference to the receiver of the other MAC, a channel we refer to henceforth as the MAC-IC-MAC. For the discrete memory-less (DM) MAC-IC-MAC, two inner bounds are obtained that are generalizations of prior inner bounds for the two-user DM interference channel (IC) due to Chong et al. For the semi-deterministic MAC-IC-MAC, it is shown that single-user coding at the non-interfering transmitters and superposition coding at the interfering transmitter of each MAC achieves a rate region that is within a quantifiable gap of the capacity region, thereby extending such a result for the two-user semi-deterministic IC by Telatar and Tse. For the Gaussian MAC-IC-MAC, an approximate capacity region that is within a constant gap of the capacity region is obtained, generalizing such a result for the two-user Gaussian IC by Etkin et al. On contrary to the aforementioned approximate capacity results for the two-user IC, whose achievability requires the union of all admissible input distributions, our gap results on the semi-deterministic and the Gaussian MAC-IC-MAC are achievable by only a subset and one of all admissible coding distributions, respectively. The symmetric generalized degrees of freedom (GDoFs) of the symmetric Gaussian MAC-IC-MAC with more than one user per cell, which is a function of the interference strength (the ratio of INR to SNR at high SNR, both expressed in dB) and the numbers of users in each cell, are V-shaped with flat shoulders. An analysis based on signal-level partitions shows that the non-interfering transmitters utilize the signal-level partitions at the receiver where they are intended that cannot be accessed by the interfering transmitters (due to the restriction of superposition coding), thereby improving the sum symmetric GDoF of up to one degree of freedom per cell under a range of SINR exponent levels, which in turn becomes wider as the number of transmitters in each cell increases. Consequently, time-sharing between interfering and non-interfering transmitters is GDoF-suboptimal in general, as is time-sharing between the two embedded MAC-Z-MACs. [ABSTRACT FROM AUTHOR]