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In general coding theory, we often assume that error is observed in transferring or storing encoded symbols, while the process of encoding itself is error-free. Motivated by recent applications of coding theory, in this paper, we consider the case where the process of encoding is distributed and prone to error. We introduce the problem of distributed encoding, comprised of a set of $K \in \mathbb {N}$ isolated source nodes and $N \in \mathbb {N}$ encoding nodes. Each source node has one symbol from a finite field, which is sent to each of the encoding nodes. Each encoding node stores an encoded symbol from the same field, as a function of the received symbols. However, some of the source nodes are controlled by the adversary and may send different symbols to different encoding nodes. Depending on the number of the adversarial nodes, denoted by $\beta \in \mathbb {N}$ , and the cardinality of the set of symbols that each one generates, denoted by $v \in \mathbb {N}$ , the process of decoding from the encoded symbols could be impossible. Assume that a decoder connects to an arbitrary subset of $t \in \mathbb {N}$ encoding nodes and wants to decode the symbols of the honest nodes correctly, without necessarily identifying the sets of honest and adversarial nodes. An important characteristic of a distributed encoding system is $t^{*} \in \mathbb {N}$ , the minimum of such $t$ , which is a function of $K$ , $N$ , $\beta $ , and $v$. In this paper, we study the distributed linear encoding system, i.e. one in which the encoding nodes use linear coding. We show that $t^{*}_{\textrm {Linear}}=K+2\beta (v-1)$ , if $N\ge K+2\beta (v-1)$ , and $t^{*}_{\textrm {Linear}}=N$ , if $N\le K+2\beta (v-1)$. In order to achieve $t^{*}_{\textrm {Linear}}$ , we use random linear coding and show that in any feasible solution that the decoder finds, the messages of the honest nodes are decoded correctly. In order to prove the converse of the fundamental limit, we show that when the adversary behaves in a particular way, it can always confuse the decoder between two feasible solutions that differ in the message of at least one honest node. [ABSTRACT FROM AUTHOR]

In this paper, we propose CodedSketch, as a distributed straggler-resistant scheme to compute an approximation of the multiplication of two massive matrices. The objective is to reduce the recovery threshold, defined as the total number of worker nodes that the master node needs to wait for to be able to recover the final result. To exploit the fact that only an approximated result is required, in reducing the recovery threshold, some sorts of pre-compression are required. However, compression inherently involves some randomness that would lose the structure of the matrices. On the other hand, considering the structure of the matrices is crucial to reduce the recovery threshold. In CodedSketch, we use count–sketch, as a hash-based compression scheme, on the rows of the first and columns of the second matrix, and a structured polynomial code on the columns of the first and rows of the second matrix. This arrangement allows us to exploit the gain of both in reducing the recovery threshold. To increase the accuracy of computation, multiple independent count–sketches are needed. This independency allows us to theoretically characterize the accuracy of the result and establish the recovery threshold achieved by the proposed scheme. To guarantee the independency of resulting count–sketches in the output, while keeping its cost on the recovery threshold minimum, we use another layer of structured codes. The proposed scheme provides an upper-bound on the recovery threshold as a function of the required accuracy of computation and the probability that the required accuracy can be violated. In addition, it provides an upper-bound on the recovery threshold for the case that the result of the multiplication is sparse, and the exact result is required. [ABSTRACT FROM AUTHOR]

In this article, we consider a secure multi-party computation problem (MPC), where the goal is to offload the computation of an arbitrary polynomial function of some massive private matrices (inputs) to a cluster of workers. The workers are not reliable. Some of them may collude to gain information about the input data (semi-honest workers). The system is initialized by sharing a (randomized) function of each input matrix to each server. Since the input matrices are massive, each share’s size is assumed to be at most $1/k$ fraction of the input matrix, for some $k \in \mathbb {N}$. The objective is to minimize the number of workers needed to perform the computation task correctly, such that even if an arbitrary subset of $t-1$ workers, for some $t \in \mathbb {N}$ , collude, they cannot gain any information about the input matrices. We propose a sharing scheme, called polynomial sharing, and show that it admits basic operations such as adding and multiplication of matrices and transposing a matrix. By concatenating the procedures for basic operations, we show that any polynomial function of the input matrices can be calculated, subject to the problem constraints. We show that the proposed scheme can offer order-wise gain in terms of the number of workers needed, compared to the approaches formed by the concatenation of job splitting and conventional MPC approaches. [ABSTRACT FROM AUTHOR]

