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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 presents explicit solutions for two related non-convex information extremization problems due to Gray and Wyner in the Gaussian case. The first problem is the Gray-Wyner network subject to a sum-rate constraint on the two private links. Here, our argument establishes the optimality of Gaussian codebooks and hence, a closed-form formula for the optimal rate region. The second problem is Wyner’s common information and a generalization thereof, where conditional independence is generalized to a limit on the conditional mutual information. We present full explicit solutions for the scalar as well as the vector case. [ABSTRACT FROM AUTHOR]

This paper employs auxiliary receivers as a mathematical tool to identify Gallager-type auxiliary random variables and write outer bounds for some basic multiuser settings. This approach is then applied to the relay, interference, and broadcast channel settings, yielding new outer bounds that improve on existing outer bounds and strictly outperform classical outer bounds. For instance, we strictly improve on: the cutset outer bound for the scalar Gaussian relay channel, the outer bounds for the Gaussian Z-interference channel, and the outer bounds for the two receiver broadcast channel. [ABSTRACT FROM AUTHOR]

The deterministic identification (DI) capacity is developed in multiple settings of channels with power constraints. A full characterization is established for the DI capacity of the discrete memoryless channel (DMC) with and without input constraints. Originally, Ahlswede and Dueck established the identification capacity with local randomness at the encoder, resulting in a double exponential number of messages in the block length $n$. In the deterministic setup, the number of messages scales exponentially, as in Shannon’s transmission paradigm, but the achievable identification rates are higher. An explicit proof was not provided for the deterministic setting. In this paper, a detailed proof is presented for the DMC. Furthermore, Gaussian channels with fast and slow fading are considered, when channel side information is available at the decoder. A new phenomenon is observed as we establish that the number of messages scales as $2^{n\log (n)R}$ by deriving lower and upper bounds on the DI capacity on this scale. Consequently, the DI capacity of the Gaussian channel is infinite in the exponential scale and zero in the double exponential scale, regardless of the channel noise. [ABSTRACT FROM AUTHOR]

Shannon showed that to achieve perfect secrecy in point-to-point communication, the message rate cannot exceed the shared secret key rate giving rise to the simple one-time pad encryption scheme. In this paper, we extend this work from point-to-point to networks. We consider a connected network with pairwise communication between the nodes and assume that each node is provided with a certain amount of secret bits before communication commences. An eavesdropper with unlimited computing power has access to all communication and can hack a subset of the nodes not known to the rest of the nodes. We investigate the limits on information-theoretic secure communication with end-to-end encryption for this network. We establish a tradeoff between the secure channel rate (for a node pair) and the secure network rate (sum over all node pair rates) and show that information-theoretic secrecy can be achieved asymptotically if and only if the sum rate of any subset of unhacked channels does not exceed the shared unhacked-secret-bit rate of these channels. We also propose a practical scheme that achieves a good balance of network and channel rates with information-theoretic secrecy guarantee. This work has a wide range of potential applications for which strong secrecy is desired, such as cyber-physical systems, distributed-control systems, and ad-hoc networks. [ABSTRACT FROM AUTHOR]

Grassmannian codes are known to be useful in error correction for random network coding. Recently, they were used to prove that vector network codes outperform scalar linear network codes, on multicast networks, with respect to the alphabet size. The multicast networks which were used for this purpose are generalized combination networks. In both the scalar and the vector network coding solutions, the subspace distance is used as the distance measure for the codes which solve the network coding problem in the generalized combination networks. In this paper, we show that the subspace distance can be replaced with two other possible distance measures which generalize the subspace distance. These two distance measures are shown to be equivalent under an orthogonal transformation. It is proved that the Grassmannian codes with the new distance measures generalize the Grassmannian codes with the subspace distance and the subspace designs with the strength of the design. Furthermore, optimal Grassmannian codes with the new distance measures have minimal requirements for the network coding solutions of some generalized combination networks. The coding problems related to these two distance measures, especially with respect to network coding, are discussed. Finally, by using these new concepts, it is proved that the codes in the Hamming scheme form a subfamily of the Grassmannian codes. [ABSTRACT FROM AUTHOR]

Coding and testing schemes and the corresponding achievable type-II error exponents are presented for binary hypothesis testing over two-hop relay networks. The schemes are based on cascade source coding techniques and unanimous decision-forwarding, the latter meaning that a terminal decides on the null hypothesis only if all previous terminals have decided on the null hypothesis. If the observations at the transmitter, the relay, and the receiver form a Markov chain in this order, then, without loss in performance, the proposed cascade source code can be replaced by two independent point-to-point source codes, one for each hop. The decoupled scheme (combined with decision-forwarding) is shown to attain the optimal type-II error exponents for various instances of “testing against conditional independence.” The same decoupling is shown to be optimal also for some instances of “testing against independence,” when the observations at the transmitter, the receiver, and the relay form a Markov chain in this order and when the relay-to-receiver link is of sufficiently high rate. For completeness, this paper also presents an analysis of the Shimokawa–Han–Amari binning scheme for the point-to-point hypothesis testing setup. [ABSTRACT FROM AUTHOR]

