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Recently, there has been a lot of success in using the deterministic approach to provide approximate characterization of Gaussian network capacity. In this paper, we take a deterministic view and revisit the problem of wiretap channel with side information. A precise characterization of the secrecy capacity is obtained for a linear deterministic model, which naturally suggests a coding scheme which we show to achieve the secrecy capacity of the degraded Gaussian model (dubbed as “secret writing on dirty paper”) to within half a bit. [ABSTRACT FROM PUBLISHER]

We compare the capacity of dirty-paper coding (DPC) to that of time-division multiple access (TDMA) for a multiple-antenna (multiple- input multiple-output (MIMO)) Gaussian broadcast channel (BC). We find that the sum-rate capacity (achievable using DPC) of the multiple-antenna BC Is at most min(M, K) times the largest single-user capacity (i.e., the TDMA sum-rate) in the system, where M is the number of transmit antennas and K is the number of receivers. This result is Independent of the number of receive antennas and the channel gain matrix, and is valid at all signal-to-noise ratios (SNRs). We investigate the tightness of this bound In a time-varying channel (assuming perfect channel knowledge at receivers and transmitters) where the channel experiences uncorrelated Rayleigh fading and In some situations we find that the dirty paper gain is upper-bounded by the ratio of transmit-to-receive antennas. We also show that min(M, K) upper-bounds the sum-rate gain of successive decoding over TDMA for the uplink channel, where M is the number of receive antennas at the base station and K is the number of transmitters. [ABSTRACT FROM AUTHOR]

In this correspondence, we compare the achievable throughput for the optimal strategy of dirty paper coding (DPC) to that achieved with suboptimal and lower complexity linear precoding techniques (zero-forcing and block diagonalization). Both strategies utilize all available spatial dimensions and therefore have the same multiplexing gain, but an absolute difference in terms of throughput does exist. The sum rate difference between the two strategies is analytically computed at asymptotically high SNR. Furthermore, the difference is not affected by asymmetric channel behavior when each user has a different average SNR. Weighted sum rate maximization is also considered. In the process, it is shown that allocating user powers in direct proportion to user weights asymptotically maximizes weighted sum rate. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the convergence speed of the Arimoto-Blahut algorithm. For many channel matrices, the convergence speed is exponential, but for some channel matrices it is slower than exponential. By analyzing the Taylor expansion of the defining function of the Arimoto-Blahut algorithm, we will make the conditions clear for the exponential or slower convergence. The analysis of the slow convergence in this paper is new. Based on this analysis, we will compare the convergence speeds of the Arimoto-Blahut algorithm numerically with the values obtained in our theorems for several channel matrices. The purpose of this paper is to obtain a complete understanding of the convergence speed of the Arimoto-Blahut algorithm. [ABSTRACT FROM AUTHOR]

We investigate the state-dependent Gaussian wiretap channel with noncausal channel state information at the transmitter (GWTC-N-CSIT), and explore whether three strategies (i.e., taking action on the state, legitimate receiver’s channel output feedback, and combining the former two strategies together) help to enhance the secrecy capacity of the GWTC-N-CSIT. To be specific, we first determine the secrecy capacity of the GWTC-N-CSIT with noiseless feedback. Next, we derive lower and upper bounds on the secrecy capacity of the GWTC-N-CSIT with action-dependent state. Finally, we derive lower and upper bounds on the secrecy capacity of the GWTC-N-CSIT with both action-dependent state and noiseless feedback, and show that these bounds meet for a special case. Numerical results of this paper indicate that all three strategies enhance the secrecy capacity of the GWTC-N-CSIT. The study of this paper offers new options for enhancing the secrecy rates of the state-dependent wiretap channel models. [ABSTRACT FROM AUTHOR]