The objective of a genome-wide association study (GWAS) is to associate subsequences of individuals’ genomes to the observable characteristics called phenotypes (e.g., high blood pressure). Motivated by the GWAS problem, in this paper we introduce the information-theoretic problem of associated subsequence retrieval, where a dataset of N (possibly high-dimensional) sequences of length G, and their corresponding observable (binary) characteristics is given. The sequences are chosen independently and uniformly at random from $\mathcal {X}^{\text {G}}$ , where $\mathcal {X}$ is a finite alphabet. The observable (binary) characteristic is only related to a specific unknown subsequence of length $L$ of the sequences, called associated subsequence. For each sequence, if the associated subsequence of it belongs to a universal finite set, then it is more likely to display the observable characteristic (i.e., it is more likely that the observable characteristic is one). The goal is to retrieve the associated subsequence using a dataset of N sequences and their observable characteristics. We demonstrate that as the parameters N, G, and L grow, a threshold effect appears in the curve of probability of error versus the rate which is defined as ${{\it\text { Gh}}(\text {L}/\text {G})}/{\text {N}}$ , where $\text {h}(\cdot)$ is the binary entropy function. This effect allows us to define the capacity of associated subsequence retrieval. We develop an achievable scheme and a matching converse for this problem, and thus characterize its capacity in two scenarios: the zero-error-rate and the $\epsilon $ -error-rate. [ABSTRACT FROM AUTHOR]

We consider the problem of massive matrix multiplication, which underlies many data analytic applications, in a large-scale distributed system comprising a group of worker nodes. We target the stragglers’ delay performance bottleneck, which is due to the unpredictable latency in waiting for slowest nodes (or stragglers) to finish their tasks. We propose a novel coding strategy, named entangled polynomial code, for designing the intermediate computations at the worker nodes in order to minimize the recovery threshold (i.e., the number of workers that we need to wait for in order to compute the final output). We demonstrate the optimality of entangled polynomial code in several cases, and show that it provides orderwise improvement over the conventional schemes for straggler mitigation. Furthermore, we characterize the optimal recovery threshold among all linear coding strategies within a factor of 2 using bilinear complexity, by developing an improved version of the entangled polynomial code. In particular, while evaluating bilinear complexity is a well-known challenging problem, we show that optimal recovery threshold for linear coding strategies can be approximated within a factor of 2 of this fundamental quantity. On the other hand, the improved version of the entangled polynomial code enables further and orderwise reduction in the recovery threshold, compared to its basic version. Finally, we show that the techniques developed in this paper can also be extended to several other problems such as coded convolution and fault-tolerant computing, leading to tight characterizations. [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]

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]

We consider a basic caching system, where a single server with a database of $N$ files (e.g., movies) is connected to a set of $K$ users through a shared bottleneck link. Each user has a local cache memory with a size of $M$ files. The system operates in two phases: a placement phase, where each cache memory is populated up to its size from the database, and a following delivery phase, where each user requests a file from the database, and the server is responsible for delivering the requested contents. The objective is to design the two phases to minimize the load (peak or average) of the bottleneck link. We characterize the rate-memory tradeoff of the above caching system within a factor of 2.00884 for both the peak rate and the average rate (under uniform file popularity), improving the state of the arts that are within a factor of 4 and 4.7, respectively. Moreover, in a practically important case where the number of files ($N$) is large, we exactly characterize the tradeoff for systems with no more than five users and characterize the tradeoff within a factor of 2 otherwise. To establish these results, we develop two new converse bounds that improve over the state of the art. [ABSTRACT FROM AUTHOR]