New capacity upper bounds are presented for the discrete-time Poisson channel with no dark current and an average-power constraint. These bounds are a consequence of techniques developed for the seemingly unrelated problem of upper bounding the capacity of binary deletion and repetition channels. Previously, the best known capacity upper bound in the regime where the average-power constraint does not approach zero was due to Martinez (JOSA B, 2007), which is re-derived as a special case of the framework developed in this paper. Furthermore, this framework is carefully instantiated in order to obtain a closed-form bound that improves the result of Martinez everywhere. Finally, capacity-achieving distributions for the discrete-time Poisson channel are studied under an average-power constraint and/or a peak-power constraint and arbitrary dark current. In particular, it is shown that the support of the capacity-achieving distribution under an average-power constraint must only be countably infinite. This settles a conjecture of Shamai (IEE Proceedings I, 1990) in the affirmative. Previously, it was only known that the support must be an unbounded set. [ABSTRACT FROM AUTHOR]

In this paper, we consider a binary erasure channel (BEC) with an unknown erasure probability of ${\delta }$ at a transmitter. In addition, we consider that ${\delta }$ has a constant value in each transmission block and the transmitter knows the probability distribution of ${\delta }$. For this problem with the infinite block length, based on the distribution of the random variable ${\delta }$ , a multi-layer encoding strategy at the transmitter and a successive decoding strategy at the receiver are proposed. In our proposed scheme, based on the value of ${\delta }$ , the receiver can decode a part of transmitted data from different transmission layers. In order to have a comparison with other erasure correction codes, we generalize the result of the infinite block length to the finite block-length transmission. We show that considering the average transmission rate, our scheme has a better performance than the other erasure correction codes such as the Raptor and the MDS codes. We also analyze both the decoding complexity and bit error rate versus the erasure probability of the channel. Besides, by using a numerical comparison, we try to show that our proposed strategy outperforms other transmission strategies. [ABSTRACT FROM AUTHOR]

Protograph-based Raptor-like low-density parity-check codes (PBRL codes) are a family of easily encodable rate-compatible low-density parity-check (LDPC) codes. PBRL codes have an excellent performance across all design rates. Quasi-cyclic (QC) PBRL code families permit high-speed decoder implementations. PBRL codes designed thus far, for both long and short block-lengths, have been based on optimizing the iterative decoding threshold of the protograph of the PBRL family at various design rates. This paper introduces a design method to obtain better QC PBRL code families at short block-lengths (of a few hundred bits) for low frame error rate (FER) requirements. We first select a protomatrix for the highest design rate. To add a new row to lower the rate, we keep all the previously obtained rows of the PBRL protomatrix fixed and select the new row that maximizes an upper bound on the minimum distance of any QC-LDPC code that can be obtained from the protomatrix. The new QC PBRL code families outperform the original PBRL codes at short block-lengths by providing a significantly better low-FER performance. The standard approach to computing the aforementioned upper bounds requires complexity that grows exponentially with the size of the protomatrix. However, we show that the structure of the PBRL protomatrix lets us obtain the upper bounds with complexity that grows only linearly with the size of the PBRL protomatrix. Using the complexity reduction results, we also establish an equivalence between the exhaustive search to design a new row for the PBRL protomatrix according to the new design method and an integer linear program. [ABSTRACT FROM AUTHOR]

It is a well-known fact that feedback does not increase the capacity of point-to-point memoryless channels, however, its effect in secure communications is not fully understood yet. In this paper, an achievable scheme for the wiretap channel with generalized feedback is presented. This scheme, which uses the feedback signal to generate a shared secret key between the legitimate users, encrypts the message to be sent at the bit level. New capacity results for a class of channels are provided, as well as some new insights into the secret key agreement problem. Moreover, this scheme recovers previously reported rate regions from the literature, and thus it can be seen as a generalization that unifies several results in the field. [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]

Marton’s inner bound is the best known achievable rate region for a general two-receiver discrete memoryless broadcast channel. In this paper, we establish improved bounds on the cardinalities of the auxiliary random variables appearing in this inner bound to the true rate region. We combine a perturbation technique, along with a representation using concave envelopes of information-theoretic functions that involve the use of auxiliary random variables, to achieve this improvement. The new cardinality bounds lead to a proof that a randomized-time-division strategy achieves every rate triple in Marton’s region for binary input broadcast channels. This extends the result by Hajek and Pursley which showed that the Cover-van der Muelen region was exhausted by the randomized-time-division strategy. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new coding scheme and establish new bounds on the capacity region for the multi-sender unicast index-coding problem. We revisit existing partitioned distributed composite coding (DCC) proposed by Sadeghi et al. and identify its limitations in the implementation of multi-sender composite coding and in the strategy of sender partitioning. We then propose two new coding components to overcome these limitations and develop a multi-sender cooperative composite coding (CCC). We show that CCC can strictly improve upon partitioned DCC, and is the key to achieve optimality for a number of index-coding instances. The usefulness of CCC and its special cases is illuminated via non-trivial examples, and the capacity region is established for each example. Comparisons between CCC and other non-cooperative schemes in recent works are also provided to further demonstrate the advantage of CCC. [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]

