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We study the problem of universal decoding for unknown discrete memoryless channels in the presence of erasure/list option at the decoder, in the random coding regime. In particular, we harness a universal version of Forney’s classical erasure/list decoder developed in earlier studies, which is based on the competitive minimax methodology, and guarantees universal achievability of a certain fraction of the optimum random coding error exponents. In this paper, we derive an exact single-letter expression for the maximum achievable fraction. Examples are given in which the maximal achievable fraction is strictly less than unity, which imply that, in general, there is no universal erasure/list decoder, which achieves the same random coding error exponents as the optimal decoder for a known channel. This is in contrast to the situation in ordinary decoding (without the erasure/list option), where optimum exponents are universally achievable, as is well known. It is also demonstrated that previous lower bounds derived for the maximal achievable fraction are not tight in general. We then analyze a generalized random coding ensemble, which incorporate a training sequence, in conjunction with a suboptimal practical decoder (“plug-in” decoder), which first estimates the channel using the available training sequence, and then decodes the remaining symbols of the codeword using the estimated channel. One of the implications of our results is setting the stage for a reasonable criterion of optimal training. Finally, we compare the performance of the “plug-in” decoder and the universal decoder, in terms of the achievable error exponents, and show that the latter is noticeably better than the former. [ABSTRACT FROM AUTHOR]

We study a noiseless broadcast link serving K users whose requests arise from a library of N files. Every user is equipped with a cache of size M files each. It has been shown that by splitting all the files into packets and placing individual packets in a random independent manner across all the caches prior to any transmission, at most N/M file transmissions are required for any set of demands from the library. The achievable delivery scheme involves linearly combining packets of different files following a greedy clique cover solution to the underlying index coding problem. This remarkable multiplicative gain of random placement and coded delivery has been established in the asymptotic regime when the number of packets per file F scales to infinity. The asymptotic coding gain obtained is roughly t=KM/N . In this paper, we initiate the finite-length analysis of random caching schemes when the number of packets F is a function of the system parameters . Furthermore, for any clique cover-based coded delivery and a large class of random placement schemes that include the existing ones, we show that the number of packets required to get a multiplicative gain of ({4}/{3})g is at least O(({g}/{K})(N/M)^{g-1})$ . We design a new random placement and an efficient clique cover-based delivery scheme that achieves this lower bound approximately. We also provide tight concentration results that show that the average (over the random placement involved) number of transmissions concentrates very well requiring only a polynomial number of packets in the rest of the system parameters. [ABSTRACT FROM AUTHOR]

It is well known that Shannon’s rate-distortion function (RDF) in the colored quadratic Gaussian (QG) case can be parametrized via a single Lagrangian variable (the water level in the reverse water filling solution). In this paper, we show that the symmetric colored QG multiple description (MD) RDF in the case of two descriptions can be parametrized in the spectral domain via two Lagrangian variables, which control the tradeoff between the side distortion, the central distortion, and the coding rate. This spectral-domain analysis is complemented by a time-domain scheme-design approach: we show that the symmetric colored QG MD RDF can be achieved by combining ideas of delta–sigma modulation and differential pulse-code modulation. In particular, two source prediction loops, one for each description, are embedded within a common noise-shaping loop, whose parameters are explicitly found from the spectral-domain characterization. [ABSTRACT FROM AUTHOR]

The compute-and-forward framework permits each receiver in a Gaussian network to directly decode a linear combination of the transmitted messages. The resulting linear combinations can then be employed as an end-to-end communication strategy for relaying, interference alignment, and other applications. Recent efforts have demonstrated the advantages of employing unequal powers at the transmitters and decoding more than one linear combination at each receiver. However, neither of these techniques fit naturally within the original formulation of compute-and-forward. This paper proposes an expanded compute-and-forward framework that incorporates both of these possibilities and permits an intuitive interpretation in terms of signal levels. Within this framework, recent achievability and optimality results are unified and generalized. [ABSTRACT FROM PUBLISHER]

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

In this paper, the unequal error protection (UEP) capability of convolutional encoders, in terms of the separation vector, is studied from an algebraic viewpoint. A simple procedure is presented for constructing a generator matrix, which is basic and has the largest separation vector for every convolutional code. Such a generator matrix would be desirable, since the corresponding encoder not only achieves UEP optimality, but also avoids undesired catastrophic error propagation. In addition, canonical generator matrices, which are both basic and reduced, are even more preferable for encoding, since they attain the lowest complexity for Viterbi decoding. However, the direct transformation from a UEP-optimal generator matrix to a canonical generator matrix may come with an unexpected loss of the separation vector. We also propose a specific type of transformation matrix that reduces the external degrees of the generator matrices, from which canonical generator matrices can be constructed that include the mitigated degradation of the separation vector. Finally, beneficial UEP convolutional codes that achieve the maximum free distances for the given code parameters are provided. [ABSTRACT FROM PUBLISHER]