We consider a basic cache network, in which a single server is connected to multiple users via a shared bottleneck link. The server has a database of files (content). Each user has an isolated memory that can be used to cache content in a prefetching phase. In a following delivery phase, each user requests a file from the database, and the server needs to deliver users’ demands as efficiently as possible by taking into account their cache contents. We focus on an important and commonly used class of prefetching schemes, where the caches are filled with uncoded data. We provide the exact characterization of the rate-memory tradeoff for this problem, by deriving both the minimum average rate (for a uniform file popularity) and the minimum peak rate required on the bottleneck link for a given cache size available at each user. In particular, we propose a novel caching scheme, which strictly improves the state of the art by exploiting commonality among user demands. We then demonstrate the exact optimality of our proposed scheme through a matching converse, by dividing the set of all demands into types, and showing that the placement phase in the proposed caching scheme is universally optimal for all types. Using these techniques, we also fully characterize the rate-memory tradeoff for a decentralized setting, in which users fill out their cache content without any coordination. [ABSTRACT FROM AUTHOR]

How can we optimally trade extra computing power to reduce the communication load in distributed computing? We answer this question by characterizing a fundamental tradeoff between computation and communication in distributed computing, i.e., the two are inversely proportional to each other. More specifically, a general distributed computing framework, motivated by commonly used structures like MapReduce, is considered, where the overall computation is decomposed into computing a set of “Map” and “Reduce” functions distributedly across multiple computing nodes. A coded scheme, named “coded distributed computing” (CDC), is proposed to demonstrate that increasing the computation load of the Map functions by a factor of $r$ (i.e., evaluating each function at $r$ carefully chosen nodes) can create novel coding opportunities that reduce the communication load by the same factor. An information-theoretic lower bound on the communication load is also provided, which matches the communication load achieved by the CDC scheme. As a result, the optimal computation-communication tradeoff in distributed computing is exactly characterized. Finally, the coding techniques of CDC is applied to the Hadoop TeraSort benchmark to develop a novel CodedTeraSort algorithm, which is empirically demonstrated to speed up the overall job execution by $1.97\times $ – $3.39\times $ , for typical settings of interest. [ABSTRACT FROM PUBLISHER]

We study the capacity region of the two-user binary fading (or erasure) interference channel, where the transmitters have no knowledge of the channel state information. We develop new inner bounds and outer bounds for this problem. We identify three regimes based on the channel parameters: weak, moderate, and strong interference regimes. Interestingly, this is similar to the generalized degrees of freedom of the two-user Gaussian interference channel, where transmitters have perfect channel knowledge. We show that for the weak interference regime, treating interference as erasure is optimal while for the strong interference regime, decoding interference is optimal. For the moderate interference regime, we provide new inner and outer bounds. The inner bound is based on a modification of the Han–Kobayashi scheme for the erasure channel, enhanced by time-sharing. We study the gap between our inner bound and our outer bounds for the moderate interference regime and compare our results to that of the Gaussian interference channel. Deriving our new outer bounds has three main steps. We first create a contracted channel that has fewer states compared with the original channel, in order to make the analysis tractable. We then prove the correlation lemma that shows an outer bound on the capacity region of the contracted channel and also serves as an outer bound for the original channel. Finally, using the conditional entropy leakage lemma, we derive our outer bound on the capacity region of the contracted channel. [ABSTRACT FROM AUTHOR]