This paper obtains the first degrees of freedom (DoFs) bound that is provably sensitive tonetworkcoherence time, i.e., coherence time in an interference network, where all channels experience the same coherence patterns. This is accomplished by a novel adaptation of the aligned image sets bound and settles various open problems noted previously by Naderi and Avestimehr and by Gouet al.For example, a necessary and sufficient condition is obtained for the optimality of 1/2 DoF per user in a partially connected interference network, where the channel state information at the receivers (CSIRs) is perfect, the channel state information at the transmitters (CSITs) is instantaneous but limited to finite precision, and the network coherence time is $T_{c}=1$. The surprising insight that emerges is that even with perfect CSIR and instantaneous finite precision CSIT, the network coherence time matters, i.e., it has a DoF impact. [ABSTRACT FROM AUTHOR]

The ordering of communication channels was first introduced by Shannon. In this paper, we aim to find characterizations of two orderings: input-degradedness and the Shannon ordering. A channel $W$ is said to be input-degraded from another channel $W'$ if $W$ can be simulated from $W'$ by randomization at the input. We provide a necessary and sufficient condition for a channel to be input-degraded from another one. We show that any decoder that is good for $W$ is also good for $W'$. We provide two characterizations for input-degradedness, one of which is similar to the Blackwell-Sherman-Stein theorem. We show that $W'$ contains $W$ (in the Shannon ordering sense) if and only if $W$ is the skew-composition of $W'$ with a convex-product $n$ channel. This fact is used to derive a characterization of the Shannon ordering that is similar to the Blackwell-Sherman-Stein theorem. [ABSTRACT FROM AUTHOR]

This paper presents finite-blocklength achievability bounds for the Gaussian multiple access channel (MAC) and random access channel (RAC) under average-error and maximal-power constraints. Using random codewords uniformly distributed on a sphere and a maximum likelihood decoder, the derived MAC bound on each transmitter’s rate matches the MolavianJazi-Laneman bound (2015) in its first- and second-order terms, improving the remaining terms to $\frac {1}2\frac {\log {n}}{n}+{O} \left ({\frac {1}{n}}\right)$ bits per channel use. The result $\vphantom {\sum ^{R}}$ then extends to a RAC model in which neither the encoders nor the decoder knows which of ${K}$ possible transmitters are active. In the proposed rateless coding strategy, decoding occurs at a time ${n}_{t}$ that depends on the decoder’s estimate ${t}$ of the number of active transmitters ${k}$. Single-bit feedback from the decoder to all encoders at each potential decoding time ${n}_{i}$ , ${i} \leq {t}$ , informs the encoders when to stop transmitting. For this RAC model, the proposed code achieves the same first-, second-, and third-order performance as the best known result for the Gaussian MAC in operation. [ABSTRACT FROM AUTHOR]

It is well known that the capacity region of an average transmit power constrained Gaussian Broadcast Channel (GBC) with independent noise realizations at the receivers is enlarged by the presence of causal noiseless feedback. When the noise variances at the receivers are identical, even passive feedback via independent memoryless Gaussian links can lead to a capacity region enlargement. The last fact remains true even when the feedback noise variance is very high, and available only from one of the receivers. While such capacity enlargements are feasible for several other feedback models in the Gaussian BC setting, it is also known that feedback does not change the capacity region for physically degraded broadcast channels. In this paper, we consider a two user GBC with independent noise realizations at the receivers, where the feedback links from the receivers are corrupted by independent additive Gaussian noise processes. We investigate the set of four noise variances, two forward and two feedback, for which no capacity enlargement is possible. A sharp characterization of this region is derived, i.e., any quadruple outside the presented region will lead to a capacity enlargement, whereas quadruples inside will leave the capacity region unchanged. Our results lead to the conclusion that when the forward noise variances are different, too noisy a feedback from one of the receivers alone is not always beneficial for enlarging the capacity region, be it from the stronger user or the weaker one, in sharp contrast to the case of equal forward noise variances. [ABSTRACT FROM AUTHOR]

One key requirement for fountain (rateless) coding schemes is to achieve a high intermediate symbol recovery rate. Recent coding schemes have incorporated the use of a feedback channel to improve the intermediate performance of traditional rateless codes; however, these codes with feedback are designed based on uniformly at random selection of input symbols. In this paper, on the other hand, we develop feedback-based fountain codes with dynamically adjusted nonuniform symbol selection distributions, and show that this characteristic can enhance the intermediate decoding rate. We provide an analysis of our codes, including bounds on computational complexity and failure probability for a maximum likelihood decoder; the latter is tighter than bounds known for classical rateless codes. Through numerical simulations, we also show that the feedback information paired with a nonuniform selection distribution can highly improve the symbol recovery rate, and that the amount of feedback sent can be tuned to the specific transmission properties of a given feedback channel. [ABSTRACT FROM PUBLISHER]