Digital contents distributed storage systems may have different reliability and access delay requirements, and erasure codes with different strengths can provide the best storage efficiency in these systems. At the same time, in such large-scale distributed storage systems, nodes fail on a regular basis, and the contents stored on them need to be regenerated from the data downloaded from the remaining nodes. The efficiency of this repair process is an important factor that affects the overall quality of service. In this paper, we formulate the problem of multilevel diversity coding with regeneration to address these considerations, for which the storage versus repair-bandwidth tradeoff is investigated. We show that the extreme point on the optimal tradeoff curve that corresponds to the minimum possible storage can be achieved by a simple coding scheme, in which contents with different reliability requirements are encoded separately with individual regenerating codes without any mixing. On the other hand, we establish the complete storage-repair-bandwidth tradeoff for the case of four storage nodes, which reveals that codes mixing different contents can, in general, strictly improve the optimal tradeoff over the separate-coding solution. [ABSTRACT FROM PUBLISHER]

In this paper, we show that the secrecy function conjecture that states that the maximum of the secrecy function of an l -modular lattice occurs at 1/\sqrt {l} is false, by proving that the four-modular lattice C^{(4)}= \mathbb {Z}\oplus \sqrt {2} \mathbb {Z}\oplus 2 \mathbb {Z} fails to satisfy this conjecture. After this, we indicate how the secrecy function must be modified in the l -modular case to provide a more meaningful comparison for l -modular lattices, and show that this new secrecy function indeed has a maximum at for various two-modular lattices and for C^(4) . We conjecture that this must hold true for all l -modular lattices. [ABSTRACT FROM PUBLISHER]

This paper investigates the first- and second-order maximum achievable rates of codes with/without cost constraints for mixed channels whose channel law is characterized by a general mixture of (at most) uncountably many stationary and memoryless discrete channels. These channels are referred to as mixed memoryless channels with general mixture and include the class of mixed memoryless channels of finitely or countably memoryless channels as a special case. For the mixed memoryless channels with general mixture, the first-order coding theorem which gives a formula for the $\varepsilon $ -capacity is established, and then a direct part of the second-order coding theorem is provided. A subclass of mixed memoryless channels whose component channels can be ordered according to their capacity is introduced, and the first- and second-order coding theorems are established. It is shown that the established formulas reduce to several known formulas for restricted scenarios. [ABSTRACT FROM PUBLISHER]

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]

This paper studies multiuser random coding techniques for channel coding with a given (possibly suboptimal) decoding rule. For the mismatched discrete memoryless multiple-access channel, an error exponent is obtained that is tight with respect to the ensemble average, and positive within the interior of Lapidoth’s achievable rate region. This exponent proves the ensemble tightness of the exponent of Liu and Hughes in the case of maximum-likelihood decoding. An equivalent dual form of Lapidoth’s achievable rate region is given, and the latter is shown to immediately extend to channels with infinite and continuous alphabets. In the setting of single-user mismatched decoding, similar analysis techniques are applied to a refined version of superposition coding, which is shown to achieve rates at least as high as standard superposition coding for any set of random-coding parameters. [ABSTRACT FROM PUBLISHER]

We define the common randomness-assisted capacity of an arbitrarily varying wiretap channel (AVWC) when the eavesdropper is kept ignorant about the common randomness. We prove a multi-letter capacity formula for this model. We prove that, if enough common randomness is used, the capacity formula can be given a single-shot form again. We then consider the opposite extremal case, where no common randomness is available, and derive the capacity. It is known that the capacity of the system can be discontinuous under these circumstances. We prove here that it is still stable in the sense that it is continuous around its positivity points. We further prove that discontinuities can only arise if the legal link is symmetrizable and characterize the points where it is positive. These results shed new light on the design principles of communication systems with embedded security features. At last, we investigate the effect of super-activation of the message transmission capacity of AVWCs under the average error criterion. We give a complete characterization of those AVWCs that may be super-activated. The effect is thereby also related to the (conjectured) super-activation of the common randomness assisted capacity of AVWCs with an eavesdropper that gets to know the common randomness. Super-activation is based on the idea of wasting a few bits of non-secret messages in order to enable provably secret transmission of a large bulk of data, a concept that may prove to be of further importance in the design of communication systems. In this paper, we provide further insight into this phenomenon by providing a class of codes that is capacity achieving and does not convey any information to the eavesdropper. [ABSTRACT FROM AUTHOR]

In distributed storage systems, regenerating codes can achieve the optimal tradeoff between storage capacity and repair bandwidth. However, a critical drawback of existing regenerating codes, in general, is the high coding and repair complexity, since the coding and repair processes involve expensive multiplication operations in finite field. In this paper, we present a design framework of regenerating codes, which employ binary addition and bitwise cyclic shift as the elemental operations, named BASIC regenerating codes. The proposed BASIC regenerating codes can be regarded as a concatenated code with the outer code being a binary parity-check code, and the inner code being a regenerating code utilizing the binary parity-check code as the alphabet. We show that the proposed functional-repair BASIC regenerating codes can achieve the fundamental tradeoff curve between the storage and repair bandwidth asymptotically of functional-repair regenerating codes with less computational complexity. Furthermore, we demonstrate that the existing exact-repair product-matrix construction of regenerating codes can be modified to exact-repair BASIC product-matrix regenerating codes with much less encoding, repair, and decoding complexity from the theoretical analysis, and with less encoding time, repair time, and decoding time from the implementation results. [ABSTRACT FROM AUTHOR]