We consider a system, comprising a library of N files (e.g., movies) and a wireless network with a K_{T} transmitters, each equipped with a local cache of size of M_{T} files and a KR receivers, each equipped with a local cache of size of MR files. Each receiver will ask for one of the $N$ files in the library, which needs to be delivered. The objective is to design the cache placement (without prior knowledge of receivers’ future requests) and the communication scheme to maximize the throughput of the delivery. In this setting, we show that the sum degrees-of-freedom (sum-DoF) of $\min \left \{{\frac {K_{T} M_{T}+K_{R} M_{R}}{N},K_{R}}\right \}$ is achievable, and this is within a factor of 2 of the optimum, under uncoded prefetching and one-shot linear delivery schemes. This result shows that (i) the one-shot sum-DoF scales linearly with the aggregate cache size in the network (i.e., the cumulative memory available at all nodes), (ii) the transmitters’ caches and receivers’ caches contribute equally in the one-shot sum-DoF, and (iii) caching can offer a throughput gain that scales linearly with the size of the network. To prove the result, we propose an achievable scheme that exploits the redundancy of the content at transmitter’s caches to cooperatively zero-force some outgoing interference, and availability of the unintended content at the receiver’s caches to cancel (subtract) some of the incoming interference. We develop a particular pattern for cache placement that maximizes the overall gains of cache-aided transmit and receive interference cancellations. For the converse, we present an integer optimization problem which minimizes the number of communication blocks needed to deliver any set of requested files to the receivers. We then provide a lower bound on the value of this optimization problem, hence leading to an upper bound on the linear one-shot sum-DoF of the network, which is within a factor of 2 of the achievable sum-DoF. [ABSTRACT FROM AUTHOR]

We introduce the blind index coding (BIC) problem, in which a single sender communicates distinct messages to multiple users over a shared channel. Each user has partial knowledge of each message as side information. However, unlike classical index coding, in BIC, the sender is uncertain of what side information is available to each user. In particular, the sender only knows the amount of bits in each user’s side information but not its content. This problem can arise naturally in caching and wireless networks. In order to blindly exploit side information in the BIC problem, we develop a hybrid coding scheme that XORs uncoded bits of a subset of messages with random combinations of bits from other messages. This scheme allows us to strike the right balance between maximizing the transmission rate to each user and minimizing the interference leakage to others. We also develop a general outer bound, which relies on a strong data processing inequality to effectively capture the senders uncertainty about the users’ side information. Additionally, we consider the case where communication takes place over a shared wireless medium, modeled by an erasure broadcast channel, and show that surprisingly, combining repetition coding with hybrid coding improves the achievable rate region and outperforms alternative strategies of coping with channel erasure and while blindly exploiting side information. [ABSTRACT FROM PUBLISHER]

We consider a network consisting of a file server connected through a shared link to a number of users, each equipped with a cache. Knowing the popularity distribution of the files, the goal is to optimally populate the caches, such as to minimize the expected load of the shared link. For a single cache, it is well known that storing the most popular files is optimal in this setting. However, we show here that this is no longer the case for multiple caches. Indeed, caching only the most popular files can be highly suboptimal. Instead, a fundamentally different approach is needed, in which the cache contents are used as side information for coded communication over the shared link. We propose such a coded caching scheme and prove that it is close to optimal. [ABSTRACT FROM AUTHOR]

Although interference alignment (IA) can theoretically achieve the optimal degrees of freedom (DoFs) in the $K$ -user Gaussian interference channel, its direct application comes at the prohibitive cost of precoding over exponentially many signaling dimensions. On the other hand, it is known that practical one-shot IA precoding (i.e., linear schemes without symbol expansion) provides a vanishing DoFs gain in large fully connected networks with generic channel coefficients. In our previous work, we introduced the concept of cellular IA for a network topology induced by hexagonal cells with sectors and nearest-neighbor interference. Assuming that neighboring sectors can exchange decoded messages (and not received signal samples) in the uplink, we showed that linear one-shot IA precoding over $M$ transmit/receive antennas can achieve the optimal $M/2$ DoFs per user. In this paper, we extend this framework to networks with omni-directional (non-sectorized) cells and consider a limited practical scenario where users have 2 antennas, and base-stations have 2, 3, or 4 antennas. We provide linear one-shot IA schemes for the $2\times 2$ , $2\times 3$ , and $2\times 4$ cases, and show the achievability of 3/4, 1, and 7/6 DoFs per user, respectively. DoFs converses for one-shot schemes require the solution of a discrete optimization problem over a number of variables that grows with the network size. We develop a new approach to transform such optimization problem into a tractable linear program with significantly fewer variables. This approach is used to show that 3/4 DoFs per user are indeed optimal for one-shot schemes over large (extended) cellular network with $2\times 2$ links. [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]