Discrete polymatroids are the multi-set analogue of matroids. In this paper, we explore the connections among linear network coding, linear index coding, and representable discrete polymatroids. We consider the vector linear solutions of networks over a field \mathbb Fq , with possibly different message and edge vector dimensions, which are referred to as linear fractional solutions. It is well known that a scalar linear solution over \mathbb Fq exists for a network if and only if the network is matroidal with respect to a matroid representable over \mathbb Fq . We define a discrete polymatroidal network and show that a linear fractional solution over a field \mathbb Fq exists for a network if and only if the network is discrete polymatroidal with respect to a discrete polymatroid representable over \mathbb Fq . An algorithm to construct the networks starting from certain class of discrete polymatroids is provided. Every representation over \mathbb Fq for the discrete polymatroid, results in a linear fractional solution over \mathbb Fq for the constructed network. Next, we consider the index coding problem, which involves a sender, which generates a set of messages X=\x1,x2,\dotso xk\ , and a set of receivers \mathcal R , which demand messages. A receiver R \in \mathcal R is specified by the tuple $(x,H)$ , where x \in X$ is the message demanded by R$ and is the side information possessed by $R$ . We first show that a linear solution to an index coding problem exists if and only if there exists a representable discrete polymatroid, satisfying certain conditions, which are determined by the index coding problem considered. Rouayheb et al. showed that the problem of finding a multi-linear representation for a matroid can be reduced to finding a perfect linear index coding solution for an index coding problem obtained from that matroid. The multi-linear representation of a matroid can be viewed as a special case of representation of an appropriate discrete polymatroid. We generalize the result of Rouayheb et al., by showing that the problem of finding a representation for a discrete polymatroid can be reduced to finding a perfect linear index coding solution for an index coding problem obtained from that discrete polymatroid. [ABSTRACT FROM PUBLISHER]

Consider an energy-harvesting receiver that uses the same received signal both for decoding information and for harvesting energy, which is employed to power its circuitry. In the scenario where the receiver has limited battery size, a signal with bursty energy content may cause power outage at the receiver, since the battery will drain during intervals with low signal energy. In this paper, we analyze subblock energy-constrained codes (SECCs), which ensure that sufficient energy is carried within every subblock duration. We consider discrete memoryless channels and characterize the SECC capacity and the SECC error exponent, and provide useful bounds for these values. We also study constant subblock-composition codes (CSCCs), which are a subclass of SECCs where all the subblocks in every codeword have the same fixed composition, and this subblock composition is chosen to maximize the rate of information transfer while meeting the energy requirement. Compared with constant composition codes (CCCs), we show that CSCCs incur a rate loss and that the error exponent for CSCCs is also related to the error exponent for CCCs by the same rate loss term. We exploit the symmetry in CSCCs to obtain a necessary and sufficient condition on the subblock length for avoiding power outage at the receiver. Furthermore, for CSCC sequences, we present a tight lower bound on the average energy per symbol within a sliding time window. We provide numerical examples highlighting the tradeoff between the delivery of sufficient energy to the receiver and achieving high information transfer rates. It is observed that the ability to use energy in real-time imposes less of penalty compared with the ability to use information in real-time. [ABSTRACT FROM PUBLISHER]

A key aspect of many resource allocation problems is the need for the resource controller to compute a function, such as the $\max $ or \mathop {\mathrm {arg\,max\kern 0pt}} , of the competing users’ metrics. Information must be exchanged between the competing users and the resource controller in order for this function to be computed. In many practical resource controllers, the competing users’ metrics are communicated to the resource controller, which then computes the desired extremization function. However, in this paper, it is shown that information rate savings can be obtained by recognizing that the controller only needs to determine the result of this extremization function. If the extremization function is to be computed losslessly, the rate savings are shown in most cases to be at most 2 b independent of the number of competing users. Motivated by the small savings in the lossless case, simple achievable schemes for both the lossy and interactive variants of this problem are considered. It is shown that both of these approaches have the potential to realize large rate savings, especially in the case where the number of competing users is large. For the lossy variant, it is shown that the proposed simple achievable schemes are in fact close to the fundamental limit given by the rate distortion function. [ABSTRACT FROM AUTHOR]

This paper presents an outage analysis for a two-user parallel Gaussian interference channel consisting of two sub-channels. Each sub-channel is modeled as a two-user Gaussian interference channel with quasi-static and flat fading. Both users employ single-layer Gaussian code-books and maintain a statistical correlation \rho between the signals transmitted over the underlying sub-channels. When joint decoding (JD) is performed at the receivers, setting \rho =0 minimizes the outage probability, regardless of the value of the signal-to-noise ratio (SNR). It is shown, however, that if the receivers treat interference as noise (TIN) or cancel interference (CI), the value of optimum \rho approaches 1 as SNR goes to infinity. Motivated by these observations, we let \rho =0 under JD and \rho =1 , it is shown that the outage probability scales like \mathrm snr^-(1-r) under both TIN and CI, while it vanishes at least as fast as \mathrm snr^-\min \2-r,4(1-r)\\log \mathrm snr under JD. This paper is concluded by extending some of the results to a two-user parallel Gaussian interference channel with an arbitrary number of sub-channels. [ABSTRACT FROM AUTHOR]

We propose two coding schemes for the two-receiver discrete memoryless broadcast channel (BC) with rate-limited feedback from one or both receivers. They improve over the no feedback capacity region for a large class of channels, including the class of strictly essentially less-noisy BCs that we introduce in this paper. Examples of strictly essentially less-noisy BCs are the binary symmetric BC or the binary erasure BC with unequal crossover or erasure probabilities at the two receivers. When the feedback rates are sufficiently large, our schemes recover all previously known capacity results for discrete memoryless BCs with feedback. In both our schemes, we let the receivers feedback quantization messages about their receive signals. In the first scheme, the transmitter simply relays the quantization information obtained from Receiver 1 to Receiver 2, and vice versa. This provides each receiver with a second observation of the input signal and can thus improve its decoding performance unless the BC is physically degraded. Moreover, each receiver uses its knowledge of the quantization message describing its own outputs so as to attain the same performance as if this message had not been transmitted at all. In our second scheme, the transmitter first reconstructs and processes the quantized output signals, and then sends the outcome as a common update information to both receivers. A special case of our second scheme also applies to memoryless BCs without feedback but with strictly causal state-information at the transmitter and causal state-information at the receivers. It recovers all previous achievable regions also for this setup with state-information. [ABSTRACT FROM AUTHOR]