In network communication, the source often transmits messages at several different information rates within a session. How to deal with information transmission and network error correction simultaneously under different rates is introduced in this paper as a variable-rate network error correction problem. Apparently, linear network error correction maximum distance separable (MDS) codes are expected to be used for these different rates guaranteeing the maximal error-correcting capability. For this purpose, designing a linear network error correction MDS code based on the existing results for each information rate is an alternative solution, but it is inefficient due to its high complexity. In order to solve the problem more efficiently, we present the concept of variable-rate linear network error correction MDS codes preserving local encoding kernels, that is, these linear network error correction MDS codes of different rates have the same local encoding kernel at each internal node. Thus, each nonsource node always uses the same local kernel for coding, no matter what the rate is. Furthermore, we propose an approach to construct such a family of variable-rate network MDS codes and give an algorithm for efficient implementation. This approach economizes the storage space for each internal node, and saves resources and time for transmissions on networks. Moreover, the performance of our proposed algorithm is analyzed, including the field size, the time complexity, the encoding complexity at the source node, and the decoding methods. Finally, a random method is introduced for constructing such a family of variable-rate network MDS codes, and a lower bound on the success probability of this random method is given, which shows that this probability will approach to one as the base field size goes to infinity. [ABSTRACT FROM AUTHOR]

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]

Partial MDS (PMDS) codes are erasure codes combining local (row) correction with global additional correction of entries, while sector-disk (SD) codes are erasure codes that address the mixed failure mode of current redundant arrays of independent disk (RAID) systems. It has been an open problem to construct general codes that have the PMDS and the SD properties, and previous work has relied on Monte-Carlo searches. In this paper, we present a general construction that addresses the case of any number of failed disks and in addition, two erased sectors. The construction requires a modest field size. This result generalizes previous constructions extending RAID 5 and RAID 6. [ABSTRACT FROM AUTHOR]

This paper investigates the linear network coding problem for erasure broadcast channel with user feedback. An innovative linear network code is shown to be uniformly optimal for the system. In general, determining the existence of innovative packets is proved to be NP-complete. When the finite field size is larger than the number of users, innovative packets always exist and the problem of finding an innovative encoding vector with smallest Hamming weight is considered. The corresponding decision problem is shown to be NP-complete. Optimal and approximate network coding algorithms for maximizing the sparsity of encoding vectors are designed. [ABSTRACT FROM AUTHOR]

In this paper, we investigate problems of communication over physically degraded, state-dependent broadcast channels (BCs) with cooperating decoders. Two different setups are considered, and their capacity regions are characterized. First, we study a setting in which one decoder can use a finite capacity link to send the other decoder information regarding the messages or the channel states. In this scenario, we analyze two cases: one, where noncausal state information, is available to the encoder and the strong decoder, and the other, where state information, is available only to the encoder in a causal manner. Second, we examine a setting in which the cooperation between the decoders is limited to taking place before the outputs of the channel are given. In this case, one decoder, which is informed of the state sequence noncausally, can cooperate only to send the other decoder rate-limited information about the state sequence. The proofs of the capacity regions introduce a new idea of coding for channels with cooperation between different users, where we exploit the link between the decoders for multiple binnings. Finally, we discuss the optimality of using rate-splitting techniques when coding for cooperative BCs. In particular, we show that rate splitting is not necessarily optimal when coding for cooperative BCs by solving an example in which our method of coding outperforms rate splitting. [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]

Gabidulin codes can be seen as the rank-metric equivalent of Reed–Solomon codes. It was recently proved, using subspace polynomials, that Gabidulin codes cannot be list decoded beyond the so-called Johnson radius. In another result, cyclic subspace codes were constructed by inspecting the connection between subspaces and their subspace polynomials. In this paper, these subspace codes are used to prove two bounds on the list size in decoding certain Gabidulin codes. The first bound is an existential one, showing that exponentially sized lists exist for codes with specific parameters. The second bound presents exponentially sized lists explicitly for a different set of parameters. Both bounds rule out the possibility of efficiently list decoding several families of Gabidulin codes for any radius beyond half the minimum distance. Such a result was known so far only for non-linear rank-metric codes, and not for Gabidulin codes. Using a standard operation called lifting, identical results also follow for an important class of constant dimension subspace codes. [ABSTRACT FROM AUTHOR]

A likelihood encoder is studied in the context of lossy source compression. The analysis of the likelihood encoder is based on the soft-covering lemma. It is demonstrated that the use of a likelihood encoder together with the soft-covering lemma yields simple achievability proofs for classical source coding problems. The cases of the point-to-point rate-distortion function, the rate-distortion function with side information at the decoder (i.e., the Wyner–Ziv problem), and the multi-terminal source coding inner bound (i.e., the Berger–Tung problem) are examined in this paper. Furthermore, a non-asymptotic analysis is used for the point-to-point case to examine the upper bound on the excess distortion provided by this method. The likelihood encoder is also related to a recent alternative technique using the properties of random binning. [ABSTRACT FROM AUTHOR]