To study the effect of lack of up-to-date channel state information at the transmitters (CSITs), we consider two-user binary fading interference channels with Delayed-CSIT. We characterize the capacity region for such channels under homogeneous assumption, where channel gains have identical and independent distributions across time and space, eliminating the possibility of exploiting time/space correlation. We introduce and discuss several novel coding opportunities created by outdated CSIT that can enlarge the achievable rate region. The capacity-achieving scheme relies on accurate combination, concatenation, and merging of these opportunities, depending on the channel statistics. The outer-bounds are based on an extremal inequality we develop for a binary broadcast channel with delayed-CSIT. We further extend the results and characterize the capacity region when output feedback links are available from the receivers to the transmitters in addition to the delayed knowledge of the channel state information. We also discuss the extension of our results to the nonhomogeneous setting. [ABSTRACT FROM AUTHOR]

Caching is a technique to reduce peak traffic rates by prefetching popular content into memories at the end users. Conventionally, these memories are used to deliver requested content in part from a locally cached copy rather than through the network. The gain offered by this approach, which we term local caching gain, depends on the local cache size (i.e., the memory available at each individual user). In this paper, we introduce and exploit a second, global, caching gain not utilized by conventional caching schemes. This gain depends on the aggregate global cache size (i.e., the cumulative memory available at all users), even though there is no cooperation among the users. To evaluate and isolate these two gains, we introduce an information-theoretic formulation of the caching problem focusing on its basic structure. For this setting, we propose a novel coded caching scheme that exploits both local and global caching gains, leading to a multiplicative improvement in the peak rate compared with previously known schemes. In particular, the improvement can be on the order of the number of users in the network. In addition, we argue that the performance of the proposed scheme is within a constant factor of the information-theoretic optimum for all values of the problem parameters. [ABSTRACT FROM AUTHOR]

Interference alignment is a key technique for communication scenarios with multiple interfering links. In several such scenarios, interference alignment was used to characterize the degrees of freedom of the channel. However, these degree-of-freedom capacity approximations are often too weak to make accurate predictions about the behavior of channel capacity at finite signal-to-noise ratios (\ssr SNRs). The aim of this paper is to significantly strengthen these results by showing that interference alignment can be used to characterize capacity to within a constant gap. We focus on real, time-invariant, frequency-flat X-channels. The only known solutions achieving the degrees of freedom of this channel are either based on real interference alignment or on layer-selection schemes. Neither of these solutions seems sufficient for a constant-gap capacity approximation. In this paper, we propose a new communication scheme and show that it achieves the capacity of the Gaussian X-channel to within a constant gap. To aid in this process, we develop a novel deterministic channel model. This deterministic model depends on the \textstyle1\over2\log (\ssr SNR) most-significant bits of the channel coefficients rather than only the single most-significant bit used in conventional deterministic models. The proposed deterministic model admits a wider range of achievable schemes that can be translated to the Gaussian channel. For this deterministic model, we find an approximately optimal communication scheme. We then translate this scheme for the deterministic channel to the original Gaussian X-channel and show that it achieves capacity to within a constant gap. This is the first constant-gap result for a general, fully-connected network requiring interference alignment. [ABSTRACT FROM AUTHOR]