This paper studies the capacity of an $n$ -dimensional vector Gaussian noise channel subject to the constraint that an input must lie in the ball of radius $R$ centered at the origin. It is known that in this setting, the optimizing input distribution is supported on a finite number of concentric spheres. However, the number, the positions, and the probabilities of the spheres are generally unknown. This paper characterizes necessary and sufficient conditions on the constraint $R$ , such that the input distribution supported on a single sphere is optimal. The maximum $\bar {R}_{n}$ , such that using only a single sphere is optimal, is shown to be a solution of an integral equation. Moreover, it is shown that $\bar {R}_{n}$ scales as $\sqrt {n}$ and the exact limit of $\frac {\bar {R}_{n}}{\sqrt {n}}$ is found. [ABSTRACT FROM AUTHOR]

The zero-error capacity of a channel is defined as the maximum rate at which it is possible to transmit information with zero probability of error. In this paper, we settle all previously unsolved cases for the zero-error capacity of binary channels with one memory. [ABSTRACT FROM AUTHOR]

The state-dependent point-to-point Gaussian channel with a helper is first studied, in which a transmitter communicates with a receiver via a state-corrupted channel. The state is not known to the transmitter nor to the receiver, but known to a helper noncausally, which then wishes to assist the receiver to cancel the state. Differently from the previous work that characterized the capacity only in the infinite state power regime, this paper explores the general case with arbitrary state power. A lower bound on the capacity is derived based on an achievable scheme that integrates direct state subtraction and single-bin dirty paper coding. By analyzing this lower bound and further comparing it with the existing upper bounds, the capacity of the channel is characterized for a wide range of channel parameters. Such an idea of characterizing the capacity is further extended to study the two-user state-dependent multiple access channel with a helper. By comparing the derived inner and outer bounds, the channel parameters are partitioned into appropriate cases, and for each case, either segments on the capacity region boundary or the full capacity region are characterized. [ABSTRACT FROM PUBLISHER]

This paper studies the low-SNR regime performance of a scalar complex $K$ -user interference channel with the Gaussian noise. The finite bandwidth case is considered, where the low-SNR regime is approached by letting the input power go to zero, while the bandwidth is small and fixed. We show that for all $\delta >0$ , there exists a set of channel coefficients with non-zero measure (probability), in which the wideband slope per user satisfies $ \mathcal {S}_{0}< {\scriptstyle {}^{\scriptstyle 2}}\hspace{-0.224em}/\hspace{-0.112em}{\scriptstyle K}+\delta $. This is quite contrary to the large bandwidth case, where a slope of 1 per user is achievable with probability 1. We also develop an interference alignment scheme for the finite bandwidth case that shows some gain in wideband slope. [ABSTRACT FROM AUTHOR]

In this paper, we examine an input-constrained erasure channel and we characterize the asymptotics of its capacity when the erasure rate is low. More specifically, for a general memoryless erasure channel with its input supported on an irreducible finite-type constraint, we derive partial asymptotics of its capacity, using some series expansion type formula of its mutual information rate; and for a binary erasure channel with its first-order Markovian input supported on the $(1, \infty )$ -RLL constraint based on the concavity of its mutual information rate with respect to some parameterization of the input, we numerically evaluate its first-order Markov capacity and further derive its full asymptotics. The asymptotics obtained in this paper, when compared with the recently derived feedback capacity for a binary erasure channel with the same input constraint, enable us to draw the conclusion that feedback may increase the capacity of an input-constrained channel, even if the channel is memoryless. [ABSTRACT FROM PUBLISHER]

Using some recent results on asymptotically equivalent sequences of matrices, we present in this paper, a new derivation of the capacity formula given by Brandenburg and Wyner for a discrete-time Gaussian multiple-input-multiple-output channel with memory. In this paper, we tackle not only the case considered by them, where the number of channel inputs and the number of channel outputs are the same, but also when both numbers are different. [ABSTRACT FROM AUTHOR]