This paper shows that the capacity region of the continuous-time Poisson broadcast channel is achieved via superposition coding for most channel parameter values. Interestingly, the channel in some subset of these parameter values does not belong to any of the existing classes of broadcast channels for which superposition coding is optimal (e.g., degraded, less noisy, and more capable). In particular, we introduce the notion of effectively less noisy broadcast channel and show that it implies less noisy but is not in general implied by more capable. For the rest of the channel parameter values, we show that there is a gap between Marton’s inner bound and the UV outer bound. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new way of constructing and decoding multipermutation codes. Multipermutations are the permutations of a multiset that generally consist of duplicate entries. We first introduce a class of binary matrices called multipermutation matrices, each of which corresponds to a unique and distinct multipermutation. By enforcing a set of linear constraints on these matrices, we define a new class of codes that we term linear program (LP)-decodable multipermutation codes. In order to decode these codes using an LP, thereby enabling soft decoding, we characterize the convex hull of multipermutation matrices. This characterization allows us to relax the coding constraints to a polytope and to derive two LP decoding problems. These two problems are, respectively, formulated by relaxing the maximum likelihood decoding problem and the minimum Chebyshev distance decoding problem. Because these codes are non-linear, we also study efficient encoding and decoding algorithms. We first describe an algorithm that maps consecutive integers, one by one, to an ordered list of multipermutations. Based on this algorithm, we develop an encoding algorithm for a code proposed by Shieh and Tsai, a code that falls into our class of LP-decodable multipermutation codes. Regarding decoding algorithms, we propose an efficient distributed decoding algorithm based on the alternating direction method of multipliers. Finally, we observe from the simulation results that the soft decoding techniques we introduce can significantly outperform hard decoding techniques that are based on quantized channel outputs. [ABSTRACT FROM AUTHOR]

Subspace codes have received an increasing interest recently due to their application in error correction for random network coding. In particular, cyclic subspace codes are possible candidates for large codes with efficient encoding and decoding algorithms. In this paper, we consider such cyclic codes and provide constructions of optimal codes for which their codewords do not have full orbits. We further introduce a new way to represent subspace codes by a class of polynomials called subspace polynomials. We present some constructions of such codes, which are cyclic and analyze their parameters. [ABSTRACT FROM AUTHOR]

We consider a K -user multiple-input single-output (MISO) broadcast channel (BC) where the channel state information (CSI) of user i(i=1,2,\ldots ,K) may be instantaneously perfect (P), delayed (D), or not known (N) at the transmitter with probabilities \lambda P^{i} , \lambda D^{i} , and \lambda \vphantom {RjN}^{i} , respectively. In this setting, according to the three possible CSI at the transmitter (CSIT) for each user, knowledge of the joint CSIT of the K users could have at most 3^{K} states. In this paper, given the marginal probabilities of CSIT (i.e., \lambda _{P}^{i} , \lambda D^{i} , and \lambda \vphantom {RjN}^{\vphantom {r^{A}}i} ), we derive an outer bound for the degrees of freedom (DoF) region of the K -user MISO BC. Subsequently, we tighten this outer bound by considering a set of inequalities that capture some of the 3^{K} states of the joint CSIT. One of the consequences of this set of inequalities is that for K\geq 3$ , it is shown that the DoF region is not completely characterized by the marginal probabilities in contrast to the two-user case. Afterwards, the tightness of these bounds is investigated through the discussion on the achievability. Finally, a two user multiple-input multiple-output BC having CSIT among P and N is considered in which an outer bound for the DoF region is provided, and it is shown that in some scenarios, it is tight. [ABSTRACT FROM AUTHOR]

We consider the problem of communication over a three-user discrete memoryless interference channel (3-IC). The current known coding techniques for communicating over an arbitrary 3-IC are based on message splitting, superposition coding, and binning using independent and identically distributed (i.i.d.) random codebooks. In this paper, we propose a new ensemble of codes—partitioned coset codes (PCCs)—that possess an appropriate mix of empirical and algebraic closure properties. We develop coding techniques that exploit the algebraic closure property of PCC to enable interference alignment over general 3-IC. We analyze the performance of the proposed coding technique to derive an achievable rate region for the general discrete 3-IC. Additive and non-additive examples are identified for which the derived achievable rate region is the capacity, moreover, strictly larger than the current known largest achievable rate regions based on the i.i.d. random codebooks. [ABSTRACT FROM AUTHOR]