Transmitter channel state information (CSIT) is crucial for the multiplexing gains offered by advanced interference management techniques such as multiuser multiple-input multiple-output (MIMO) and interference alignment. Such CSIT is usually obtained by feedback from the receivers, but the feedback is subject to delays. The usual approach is to use the fed back information to predict the current channel state and then apply a scheme designed assuming perfect CSIT. When the feedback delay is large compared to the channel coherence time, such a prediction approach completely fails to achieve any multiplexing gain. In this paper, we show that even in this case, the completely stale CSI is still very useful. More concretely, we show that in an MIMO broadcast channel with K transmit antennas and K receivers each with 1 receive antenna, K\over1+1\over2+\ldots+1\overK(>1) degrees of freedom is achievable even when the fed back channel state is completely independent of the current channel state. Moreover, we establish that if all receivers have independent and identically distributed channels, then this is the optimal number of degrees of freedom achievable. In the optimal scheme, the transmitter uses the fed back CSI to learn the side information that the receivers receive from previous transmissions rather than to predict the current channel state. Our result can be viewed as the first example of feedback providing a degree-of-freedom gain in memoryless channels. [ABSTRACT FROM PUBLISHER]

For a wide class of multiuser systems, a subset of capacity region which includes the corner points and the sum—capacity facet has a special structure known as polymatroid. Multiple-access channels with fixed input distributions and multiple-antenna broadcast channels are examples of such systems. Any interior point of the sum—capacity facet can be achieved by time-sharing among corner points or by an alternative method known as rate-splitting. The main purpose of this paper is to find a point on the sum—capacity facet which satisfies a notion of fairness among the active users. This problem is addressed in two cases: i) where the complexity of achieving interior points is not feasible, and ii) where the complexity of achieving interior points is feasible. For the first case, the corner point for which the minimum rate of the active users is maximized is desired. A simple greedy algorithm is introduced to find such an optimum corner point. In addition, it is shown for single-antenna Gaussian multiple-access channels, the resulting corner point is leximin maximal with respect to the set of the corner points. For the second case, the properties of the unique leximin maximal rate vector with respect to the polymatroid are reviewed. It is shown that the problems of deriving the time-sharing coefficients or rate-splitting scheme to attain the leximin maximal vector can be solved by decomposing the problem into some lower dimensional subproblems. In addition, a fast algorithm to compute the time-sharing coefficients to attain a general point on the sum—capacity facet is presented. [ABSTRACT FROM AUTHOR]

In a multiple-antenna system with two transmitters and two receivers, a scenario of data communication, known as the X channel, is studied in which each receiver receives data from both transmitters. In this scenario, it is assumed that each transmitter is unaware of the other transmitter's data (noncooperative scenario). This system can be considered as a combination of two broadcast channels (from the transmitters' points of view) and two multiple-access channels (from the receivers' points of view). Taking advantage of both perspectives, two signaling schemes for such a scenario are developed. In these schemes, some linear filters are employed at the transmitters and at the receivers which decompose the system into either two noninterfering multiple-antenna broadcast subchannels or two noninterfering multiple-antenna multiple. access subchannels. The main objective in the design of the filters is to exploit the structure of the channel matrices to achieve the highest multiplexing gain (MG). It is shown that the proposed noncooperative signaling schemes outperform other known noncooperative schemes in terms of the achievable MG. In particular, it is shown that in some specific cases, the achieved MG is the same as the MG of the system if full cooperation is provided either between the transmitters or between the receivers. In the second part of the paper, it is shown that by using mixed design schemes, rather than decomposition schemes, and taking the statistical properties of the interference terms into account, the power offset of the system can be improved. The power offset represents the horizontal shift in the curve of the sum-rate versus the total power in decibels. [ABSTRACT FROM AUTHOR]

A simple signaling method for broadcast channels with multiple-transmit multiple-receive antennas is proposed. In this method, for each user, the direction in which the user has the maximum gain is determined. The best user in terms of the largest gain is selected. The corresponding direction is used as the modulation vector (MV) for the data stream transmitted to the selected user. The algorithm proceeds in a recursive manner where in each step, the search for the best direction is performed in the null space of the previously selected MVs. It is demonstrated that with the proposed method, each selected MV has no interference on the previously selected MVs. Dirty-paper coding is used to cancel the remaining interference. For the case that each receiver has one antenna, the presented scheme coincides with the known scheme based on Gram-Schmidt orthogonalization (QR decomposition). To analyze the performance of the scheme, an upper bound on the cumulative distribution function (CDF) of each subchannel is derived which is used to establish the diversity order and the asymptotic sum-rate of the scheme. It is shown that using fixed rate codebooks, the diversity order of the jth data stream, 1 ≤ j ≤ M, is equal to N(M - j + 1)(K - j + 1), where M, N, and K indicate the number of transmit antennas, the number of receive antennas, and the number of users, respectively. Furthermore, it is proven that the throughput of this scheme scales as M log log(K) and asymptotically (K → ∞) tends to the sum--capacity of the multiple-input multiple-output (MIMO) broadcast channel. The simulation results indicate that the achieved sum--rate is close to the sum--capacity of the underlying broadcast channel. [ABSTRACT FROM AUTHOR]