This paper studies a memoryless state-dependent multiple access channel (MAC) where two transmitters wish to convey a message to a receiver under the assumption of causal and imperfect channel state information at transmitters (CSIT) and imperfect channel state information at receiver (CSIR). In order to emphasize the limitation of transmitter cooperation between physically distributed nodes, we focus on the so-called distributed CSIT assumption, i.e., where each transmitter has its individual channel knowledge, while the message can be assumed to be partially or entirely shared a priori between transmitters by exploiting some on-board memory. Under this setup, the first part of the paper characterizes the common message capacity of the channel at hand for arbitrary CSIT and CSIR structure. The optimal scheme builds on Shannon strategies, i.e., optimal codes are constructed by letting the channel inputs be a function of current CSIT only. For a special case when CSIT is a deterministic function of CSIR, the considered scheme also achieves the capacity region of a common message and two private messages. The second part addresses an important instance of the previous general result in a context of a cooperative multi-antenna Gaussian channel under i.i.d. fading operating in frequency-division duplex mode, such that CSIT is acquired via an explicit feedback of perfect CSIR. The capacity of the channel at hand is achieved by distributed linear precoding applied to Gaussian codes. Surprisingly, we demonstrate that it is suboptimal to send a number of data streams bounded by the number of transmit antennas as typically considered in a centralized CSIT setup. Finally, numerical examples are provided to evaluate the sum capacity of the binary MAC with binary states as well as the Gaussian MAC with i.i.d. fading. [ABSTRACT FROM AUTHOR]

In the $q$ -ary online (or “causal”) channel coding model, a sender wishes to communicate a message to a receiver by transmitting a codeword $\mathbf {x} =(x_{1},\ldots,x_{n}) \in \{0,1,\ldots,q-1\}^{n}$ symbol-by-symbol via a channel limited to at most $pn$ errors and $p^{*} n$ erasures. The channel is “online” in the sense that at the $i$ th step of communication the channel decides whether to corrupt the $i$ th symbol or not based on its view so far, i.e., its decision depends only on the transmitted symbols $(x_{1},\ldots,x_{i})$. This is in contrast to the classical adversarial channel in which the corruption is chosen by a channel that has full knowledge of the sent codeword $\mathbf {x}$. In this paper, we study the capacity of $q$ -ary online channels for a combined corruption model, in which the channel may impose at most $pn$ errors and at most $p^{*} n$ erasures on the transmitted codeword. The online channel (in both the error and erasure case) has seen a number of recent studies, which present both upper and lower bounds on its capacity. In this paper, we give a full characterization of the capacity as a function of $q,p$ , and $p^{*}$. [ABSTRACT FROM AUTHOR]

Sparse superposition codes, or sparse regression codes, are a recent class of codes for reliable communication over the AWGN channel at rates approaching the channel capacity. Approximate message passing (AMP) decoding, a computationally efficient technique for decoding SPARCs, has been proven to be asymptotically capacity-achieving for the AWGN channel. In this paper, we refine the asymptotic result by deriving a large deviation bound on the probability of an AMP decoding error. This bound gives insight into the error performance of the AMP decoder for large but finite problem sizes, giving an error exponent as well as guidance on how the code parameters should be chosen at finite block lengths. For an appropriate choice of code parameters, we show that for any fixed rate less than the channel capacity, the decoding error probability decays exponentially in $n/(\log n)^{2T}$ , where $T$ , the number of AMP iterations required for successful decoding, is bounded in terms of the gap from capacity. [ABSTRACT FROM AUTHOR]

In 2010, Silva et al. studied certain classes of finite-field matrix channels in order to model random linear network coding where exactly $t$ random errors are introduced. In this paper, we consider a generalization of these matrix channels where the number of errors is not required to be constant, indeed the number of errors may follow any distribution. We show that a capacity-achieving input distribution can always be taken to have a very restricted form (the distribution should be uniform given the rank of the input matrix). This result complements, and is inspired by a paper of Nobrega et al., which establishes a similar result for a class of matrix channels that model network coding with link erasures. Our result shows that the capacity of our channels can be expressed as maximization over probability distributions on the set of possible ranks of input matrices: a set of linear rather than exponential size. [ABSTRACT FROM AUTHOR]