We consider the transmission of a memoryless bivariate Gaussian source over a two-user additive Gaussian multiple-access channel with unidirectional conferencing encoders. Here, prior to each transmission block, Encoder 1, which observes the first source component, is allowed to communicate with Encoder 2, which observes the second source component, via a unidirectional noise-free bit-pipe of given capacity. The main results of this paper are sufficient conditions and a necessary condition for the achievability of a distortion pair expressed as a function of the channel \sf SNR and of the source correlation. The main sufficient condition is obtained by an extension of the vector-quantizer scheme suggested by Lapidoth–Tinguely, for the case without conferencing, to the case with unidirectional conference. In the high- \sf SNR regime, and when the capacity of the conference channel is unlimited, these necessary and sufficient conditions are shown to agree. We evaluate the precise high- \sf SNR asymptotics for a subset of distortion pairs when the capacity of the conference channel is unlimited in which case we show that a separation-based scheme attains these optimal distortion pairs. However, with symmetric average-power constraints and fixed conferencing capacity, at high- \sf SNR , the latter separation-based scheme is shown to be suboptimal. [ABSTRACT FROM AUTHOR]

Non-malleable codes, introduced by Dziembowski et al., encode messages s in a manner, so that tampering the codeword causes the decoder to either output s or a message that is independent of s . While this is an impossible goal to achieve against unrestricted tampering functions, rather surprisingly non-malleable coding becomes possible against every fixed family of tampering functions that is not too large (for instance, when | \mathcal {F}| \leqslant 2^{2^{\vphantom {R^{a}}\alpha n}} for some \alpha <1 , where n is the number of bits in a codeword). In this paper, we study the capacity of non-malleable codes, and establish optimal bounds on the achievable rate as a function of the family size, answering an open problem from Dziembowski et al. Specifically, We prove that for every family \mathcal {F} with | \mathcal {F}| \leqslant 2^{2^{\vphantom {R^{}}\alpha n}} , there exist non-malleable codes against \mathcal F with rate arbitrarily close to 1-\alpha [this is achieved with high probability (w.h.p.) by a randomized construction]. We show the existence of families of size \exp (n^O(1) 2^\alpha n) against which there is no non-malleable code of rate $1-\alpha $ (in fact this is the case w.h.p for a random family of this size). We also show that 1-\alpha $ is the best achievable rate for the family of functions, which are only allowed to tamper the first \alpha n$ bits of the codeword, which is of special interest. As a corollary, this implies that the capacity of non-malleable coding in the split-state model (where the tampering function acts independently but arbitrarily on the two halves of the codeword, a model which has received some attention recently) equals 1/2. We also give an efficient Monte Carlo construction of codes of rate close to 1 with polynomial time encoding and decoding that is non-malleable against any fixed c > 0 of size 2^{n^{c}} , in particular tampering functions with, say, cubic size circuits. [ABSTRACT FROM PUBLISHER]

We consider a wireless device-to-device (D2D) network where communication is restricted to be single-hop. Users make arbitrary requests from a finite library of files and have pre-cached information on their devices, subject to a per-node storage capacity constraint. A similar problem has already been considered in an infrastructure setting, where all users receive a common multicast (coded) message from a single omniscient server (e.g., a base station having all the files in the library) through a shared bottleneck link. In this paper, we consider a D2D infrastructureless version of the problem. We propose a caching strategy based on deterministic assignment of subpackets of the library files, and a coded delivery strategy where the users send linearly coded messages to each other in order to collectively satisfy their demands. We also consider a random caching strategy, which is more suitable to a fully decentralized implementation. Under certain conditions, both approaches can achieve the information theoretic outer bound within a constant multiplicative factor. In our previous work, we showed that a caching D2D wireless network with one-hop communication, random caching, and uncoded delivery (direct file transmissions) achieves the same throughput scaling law of the infrastructure-based coded multicasting scheme, in the regime of large number of users and files in the library. This shows that the spatial reuse gain of the D2D network is order-equivalent to the coded multicasting gain of single base station transmission. It is, therefore, natural to ask whether these two gains are cumulative, i.e., if a D2D network with both local communication (spatial reuse) and coded multicasting can provide an improved scaling law. Somewhat counterintuitively, we show that these gains do not cumulate (in terms of throughput scaling law). This fact can be explained by noticing that the coded delivery scheme creates messages that are useful to multiple nodes, such that it benefits from broadcasting to as many nodes as possible, while spatial reuse capitalizes on the fact that the communication is local, such that the same time slot can be reused in space across the network. Unfortunately, these two issues are in contrast with each other. [ABSTRACT FROM AUTHOR]