We consider a communication system in which status updates arrive at a source node, and should be transmitted through a network to the intended destination node. The status updates are samples of a random process under observation, transmitted as packets, which also contain the time stamp to identify when the sample was generated. The age of the information available to the destination node is the time elapsed, since the last received update was generated. In this paper, we model the source-destination link using the queuing theory, and we assume that the time it takes to successfully transmit a packet to the destination is an exponentially distributed service time. We analyze the age of information in the case that the source node has the capability to manage the arriving samples, possibly discarding packets in order to avoid wasting network resources with the transmission of stale information. In addition to characterizing the average age, we propose a new metric, called peak age, which provides information about the maximum value of the age, achieved immediately before receiving an update. [ABSTRACT FROM AUTHOR]

This paper considers the signal-to-noise ratio (SNR)-evolution, meaning the behavior as a function of the SNR, of the minimum mean-square error (MMSE) function of code sequences in several multi-user settings in the additive white Gaussian noise regime. The settings investigated in this context include the Gaussian wiretap channel, the Gaussian broadcast channel (BC), and the Gaussian BC with confidential messages (BCC). This paper shows that the specific properties of the SNR-evolution of the MMSE and conditional MMSE functions are necessary and sufficient conditions for capacity or equivocation achieving code sequences. In some cases, the complete SNR-evolution of a family of code sequences can be determined, providing significant insight into the disturbance (in terms of MMSE) such codes have on unintended receivers at other SNRs. Moreover, the effects of an additional MMSE constraint on the capacity region and on the SNR-evolution of code sequences are considered in the BC and BCC settings. Such an analysis emphasizes the tradeoff between rates and limited disturbance on unintended receivers. [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]

Despite the simplicity of the scheme of treating interference as noise (TIN), it was shown to be sum-capacity optimal in the Gaussian interference channel (IC) with very-weak (noisy) interference. In this paper, the two-user IC is altered by introducing an additional transmitter that wants to communicate with one of the receivers of the IC. The resulting network thus consists of a point-to-point channel interfering with a multiple access channel (MAC) and is denoted by PIMAC. The sum-capacity of the PIMAC is studied with main focus on the optimality of TIN. It turns out that TIN in its naive variant, where all transmitters are active and both receivers use TIN for decoding, is not the best choice for the PIMAC. In fact, a scheme that combines both time division multiple access and TIN (TDMA–TIN) strictly outperforms the naive-TIN scheme. Furthermore, it is shown that in some regimes, TDMA–TIN achieves the sum-capacity for the deterministic PIMAC and the sum-capacity within a constant gap for the Gaussian PIMAC. In addition, it is shown that, even for very-weak interference, there are some regimes where a combination of interference alignment with power control and TIN at the receiver side outperforms TDMA–TIN. As a consequence, on the one hand, TIN in a cellular uplink is approximately optimal in certain regimes. On the other hand, those regimes cannot be simply described by the strength of interference. [ABSTRACT FROM PUBLISHER]

In this paper, a random access scheme is introduced, which relies on the combination of packet erasure correcting codes and successive interference cancellation (SIC). The scheme is named coded slotted ALOHA. A bipartite graph representation of the SIC process, resembling iterative decoding of generalized low-density parity-check codes over the erasure channel, is exploited to optimize the selection probabilities of the component erasure correcting codes through a density evolution analysis. The capacity (in packets per slot) of the scheme is then analyzed in the context of the collision channel without feedback. Moreover, a capacity bound is developed, and component code distributions tightly approaching the bound are derived. [ABSTRACT FROM AUTHOR]

Traditionally paired with impulsive communications, time-hopping code-division multiple access (TH-CDMA) is a multiple access technique that separates users in time by coding their transmissions into pulses occupying a subset of N_ \mathsf s chips out of the total N included in a symbol period, in contrast with the traditional direct-sequence CDMA (DS-CDMA), where N_ \mathsf {s}=N . This paper analyzes the TH-CDMA with random spreading, by determining whether peculiar theoretical limits are identifiable, with both optimal and suboptimal receiver structures, in particular in the archetypal case of sparse spreading, that is, N_ \mathsf {s}=1$ . Results indicate that the TH-CDMA has a fundamentally different behavior than DS-CDMA, where the crucial role played by energy concentration, typical of TH, directly relates with its intrinsic uneven use of degrees of freedom. [ABSTRACT FROM PUBLISHER]