This paper studies the two-user causal cognitive interference channel (CCIC), where two transmitters aim to communicate independent messages to two different receivers via a common channel. One source, referred to as the cognitive, is capable of overhearing the other source, referred to as the primary, through a noisy in-band link and thus can assist in sending the primary’s data. The authors of this paper recently characterized to within a constant gap the capacity of the symmetric Gaussian CCIC in: 1) the strong interference regime and 2) for a subset of the weak interference regime when the cooperation link is larger than a given threshold. This paper characterizes to within a constant gap the capacity for the symmetric Gaussian CCIC in the regime that was still open. To this end, two novel outer bounds of the types 2 R\mathsf {p}+ R\mathsf {c} and R\mathsf {p}+2 R\mathsf {c} are derived for the class of injective semideterministic CCICs, where the noises at the different source-destination pairs are independent. These outer bounds, as well as an achievable rate region based on Gelfand-Pinsker binning, superposition coding, and simultaneous decoding at the receivers, are then specialized to the Gaussian noise case. It is shown that the novel outer bounds are necessary to characterize the capacity within a constant gap when the cooperation link is weaker than the direct links, that is, in this regime unilateral cooperation leaves some system resources underutilized. [ABSTRACT FROM PUBLISHER]

In their seminal 1996 paper, Anantharam and Verdú showed that feedback does not increase the capacity of a queue under First-in-First-Out service policy and exponentially distributed service time. Since the channel has memory, this negative result raises the question whether it extends to other non-trivial combinations of service policy and service time. This paper addresses this question by providing two sufficient conditions under which feedback either increases capacity or does not increase capacity. The first is a sufficient condition on the service time distribution for feedback to increase capacity under First-In-First-Out service policy. The second is a sufficient condition for feedback not to increase capacity and is general in that it depends on the output distribution of the queue, but explicitly depends neither on the queue policy nor on the service time distribution. This condition is satisfied, for instance, by queues with Last-Come-First-Serve service policy and bounded service times. [ABSTRACT FROM AUTHOR]

Shannon in his 1956 seminal paper introduced the concept of the zero error capacity, C0 , of a noisy channel. This is defined as the least upper bound of rates, at which, it is possible to transmit information with zero probability of error. At present not many codes are known to achieve the zero error capacity. In this paper, some codes which achieve zero error capacities in limited magnitude error channels are described. The code lengths of these zero error capacity achieving codes can be of any finite length $n=1,2,\ldots$ , in contrast to the long lengths required for the known regular capacity achieving codes, such as turbo codes, LDPC codes, and polar codes. Both wrap around and non-wrap around limited magnitude error models are considered in this paper. For non-wrap around error model, the exact value of zero error capacities is derived, and optimal non-systematic and systematic codes are designed. The non-systematic codes achieve the zero error capacity with any finite length. The optimal systematic codes achieve the systematic zero error capacity of the channel, which is defined as the zero error capacity with the additional requirements that the communication must be carried out with a systematic code. It is also shown that the rates of the proposed systematic codes are equal to or approximately equal to the zero error capacity of the channel. For the wrap around model bounds are derived for the zero error capacity and in many cases the bounds give the exact value. In addition, optimal wrap around non-systematic and systematic codes are developed which either achieve or are close to achieving the zero error capacity with finite length. [ABSTRACT FROM PUBLISHER]

We study the channel capacity of a general discrete energy harvesting channel with a finite battery. Contrary to traditional communication systems, the transmitter of such a channel is powered by a device that harvests energy from a random exogenous energy source and has a finite-sized battery. As a consequence, at each transmission opportunity, the system can only transmit a symbol whose energy is no more than the energy currently available. This new type of power supply introduces an unprecedented input constraint for the channel, which is simultaneously random, instantaneous, and influenced by the full history of the inputs and the energy harvesting process. Furthermore, naturally, in such a channel, the energy information is observed causally at the transmitter. Both of these characteristics pose great challenges for the analysis of the channel capacity. In this paper, we use techniques developed for channels with side information and finite-state channels, to obtain lower and upper bounds on the capacity of energy harvesting channels. In particular, in a general case with Markov energy harvesting processes, we use stationarity and ergodicity theory to compute and optimize the achievable rates for the channels, and derive a series of computable capacity upper and lower bounds. [ABSTRACT FROM AUTHOR]