In this paper, the multiple access channel (MAC) with combined cooperation and partial cribbing is studied, and its capacity region is characterized. Cooperation means that each of the two encoders sends a message to the other via a rate-limited link prior to transmission, while partial cribbing means that each of the two encoders obtains a deterministic function of the other encoder’s output with or without delay. Prior work in this field dealt separately with cooperation and partial cribbing, but by combining these two methods, we can achieve significantly higher rates. Surprisingly, the capacity region of the MAC with combined cooperation and partial cribbing can be expressed using only one auxiliary random variable (RV) similar to the capacity regions of the MAC with cooperation and with partially cribbing encoders. The reason is that in an optimal coding scheme, the encoders use both cooperation and partial cribbing to generate a common message between the encoders. Furthermore, the Gaussian MAC with combined one-sided cooperation and quantized cribbing is studied. For this model, an achievability scheme is given. This scheme shows how many cooperation or quantization bits are required to practically achieve the capacity region of the Gaussian MAC with full message cooperation or perfect cribbing. To ratify the main results, two additional models are studied. In both models, only one auxiliary RV is needed. The first is a rate distortion dual setting for the MAC with degraded message set and combined cooperation and cribbing. The second is a state-dependent MAC with cooperation, where the state is known at a partially cribbing encoder and at the decoder. However, there are cases where more than one auxiliary RV is needed, e.g., when the cooperation and the cribbing are not used for the same purposes. The MAC with an action-dependent state is presented, where the action is based on the cooperation but not on the cribbing. Therefore, in this case, more than one auxiliary RV is needed. As a result, when the common information shared by the two encoders is used unevenly by the users in the channel, more than one auxiliary RV is needed to express the capacity region. [ABSTRACT FROM AUTHOR]

In a network, a node is said to incur a delay if its encoding of each transmitted symbol involves only its received symbols obtained before the time slot in which the transmitted symbol is sent (hence the transmitted symbol sent in a time slot cannot depend on the received symbol obtained in the same time slot). A node is said to incur no delay if its received symbol obtained in a time slot is available for encoding its transmitted symbol sent in the same time slot. Under the classical model, every node in the network incurs a delay. In this paper, we investigate the multimessage multicast network (MMN) under a generalized-delay model which allows some nodes to incur no delay. We obtain the capacity regions for three classes of MMNs with zero-delay nodes, namely, the deterministic network dominated by product distributions, the MMN consisting of independent DMCs, and the wireless erasure network. In addition, we show that for any MMN belonging to one of the above three classes, the set of achievable rate tuples under the generalized-delay model and under the classical model are the same, which implies that the set of achievable rate tuples for the MMN does not depend on the delay amounts incurred by the nodes in the network. [ABSTRACT FROM PUBLISHER]

In this paper, a forward decoding procedure is developed for the compress-and-forward (CF) relaying scheme. This procedure uses a layered framework and is based on exploiting a feature of the $N$ -to-1 mapping inherent in the underlying Wyner–Ziv binning. It is shown that exploiting this mapping enables the relaxation of the constraint on the rate of the relay codewords representing the bin indices. For the cooperative multimessage network, the proposed procedure achieves the same rate region as the short-message noisy network coding (SNNC) scheme. However, this procedure is more advantageous for other networks including the two networks presented herein. The first network is a relay chain one with two destinations, whereas the second network is a partially cooperative multimessage one with three destinations. In both networks, side information is available to a subset of the decoding nodes, but not to the rest of the nodes, and in both cases, the network benefits from the relaxation of the rate of the CF bin indices. This relaxation results in rate regions larger than those achieved by the conventional CF and SNNC. [ABSTRACT FROM PUBLISHER]

The $K$ -user multiple-input multiple-output (MIMO) multi-way relay channel (Y-channel) consisting of $K$ users with $M$ antennas each and a common relay node with $N$ antennas is studied in this paper. Each user wants to exchange messages with all the other users through the relay. A transmission strategy is proposed for this channel. The proposed strategy is based on two steps: 1) channel diagonalization and 2) cyclic communication. The channel diagonalization is applied by using zero-forcing beam-forming. After the channel diagonalization, the channel is decomposed into parallel sub-channels. Cyclic communication is then applied, where signal-space alignment for network-coding is used over each sub-channel. The proposed strategy achieves the optimal degree-of-freedom (DoF) region of the channel if $N\leq M$ . To prove this, a new DoFs outer bound is derived. As a by-product, we conclude that the MIMO Y-channel is not separable, i.e., independent coding on separate sub-channels is not enough, and one has to code jointly over several sub-channels. [ABSTRACT FROM AUTHOR]

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]

In this paper, we study the capacity of the diamond channel. We focus on the special case where the channel between the source node and the two relay nodes are two separate links with finite capacities and the link from the two relay nodes to the destination node is a Gaussian multiple access channel. We call this model the Gaussian multiple access diamond channel. We first propose an upper bound on the capacity. This upper bound is a single-letterization of an $n$ -letter upper bound proposed by Traskov and Kramer, and is tighter than the cut-set bound. As for the lower bound, we propose an achievability scheme based on sending correlated codes through the multiple access channel with superposition structure. We then specialize this achievable rate to the Gaussian multiple access diamond channel. Noting the similarity between the upper and lower bounds, we provide sufficient and necessary conditions that a Gaussian multiple access diamond channel has to satisfy such that the proposed upper and lower bounds meet. Thus, for a Gaussian multiple access diamond channel that satisfies these conditions, we have found its capacity. [ABSTRACT FROM PUBLISHER]

Piggybacking is an efficient method to decrease the repair bandwidth of maximum distance separable codes. In this paper, in order to reduce the repair bandwidth of parity nodes of the known minimum storage regenerating (MSR) codes with high rate, which is usually the whole amount of the original data, i.e., the maximal, a new systematic piggybacking design is proposed through an in-depth analysis of the design of piggybacking. As a result, new MSR codes are obtained with almost optimal repair bandwidth of parity nodes while retaining the optimal repair bandwidth of systematic nodes. Furthermore, MSR codes with balanced download during node repair process are presented based on the new piggybacking design. [ABSTRACT FROM PUBLISHER]