A network of n communication links, operating over a shared wireless channel, is considered. Fading is assumed to be the dominant factor affecting the strength of the channels between transmitter and receiver terminals. It is assumed that each link can be active and transmit with a constant power P or remain silent. The objective is to maximize the throughput over the selection of active links. By deriving an upper bound and a lower bound, it is shown that in the case of Rayleigh fading: (i) the maximum throughput scales like log n; (ii) the maximum throughput is achievable in a distributed fashion. The upper bound is obtained using probabilistic methods, where the key point is to upper bound the throughput of any random set of active links by a chi-squared random variable. To obtain the lower bound, a decentralized link activation strategy is proposed and analyzed. [ABSTRACT FROM AUTHOR]

The capacity of time-varying channels with periodic feedback at the transmitter is evaluated. It is assumed that the channel-state information (CSI) is perfectly known at the receiver and is fed back to the transmitter at the regular time intervals. The system capacity is investigated in two cases: 1) finite-state Markov channel, and 2) additive white Gaussian noise channel with time-correlated fading. In the first case, it is shown that the capacity is achievable by multiplexing multiple codebooks across the channel. In the second case, the channel capacity and the optimal adaptive coding is obtained. It is shown that the optimal adaptation can be achieved by a single Gaussian codebook, while adaptively allocating the total power based on the side information at the transmitter. [ABSTRACT FROM AUTHOR]

caching of popular content during off-peak hours is a strategy to reduce network loads during peak hours. Recent work has shown significant benefits of designing such caching strategies not only to locally deliver the part of the content, but also to provide coded multicasting opportunities even among users with different demands. Exploiting both of these gains was shown to be approximately optimal for caching systems with a single layer of caches. Motivated by practical scenarios, we consider, in this paper, a hierarchical content delivery network with two layers of caches. We propose a new caching scheme that combines two basic approaches. The first approach provides coded multicasting opportunities within each layer; the second approach provides coded multicasting opportunities across multiple layers. By striking the right balance between these two approaches, we show that the proposed scheme achieves the optimal communication rates to within a constant multiplicative and additive gap. We further show that there is no tension between the rates in each of the two layers up to the aforementioned gap. Thus, both the layers can simultaneously operate at approximately the minimum rate. [ABSTRACT FROM AUTHOR]

In this paper, we develop the machinery of real interference alignment. This machinery is extremely powerful in achieving the sum degrees of freedom (DoF) of single antenna systems. The scheme of real interference alignment is based on designing single-layer and multilayer constellations used for modulating information messages at the transmitters. We show that constellations can be aligned in a similar fashion as that of vectors in multiple antenna systems and space can be broken up into fractional dimensions. The performance analysis of the signaling scheme makes use of a recent result in the field of Diophantine approximation, which states that the convergence part of the Khintchine–Groshev theorem holds for points on nondegenerate manifolds. Using real interference alignment, we obtain the sum DoF of two model channels, namely the Gaussian interference channel (IC) and the \(X\) channel. It is proved that the sum DoF of the \(K\) -user IC is \(({K}/{2})\) for almost all channel parameters. We also prove that the sum DoF of the \(X\) -channel with \(K\) transmitters and \(M\) receivers is \(({KM}/{K+M-1})\) for almost all channel parameters. [ABSTRACT FROM PUBLISHER]