The Ising channel, which was introduced in 1990, is a channel with memory that models intersymbol interference. In this paper, we consider the Ising channel with feedback and find the capacity of the channel together with a capacity-achieving coding scheme. To calculate the channel capacity, an equivalent dynamic programming (DP) problem is formulated and solved. Using the DP solution, we establish that the feedback capacity is the expression \(C=({2H_{b}(a)}/{3+a})\approx 0.575522\) , where \(a\) is a particular root of a fourth-degree polynomial and \(H_{b}(x)\) denotes the binary entropy function. Simultaneously, \(a=\arg \max _{0\leq x \leq 1} ({2H_{b}(x)}/{3+x})\) . Finally, an error-free, capacity-achieving coding scheme is provided together with the outlining of a strong connection between the DP results and the coding scheme. [ABSTRACT FROM AUTHOR]

Consider a binary Reed–Muller code RM (r,m) defined on the m -dimensional hypercube \mathbb F2^{m} . In this paper, we study punctured Reed–Muller codes Pr(m,b) , whose positions are restricted to the m -tuples of a given Hamming weight b . In combinatorial terms, this paper concerns m -variate Boolean polynomials of any degree r , which are evaluated on a Hamming sphere of some radius b . Codes Pr(m,b) inherit some recursive properties of RM codes. In particular, they can be built from the shorter codes, by decomposing a spherical b -layer into sub-layers of smaller dimensions. However, these sub-layers have different sizes and do not form the classical Plotkin construction. We analyze recursive properties of the spherically punctured codes Pr(m,b) and find their distances for the arbitrary values of parameters $r,m$ , and $b$ . Finally, we describe recursive (successive cancellation) decoding of these codes. [ABSTRACT FROM AUTHOR]

This paper studies a large random matrix system (LRMS) model involving an arbitrary signal distribution and forward error control (FEC) coding. We establish an area property based on the approximate message passing (AMP) algorithm. Under the assumption that the state evolution for AMP is correct for the coded system, the achievable rate of AMP is analyzed. We prove that AMP achieves the constrained capacity of the LRMS with an arbitrary signal distribution provided that a matching condition is satisfied. As a byproduct, we provide an alternative derivation for the constraint capacity of an LRMS using a proved property of AMP. We discuss realization techniques for the matching principle of binary signaling using irregular low-density parity-check (LDPC) codes and provide related numerical results. We show that the optimized codes demonstrate significantly better performance over un-matched ones under AMP. For quadrature phase shift keying (QPSK) modulation, bit error rate (BER) performance within 1 dB from the constrained capacity limit is observed. [ABSTRACT FROM AUTHOR]

We study the list decodability of different ensembles of codes over the real alphabet under the assumption of an omniscient adversary. It is a well-known result that when the source and the adversary have power constraints $P $ and $N $ respectively, the list decoding capacity is equal to $\frac {1}{2}\log \frac {P}{N}$. Random spherical codes achieve constant list sizes, and the goal of the present paper is to obtain a better understanding of the smallest achievable list size as a function of the gap to capacity. We show a reduction from arbitrary codes to spherical codes, and derive a lower bound on the list size of typical random spherical codes. We also give an upper bound on the list size achievable using nested Construction-A lattices and infinite Construction-A lattices. We then define and study a class of infinite constellations that generalize Construction-A lattices and prove upper and lower bounds for the same. Other goodness properties such as packing goodness and AWGN goodness of infinite constellations are proved along the way. Finally, we consider random lattices sampled from the Haar distribution and show that if a certain conjecture that originates in analytic number theory is true, then the list size grows as a polynomial function of the gap-to-capacity. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the additivity phenomenon in the quantum dynamic capacity region of a quantum channel for trading the resources of classical communication, quantum communication, and entanglement. Understanding such an additivity property is important if we want to optimally use a quantum channel for general communication purposes. However, in a lot of cases, the channel one will be using only has an additive single or double resource capacity region, and it is largely unknown if this could lead to a strictly superadditive double or triple resource capacity region, respectively. For example, if a channel has additive classical and quantum capacities, can the classical-quantum capacity region be strictly superadditive? In this paper, we answer such questions affirmatively. We give proof-of-principle requirements for these channels to exist. In most cases, we can provide an explicit construction of these quantum channels. The existence of these superadditive phenomena is surprising in contrast to the result that the additivity of both classical-entanglement and classical-quantum capacity regions imply the additivity of the triple resource capacity region for a given channel. [ABSTRACT FROM AUTHOR]