Communication systems are traditionally designed to have tight transmitter–receiver synchronization. This requirement has negligible overhead in the high-signal-to-noise ratio (SNR) regime. However, in many applications, such as wireless sensor networks, communication needs to happen primarily in the energy-efficient regime of low SNR, where requiring tight synchronization can be highly suboptimal. In this paper, we model the noisy channel with synchronization errors as a duplication/deletion/substitution channel. For this channel, we propose a new communication scheme that requires only loose transmitter–receiver synchronization. We show that the proposed scheme is asymptotically optimal for the Gaussian channel with synchronization errors in terms of energy efficiency as measured by the rate per unit energy. In the process, we also establish that the lack of synchronization causes negligible loss in energy efficiency. We further show that, for a general discrete memoryless channel with synchronization errors and a general input cost function admitting a zero-cost symbol, the rate per unit cost achieved by the proposed scheme is within a factor two of the information-theoretic optimum. [ABSTRACT FROM PUBLISHER]

Precoding schemes in the framework of vector perturbation (VP) for the multiple-input multiple-output (MIMO) Gaussian broadcast channel (GBC) are investigated. The VP scheme, originally a “one-shot” technique, is generalized to encompass processing over multiple time instances. Using lattice-based extended alphabets (“perturbations”), and considering the infinite time-span extension limit, a lower bound on the achievable sum-rate using the generalized VP scheme is analytically obtained. The lower bound is shown to asymptotically achieve the optimum sum-rate in the high signal-to-noise ratio (SNR) regime (both in terms of degrees-of-freedom and power offset), for any number of users and transmit antennas. For the two-user cases, it is shown that the lower bound coincides with the sum-capacity for low SNR. The above lower bound is constructively obtained by means of an efficient practically oriented suboptimal transmit energy minimization algorithm, which exhibits a polynomial complexity in the number of users. The proposed precoding scheme demonstrates that the “shaping gain” is achievable for VP schemes, when employing “good” multidimensional lattices. It is also shown that the suboptimum algorithm has its merits, even when processing over multiple time instances is not employed. For the $2\times 2$ MIMO GBC, the VP scheme is generalized further, and an inner bound for the entire achievable rate region is obtained, by which an interesting correspondence is identified with the ultimate capacity region, as obtained by “dirty paper coding”. [ABSTRACT FROM PUBLISHER]

This paper investigates the capacity region of the three-receiver AWGN broadcast channel where the receivers: 1) have private-message requests and 2) may know some of the messages requested by other receivers as side information. We first classify all 64 possible side information configurations into eight groups, each consisting of eight members. We next construct transmission schemes, and derive new inner and outer bounds for the groups. This establishes the capacity region for 52 out of 64 possible side information configurations. For six groups (i.e., groups 1, 2, 3, 5, 6, and 8 in our terminology), we establish the capacity region for all their members, and show that it tightens both the best-known inner and outer bounds. For group 4, our inner and outer bounds tighten the best-known inner bound and/or outer bound for all the group members. Moreover, our bounds coincide at certain regions, which can be characterized by two thresholds. For group 7, our inner and outer bounds coincide for four members, and thereby establishing the capacity region. For the remaining four members, our bounds tighten both the best-known inner and outer bounds. [ABSTRACT FROM PUBLISHER]

Traditionally, the capacity region of a coherent fading multiple access channel (MAC) is analyzed in two popular contexts. In the first, a centralized system with full channel state information at the transmitters (CSITs) is assumed, and the transmit power and data-rate can be jointly chosen for every fading vector realization. On the other hand, in fast-fading links with distributed CSIT, the lack of full CSI is compensated by performing ergodic averaging over sufficiently many channel realizations. Notice that the distributed CSI may necessitate decentralized power-control for optimal data-transfer. Apart from these two models, the case of slow-fading links and distributed CSIT, though relevant to many systems, has received much less attention. In this paper, a block-fading additive white Gaussian noise MAC with full CSI at the receiver and distributed CSI at the transmitters is considered. The links undergo independent fading, but otherwise have arbitrary fading distributions. The channel statistics and respective long-term average transmit powers are known to all parties. We first consider the case where each encoder has knowledge only of its own link quality, and not of others. For this model, we compute the adaptive capacity region, i.e., the collection of average rate-tuples under blockwise coding/decoding such that the rate-tuple for every fading realization is inside the instantaneous MAC capacity region. The key step in our solution is an optimal rate allocation function for any given set of distributed power control laws at the transmitters. This also allows us to structurally characterize the optimal power control for a wide class of fading models. Further extensions are also proposed for the case where each encoder has additional partial CSI about the other links. [ABSTRACT FROM PUBLISHER]

This paper investigates the maximal channel coding rate achievable at a given blocklength $ n$ and error probability \epsilon $ , when the codewords are subjected to a long-term (i.e., averaged-over-all-codeword) power constraint. The second-order term in the large-n expansion of the maximal channel coding rate is characterized both for additive white Gaussian noise (AWGN) channels and for quasi-static fading channels with perfect channel state information available at both the transmitter and the receiver. It is shown that in both the cases, the second-order term is proportional to ({n ^{-1}\ln n })^{1/2} . For the quasi-static fading case, this second-order term is achieved by truncated channel inversion, namely, by concatenating a dispersion-optimal code for an AWGN channel subject to a short-term power constraint, with a power controller that inverts the channel whenever the fading gain is above a certain threshold. Easy-to-evaluate approximations of the maximal channel coding rate are developed for both the AWGN and the quasi-static fading case. [ABSTRACT FROM AUTHOR]