In this paper, we study the capacity regions of two-way diamond channels. We show that for a linear deterministic model the capacity of the diamond channel in each direction can be simultaneously achieved for all values of channel parameters, where the forward and backward channel parameters are not necessarily the same. We divide the achievability scheme into three cases, depending on the forward and backward channel parameters. For the first case, we use a reverse amplify-and-forward strategy in the relays. For the second case, we use four relay strategies based on the reverse amplify-and-forward with some modifications in terms of replacement and repetition of some stream levels. For the third case, we use two relay strategies based on performing two rounds of repetitions in a relay. The proposed schemes for deterministic channels are used to find the capacity regions within constant gaps for two special cases of the Gaussian two-way diamond channel. First, for the general Gaussian two-way relay channel, the capacity within a constant gap is achieved with a simpler coding scheme as compared with the prior works. Then, a special symmetric Gaussian two-way diamond model is considered and the capacity region is achieved within four bits. [ABSTRACT FROM PUBLISHER]

The deterministic-coding capacity of a network is the capacity of a network when nodes are restricted to transmitting reliable information, that is, (asymptotically) deterministic functions of the source messages. This is a generalization of network coding to wireless networks. The main contribution of this paper is to develop new outer bounds on the deterministic-coding capacity in the low-power regime, \mathrm SNR\to 0 . This is accomplished by developing a technique for finding the limits of single letter bounds for \mathrm SNR\to 0 even when these cannot be evaluated for finite SNR. It is shown that these outer bounds are tight in a number of cases, including the butterfly network of Ahlswede et al. in a wireless setting. [ABSTRACT FROM PUBLISHER]

In this paper, we consider the problem of partitioning active users in a manner that facilitates multi-access without collision. The setting is of a noisy, synchronous, Boolean, and multi-access channel, where K active users (out of a total of N users) seek channel access. A solution to the partition problem places each of the N users in one of K groups (or blocks), such that no two active nodes are in the same block. We consider a simple, but non-trivial and illustrative, case of K=2 active users and study the number of steps , where C_{1} and \xi _{1} are positive constants (independent of N ), and where \xi _{1} can be arbitrary small, the partition problem can be solved with error probability P_{e}^{\vphantom {R^{A}}(N)} \to 0 , for large N . Under the same scheme, we also bound T from the other direction, establishing that, for any , the error probability Pe^{(N)} \to 1 for large N ; again, C2 and \xi 2 are constants, and \xi 2 can be arbitrarily small. These bounds on the number of steps are lower than the tight achievable lower bound in terms of T \geq (Cg +\xi )\log N for group testing (in which all active users are identified, rather than just partitioned). Thus, partitioning may prove to be a more efficient approach for multi-access than group testing. [ABSTRACT FROM PUBLISHER]

Practical implementations of secret-key generation are often based on sequential strategies, which handle reliability and secrecy in two successive steps, called reconciliation and privacy amplification. In this paper, we propose an alternative approach based on polar codes that jointly deals with reliability and secrecy. Specifically, we propose secret-key capacity-achieving polar coding schemes for the following models: (i) the degraded binary memoryless source (DBMS) model with rate-unlimited public communication, (ii) the DBMS model with one-way rate-limited public communication, (iii) the 1-to-m broadcast model and (iv) the Markov tree model with uniform marginals. For models (i) and (ii) our coding schemes remain valid for non-degraded sources, although they may not achieve the secret-key capacity. For models (i), (ii) and (iii), our schemes rely on pre-shared secret seed of negligible rate; however, we provide special cases of these models for which no seed is required. Finally, we show an application of our results to secrecy and privacy for biometric systems. We thus provide the first examples of low-complexity secret-key capacity-achieving schemes that are able to handle vector quantization for model (ii), or multiterminal communication for models (iii) and (iv). [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]

This paper studies the mismatched decoding problem for binary-input discrete memoryless channels. An example is provided for which an achievable rate based on superposition coding exceeds the Csiszár-Körner-Hui rate, thus providing a counter-example to a previously reported converse result. Both numerical evaluations and theoretical results are used in establishing this claim. [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 secrecy capacity of the wiretap broadcast channel (WBC) with an external eavesdropper where a source wishes to communicate two private messages over a broadcast channel (BC) while keeping them secret from the eavesdropper. We derive a nontrivial outer bound on the secrecy capacity region of this channel which, in absence of security constraints, reduces to the best known outer bound to the capacity of the standard BC. An inner bound is also derived, which follows the behavior of both the best known inner bound for the BC and the wiretap channel. These bounds are shown to be tight for the deterministic BC with a general eavesdropper, the semideterministic BC with a more noisy eavesdropper, and the wiretap BC where users exhibit a less noisiness order between them. Finally, by rewriting our outer bound to encompass the characteristics of parallel channels, we also derive the secrecy capacity region of the product of two inversely less noisy BCs with a more noisy eavesdropper. We illustrate our results by studying the impact of security constraints on the capacity of the WBC with binary erasure and binary symmetric components. [ABSTRACT FROM PUBLISHER]