Polar codes are a family of capacity-achieving codes that have explicit and low-complexity construction, encoding, and decoding algorithms. Decoding of polar codes is based on the successive-cancellation decoder, which decodes in a bit-wise manner. A decoding error occurs when at least one bit is erroneously decoded. The various codeword bits are correlated, yet performance analysis of polar codes ignores this dependence: the upper bound is based on the union bound, and the lower bound is based on the worst-performing bit. Improvement of the lower bound is afforded by considering error probabilities of two bits simultaneously. These are difficult to compute explicitly due to the large alphabet size inherent to polar codes. In this paper, we propose a method to lower-bound the error probabilities of bit pairs. We develop several transformations on pairs of synthetic channels that make the resultant synthetic channels amenable to alphabet reduction. Our method yields lower bounds that significantly improve upon currently known lower bounds for polar codes under successive-cancellation decoding. [ABSTRACT FROM AUTHOR]

Consider a memoryless relay channel, where the relay is connected to the destination with an isolated bit pipe of capacity $C_{0}$. Let $C(C_{0})$ denote the capacity of this channel as a function of $C_{0}$. What is the critical value of $C_{0}$ , such that $C(C_{0})$ first equals $C(\infty)$ ? This is a long-standing open problem posed by Cover and named “The Capacity of the Relay Channel,” in Open Problems in Communication and Computation, Springer-Verlag, 1987. In this paper, we answer this question in the Gaussian case and show that $C(C_{0})$ cannot equal to $C(\infty)$ unless $C_{0}=\infty $ , regardless of the SNR of the Gaussian channels. This result follows as a corollary to a new upper bound we develop on the capacity of this channel. Instead of “single-letterizing” expressions involving information measures in a high-dimensional space as is typically done in converse results in information theory, our proof directly quantifies the tension between the pertinent $n$ -letter forms. This is done by translating the information tension problem to a problem in high-dimensional geometry. As an intermediate result, we develop an extension of the classical isoperimetric inequality on a high-dimensional sphere, which can be of interest in its own right. [ABSTRACT FROM AUTHOR]

This paper establishes a general theory of energy-constrained quantum and private capacities of quantum channels. We begin by defining various energy-constrained communication tasks, including quantum communication with a uniform energy constraint, entanglement transmission with an average energy constraint, private communication with a uniform energy constraint, and secret key transmission with an average energy constraint. We develop several code conversions, which allow us to conclude non-trivial relations between the capacities corresponding to the above tasks. We then show how the regularized, energy-constrained coherent information is equal to the capacity for the first two tasks and is an achievable rate for the latter two tasks, whenever the energy observable satisfies the Gibbs condition of having a well-defined thermal state for all temperatures and the channel satisfies a finite output-entropy condition. For degradable channels satisfying these conditions, we find that the single-letter energy-constrained coherent information is equal to all of the capacities. We finally apply our results to degradable quantum Gaussian channels and recover several results already established in the literature (in some cases, we prove new results in this domain). Contrary to what may appear from some statements made in the literature recently, proofs of these results do not require the solution of any kind of minimum output entropy conjecture or entropy photon-number inequality. [ABSTRACT FROM AUTHOR]