This paper considers the covert identification problem in which a sender aims to reliably convey an identification (ID) message to a set of receivers via a binary-input discrete memoryless channel (BDMC), and simultaneously to guarantee that the communication is covert with respect to a warden who monitors the communication via another independent BDMC. We prove a square-root law for the covert identification problem. This states that an ID message of size $\exp (\exp (\Theta (\sqrt {\text {n}})))$ can be transmitted over n channel uses. We then characterize the exact pre-constant in the $\Theta (\cdot)$ notation. This constant is referred to as the covert identification capacity. We show that it equals the recently developed covert capacity in the standard covert communication problem, and somewhat surprisingly, the covert identification capacity can be achieved without any shared key between the sender and receivers. The achievability proof relies on a random coding argument with pulse-position modulation (PPM), coupled with a second stage which performs code refinements. The converse proof relies on an expurgation argument as well as results for channel resolvability with stringent input constraints. [ABSTRACT FROM AUTHOR]

The correspondence cited in the above article derived ergodic capacity of the coherent multiple-input multiple-output (MIMO) channel in independent and identically distributed (IID) Rayleigh fading. While the theoretical results are correct, several plots in the paper are incorrect. In this correspondence, we correct the plots. More importantly, the corrected plots present an interesting and compelling contrast between performances of the coherent MIMO systems with and without channel state information at the transmitter; whereas this view is somewhat limited in the above article because of flaws in the capacity curves. [ABSTRACT FROM AUTHOR]

This paper considers the problem of optimal zero-delay jamming over an additive noise channel. Building on a sequence of recent results on conditions for linearity of optimal estimation, and of optimal mappings in source-channel coding, the saddle-point solution to the jamming problem is derived for general sources and channels, without recourse to Gaussianity assumptions. The linearity conditions are shown to play a pivotal role in jamming, in the sense that the optimal jamming strategy is to effectively force both the transmitter and the receiver to default to linear mappings, i.e., the jammer ensures, whenever possible, that the transmitter and the receiver cannot benefit from non-linear strategies. This result is shown to subsume the known result for Gaussian source and channel. The conditions and general settings where such unbeatable strategy can indeed be achieved by the jammer are analyzed. Moreover, a numerical procedure is provided to approximate the optimal jamming strategy in the remaining (source-channel) cases where the jammer cannot impose linearity on the transmitter and the receiver. Next, the analysis is extended to vector sources and channels. This extension involves a new aspect of optimization: the allocation of available transmit and jamming power over source and channel components. Similar to the scalar setting, the saddle-point solution is derived using the linearity conditions in vector spaces. The optimal power allocation strategies for the jammer and the transmitter have an intuitive interpretation as the jammer allocates power according to water-filling over the channel eigenvalues, while the transmitter performs water-pouring (reverse water-filling) over the source eigenvalues. [ABSTRACT FROM PUBLISHER]

In the case of ordinary identification coding, a code is devised to identify a single object among $N$ objects. But, in this paper, we consider a coding problem to identify K$ objects at once among N$ objects in the both cases that K$ objects are ranked or not ranked. By combining Moulin–Koetter scheme with the \varepsilon $ -almost strongly universal class of hash functions used in Kurosawa–Yoshida scheme, an efficient and explicit coding scheme is proposed for K$ -multiple-object identification ( KK$-MOID}} , which is the maximum achievable coding rate in the K -MOID coding, is equal to the ordinary channel capacity, and the proposed scheme can attain C_{\text {K$-MOID}}$ . [ABSTRACT FROM PUBLISHER]

This paper studies a decentralized wireless network of asynchronous transmitter–receiver pairs with burst transmissions. Each receiver learns about the number of active users, channel coefficients, and mutual delays based on locally available measurements. The estimates for the mutual delays are not perfect, however, they are reliable enough to guarantee successful decoding. Two signalling schemes are addressed, namely, randomized masking (RM) and reduced cycle transmission (RCT). Under RM, the $n$ symbols of a codeword are generated according to a Bernoulli–Gaussian distribution with activity factor $0<\theta \leq 1$ . This is in contrast to RCT where each codeword consists of $\lfloor \theta n\rfloor $ Gaussian symbols followed by $n-\lfloor \theta n\rfloor $ zeros. Assuming the transmitters are unaware of the number of users, channel coefficients, and mutual delays, the probability of outage under RM is considerably lower compared with RCT if the signal-to-noise ratio (SNR) is sufficiently large. A generalized RCT scheme is also examined where the $n-\lfloor \theta n\rfloor $ zero symbols are not necessarily located at the end of a codeword. In the asymptote of large SNR, the outage probability becomes vanishingly small under RM, however, it is bounded away from zero for generalized RCT regardless of the value of SNR. [ABSTRACT FROM PUBLISHER]

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]

An online fountain code is defined as a fountain code for which an optimal encoding strategy can be found efficiently given any instantaneous decoding state. This property is important for data distribution in practical networks. In this paper, we formalize the problem of online fountain code construction, and propose new online fountain codes that outperform known ones in having factor 3–5 lower redundancy overhead. The bounding of the code overhead is carried out using the analysis of the dynamics of random-graph processes. [ABSTRACT FROM AUTHOR]