The newly presented $(k+m,k)$ Hadamard minimum storage regenerating (MSR) codes are a class of high rate storage codes with optimal repair property for single node failure. In this paper, we propose a new simple optimal repair strategy for $(k+m,k)$ Hadamard MSR codes, which can considerably reduce the computation compared with the original one during the node repair. [ABSTRACT FROM PUBLISHER]

In this paper, we consider the use of lattice codes over Eisenstein integers for implementing a compute-and-forward protocol in wireless networks when channel state information is not available at the transmitter. We extend the compute-and-forward paradigm of Nazer and Gastpar to decoding Eisenstein integer combinations of transmitted messages at relays by proving the existence of a sequence of pairs of nested lattices over Eisenstein integers in which the coarse lattice is good for covering and the fine lattice can achieve the Poltyrev limit. Using this result, we show that both the outage performance and error-correcting performance of the nested lattice codebooks over Eisenstein integers surpass those of lattice codebooks over integers considered by Nazer and Gastpar with no additional computational complexity. [ABSTRACT FROM PUBLISHER]

We consider the coded cooperative data exchange problem for general graphs, both undirected and directed. In this problem, given a graph $G=(V,E)$ representing clients in a broadcast network, each of which initially hold a (not necessarily disjoint) set of information packets; one wishes to design a communication scheme in which eventually all clients will hold all the packets of the network. Communication is performed in rounds, where in each round a single client broadcasts a single (possibly encoded) information packet to its neighbors in G$ . The objective is to design a broadcast scheme that satisfies all clients with the minimum number of broadcast rounds. The coded cooperative data exchange problem has seen significant research over the last few years; mostly when the graph G$ is the complete broadcast graph in which each client is adjacent to all other clients in the network, but also on general topologies, both in the fractional and integral setting. In this paper, we focus on the integral setting in general topologies G$ , both undirected and directed. For undirected graphs, we tie the coded cooperative data exchange problem on G is intractable (i.e., NP-hard). We then turn to study efficient data exchange schemes for undirected topologies yielding a number of communication rounds comparable with our intractability result. Last, we tie the coded cooperative data exchange problem for directed topologies to the directed Steiner tree problem, yielding efficient data exchange approximation schemes. Our communication schemes do not involve encoding, and in such yield bounds on the coding advantage in the setting at hand. [ABSTRACT FROM PUBLISHER]

Most of the attention in statistical compression is given to the space used by the compressed sequence, a problem completely solved with optimal prefix codes. However, in many applications, the storage space used to represent the prefix code itself can be an issue. In this paper, we introduce and compare several techniques to store prefix codes. Let N be the sequence length and n be the alphabet size. Then, a naive storage of an optimal prefix code uses \mathcal O \hspace -.5ex \left ( n\log n \right ) bits. Our first technique shows how to use \mathcal O \hspace -.5ex \left ( n\log \log (N/n) \right ) bits to store the optimal prefix code. Then, we introduce an approximate technique that, for any 0<\epsilon <1/2 , takes {\mathcal {O} \hspace {-.5ex} \left ({ {n \log \log (1 / \epsilon )} }\right )} bits to store a prefix code with an average codeword length within an additive \epsilon of the minimum. Finally, a second approximation takes, for any constant c > 1 , \vphantom {\sum ^{R^{R}}}\mathcal {O}(n^{1 / c} \log n) bits to store a prefix code with an average codeword length at most c$ times the minimum. In all cases, our data structures allow encoding and decoding of any symbol in {\mathcal {O} \hspace {-.5ex} \left ({ {1} }\right )} time. We experimentally compare our new techniques with the state of the art, showing that we achieve sixfold-to-eightfold space reductions, at the price of a slower encoding (2.5–8 times slower) and decoding (12–24 times slower). The approximations further reduce this space and improve the time significantly, up to recovering the speed of classical implementations, for a moderate penalty in the average code length. As a byproduct, we compare various heuristic, approximate, and optimal algorithms to generate length-restricted codes, showing that the optimal ones are clearly superior and practical enough to be implemented. [ABSTRACT FROM PUBLISHER]

In wireless sensor networks, various applications involve learning one or multiple functions of the measurements observed by sensors, rather than the measurements themselves. This paper focuses on the class of type-threshold functions, e.g., the maximum and the indicator functions. A simple network model capturing both the broadcast and superposition properties of wireless channels is considered: the collocated Gaussian network. A general multiround coding scheme exploiting superposition and interaction (through broadcast) is developed. Through careful scheduling of concurrent transmissions to reduce redundancy, it is shown that given any independent measurement distribution, all type-threshold functions can be computed reliably with a nonvanishing rate in the collocated Gaussian network, even if the number of sensors tends to infinity. [ABSTRACT FROM AUTHOR]