We study the problem of computing the capacity of a discrete memoryless channel under uncertainty affecting the channel law matrix, and possibly with a constraint on the average cost of the input distribution. The problem has been formulated in the literature as a max–min problem. We use the robust optimization methodology to convert the max–min problem to a standard convex optimization problem. For small-sized problems, and for many types of uncertainty, such a problem can be solved in principle using interior point methods (IPMs). However, for large-scale problems, IPMs are not practical. Here, we suggest an $\mathcal {O}(1/T)$ first-order algorithm based on which is applied directly to the max–min problem. [ABSTRACT FROM AUTHOR]

Consider communication over a channel whose probabilistic model is completely unknown vector-wise and is not assumed to be stationary. Communication over such channels is challenging because knowing the past does not indicate anything about the future. The existence of reliable feedback and common randomness is assumed. In a previous paper, it was shown that the Shannon capacity cannot be attained, in general, if the channel is not known. An alternative notion of capacity was defined, as the maximum rate of reliable communication by any block-coding system used over consecutive blocks. This rate was shown to be achievable for the modulo-additive channel with an individual, unknown noise sequence, and not achievable for some channels with memory. In this paper, this capacity is shown to be achievable for general channel models possibly including memory, as long as this memory fades with time. In other words, there exists a system with feedback and common randomness that, without knowledge of the channel, asymptotically performs as well as any block code, which may be designed knowing the channel. For channels in which memory does not fade with time, a weaker type of capacity is shown to be achievable. [ABSTRACT FROM AUTHOR]

This paper investigates the secret key-authenticated-capacity region, where information-theoretic authentication is defined by the ability of the decoder to accept and decode messages originating from a valid encoder while rejecting messages from other invalid sources. The model considered here consists of a valid encoder-decoder pairing that can communicate through a channel controlled by an adversary who is also able to eavesdrop on the encoder’s transmissions. Prior to the encoder’s transmission, the adversary decides whether or not to replace the decoder’s observation with an arbitrary one of the adversary’s choosing, with the adversary’s objective being to have the decoder accept and decode their observation to a valid message (different from that of the encoder). To combat the adversary, the encoder and decoder share a secret key. The secret key-authenticated-capacity region is defined as the region of jointly achievable message rate, authentication rate (a to be defined per symbol measure that will generally represent the likelihood that an adversary can fool the decoder), and the key-consumption rate (how many bits of secret key are needed per symbol sent). This is the second of a two-part study, with the parts differing in their measure of the authentication rate. For this second study, the probability of false authentication is considered as a function of the system state, where the system state is defined by the message being transmitted, the value of the secret key, the adversary’s channel observations, and the adversary’s (possibly stochastic) choice for the decoder’s observation. Termed the typical-authentication rate, the authentication measure considered here corresponds to an upper bound on the probability of false authentication for the majority of system states. For this measure, we derive matching inner and outer bounds for the secret key-enabled authenticated capacity region in terms of traditional information-theoretic measures. In doing so, it is shown that the typical-authentication rate and the message rate exhibit a one-to-one trade-off in the capacity region. [ABSTRACT FROM AUTHOR]

This paper investigates the secret-key-authenticated-capacity region, where information-theoretic authentication is defined by the ability of the decoder to accept and decode messages originating from a valid encoder while rejecting messages from other invalid sources. The model considered here consists of a valid encoder-decoder pairing that can communicate through a channel controlled by an adversary who is also able to eavesdrop on the encoder’s transmissions. Over multiple rounds of communication, the adversary first decides whether or not to replace the decoder’s observation with an arbitrary one of the adversary’s choosing, with the goal of the adversary being to have the decoder accept and decode their observation as a valid message (different from that of the encoder). To combat the adversary, the encoder and decoder share a secret key. The secret-key-authenticated-capacity region here is then defined as the region of jointly achievable message rate, authentication rate (a to be defined per symbol measure that will generally represent the likelihood that an adversary can fool the decoder), and the key-consumption rate (how many bits of secret key are needed per symbol sent). This is the first of a two-part study, with the parts differing in their measure of the authentication rate. In this first study, the authentication rate is the exponent of blocklength-normalized exponent of the expected probability of false authentication. For this metric, we provide an inner bound which improves on those existing in the literature. This is achieved by adopting and merging different classical techniques in novel ways. Within these classical secret-key-based authentication techniques, one technique derives authentication capability from secure channel coding to send the secret key with the message, and the other technique derives its authentication capability directly from obscuring the source. [ABSTRACT FROM AUTHOR]