A novel information theoretic approach is proposed to solve the secret sharing problem, in which a dealer distributes one or multiple secrets among a set of participants in such a manner that for each secret only qualified sets of users can recover this secret by pooling their shares together while nonqualified sets of users obtain no information about the secret even if they pool their shares together. While existing secret sharing systems (implicitly) assume that communications between the dealer and participants are noiseless, this paper takes a more practical assumption that the dealer delivers shares to the participants via a noisy broadcast channel. Thus, in contrast to the existing solutions that are mainly based on number theoretic tools, an information theoretic approach is proposed, which exploits the channel randomness during delivery of shares as additional resources to achieve secret sharing requirements. In this way, secret sharing problems can be reformulated as equivalent secure communication problems via wiretap channel models, and can hence be solved by employing the powerful information theoretic security techniques. This approach is first developed for the classic secret sharing problem, in which only one secret is to be shared. This classic problem is shown to be equivalent to a communication problem over a compound wiretap channel. Thus, the lower and upper bounds on the secrecy capacity of the compound channel provide the corresponding bounds on the secret sharing rate, and the secrecy scheme designed for the compound channel provides the secret sharing schemes. The power of the approach is further demonstrated by a more general layered multisecret sharing problem, which is shown to be equivalent to the degraded broadcast multiple-input multiple-output (MIMO) channel with layered decoding and secrecy constraints. The secrecy capacity region for the degraded MIMO broadcast channel is characterized, which provides the secret sharing capacity region. Furthermore, the secure encoding scheme that achieves the secrecy capacity region provides an information theoretic scheme for sharing the secrets. [ABSTRACT FROM AUTHOR]

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]

The problem of sending two correlated vector Gaussian sources over a bandwidth-matched two-user scalar Gaussian broadcast channel is studied in this paper, where each receiver wishes to reconstruct its target source under a covariance distortion constraint. We derive a lower bound on the optimal tradeoff between the transmit power and the achievable reconstruction distortion pair. Our derivation is based on a new bounding technique which involves the introduction of appropriate remote sources. Furthermore, it is shown that this lower bound is achievable by a class of hybrid schemes for the special case, where the weak receiver wishes to reconstruct a scalar source under the mean squared error distortion constraint. [ABSTRACT FROM AUTHOR]

Kudekar et al. proved that the belief-propagation (BP) performance for low-density parity check codes can be boosted up to the maximum a posteriori (MAP) performance by spatial coupling. In this paper, spatial coupling is applied to sparsely spread code-division multiple-access systems to improve the performance of iterative multiuser detection based on BP. Two iterative receivers based on BP are considered: 1) one receiver is based on exact BP and 2) the other on an approximate BP with Gaussian approximation. The performance of the two BP receivers is evaluated via density evolution (DE) in the dense limit after taking the large-system limit, in which the number of users and the spreading factor tend to infinity while their ratio is kept constant. The two BP receivers are shown to achieve the same performance as each other in these limits. Furthermore, taking a continuum limit for the obtained DE equations implies that the performance of the two BP receivers can be improved up to the performance achieved by the symbol-wise MAP detection, called individually optimal detection, via spatial coupling. Numerical simulations show that spatial coupling can provide a significant improvement in bit-error rate for finite-sized systems especially in the region of high system loads. [ABSTRACT FROM AUTHOR]

Interference alignment promises that, in Gaussian interference channels, each link can support half of a degree of freedom (DoF) per pair of transmit–receive antennas. However, in general, this result requires to precode the data bearing signals over a signal space of asymptotically large diversity, e.g., over an infinite number of dimensions for time-frequency varying fading channels, or over an infinite number of rationally independent signal levels, in the case of time-frequency invariant channels. In this paper, we consider a wireless cellular system scenario where the promised optimal DoFs are achieved with linear precoding in one-shot (i.e., over a single time-frequency slot). We focus on the uplink of a symmetric cellular system, where each cell is split into three sectors with orthogonal intrasector multiple access. In our model, interference is local, i.e., it is due to transmitters in neighboring cells only. We consider a noniterative local cooperation scheme where base stations pass to their neighbors their decoded messages such that interference from already decoded messages can be canceled. Therefore, for a given decoding order, the interference between sectors is described by a directed locally connected graph. The problem consists of maximizing the per-sector DoFs over all possible decoding orders and precoding schemes. In particular, we provide a decoding order and a one-shot interference alignment scheme able to achieve optimal per-sector DoFs, up to an additive gap due to boundary effects, that vanishes as the size of the network becomes large. Then, we extend our treatment by considering the case of intersector interference with joint processing of the three sector at each cell site. In order to avoid signaling schemes relying on the strength of interference, we further introduce the notion of topologically robust schemes, which are able to guarantee a minimum rate (or DoFs) irrespectively of the strength of the interfering links. Toward this end, we design a different decoding order and alignment scheme, which is topologically robust and still achieves the same optimum DoFs. Finally, we provide a new scheme for the downlink, based on local base station cooperation, where base stations pass to their neighbors a quantized version of their dirty-paper coded signals. For the proposed downlink scheme, we can prove a DoFs duality result showing that, for an appropriate choice of the precoding order and of the alignment beamforming vectors, it can achieve the same per-sector DoFs of the corresponding uplink schemes. [ABSTRACT FROM PUBLISHER]