In a breakthrough, Hastings showed that there exist quantum channels whose classical Holevo capacity is superadditive i.e. more classical information can be transmitted by quantum encoding strategies entangled across multiple channel uses as compared to unentangled quantum encoding strategies. Hastings’ proof used Haar random unitaries to exhibit superadditivity. In this paper we show that a unitary chosen uniformly at random from an approximate $n^{2/3}$ -design gives rise to a quantum channel with superadditive classical Holevo capacity, where $n$ is the dimension of the unitary exhibiting the Stinespring dilation of the channel superoperator. We follow the geometric functional analytic approach of Aubrun, Szarek and Werner in order to prove our result. More precisely we prove a sharp Dvoretzky-like theorem stating that, with high probability under the choice of a unitary from an approximate $t$ -design, random subspaces of large dimension make a Lipschitz function take almost constant value. Such theorems were known earlier only for Haar random unitaries. We obtain our result by appealing to Low’s technique for proving concentration of measure for an approximate $t$ -design, combined with a stratified analysis of the variational behaviour of Lipschitz functions on the unit sphere in high dimension. The stratified analysis is the main technical advance of this work. Haar random unitaries require at least $\Omega (n^{2})$ random bits in order to describe them with good precision. In contrast, there exist exact $n^{2/3}$ -designs using only $O(n^{2/3} \log n)$ random bits. Thus, our work can be viewed as a partial derandomisation of Hastings’ result, and a step towards the quest of finding an explicit quantum channel with superadditive classical Holevo capacity. Finally we also show that for any $p > 1$ , approximate unitary $n^{1.7}$ -designs give rise to channels violating subadditivity of Rényi $p$ -entropy. In addition to stratified analysis, the proof of this result uses a new technique of approximating a monotonic differentiable function defined on a closed bounded interval and its derivative by moderate degree polynomials which should be of independent interest. [ABSTRACT FROM AUTHOR]

In an acyclic multicast network, it is well known that a linear network coding solution over GF( q ) exists when q is sufficiently large. In particular, for each prime power q no smaller than the number of receivers, a linear solution over GF( q ) can be efficiently constructed. In this paper, we reveal that a linear solution over a given finite field does not necessarily imply the existence of a linear solution over all larger finite fields. In particular, we prove by construction that: 1) for every \omega \geq 3 , there is a multicast network with source outdegree \omega linearly solvable over GF(7) but not over GF(8), and another multicast network linearly solvable over GF(16) but not over GF(17); 2) there is a multicast network linearly solvable over GF(5) but not over such GF( q ) and over GF( q^m2 ) is not necessarily linearly solvable over GF( q^{m1 + m2} ); and 4) there exists a class of multicast networks with a set T of receivers such that the minimum field size q_{\mathrm{ min}} for a linear solution over GF( q_{\mathrm{ min}} ) is lower bounded by \Theta (\sqrt T) , but not every larger field than GF( q\mathrm{ min} ) suffices to yield a linear solution. The insight brought from this paper is that not only the field size but also the order of subgroups in the multiplicative group of a finite field affects the linear solvability of a multicast network. [ABSTRACT FROM AUTHOR]

New nonasymptotic random coding theorems (with error probability $\epsilon $ and finite block length $n$ ) based on Gallager parity check ensemble and general parity check ensembles are derived in this paper. The resulting nonasymptotic achievability bounds, when combined with nonasymptotic equipartition properties developed in this paper, can be easily computed. Analytically, these nonasymptotic achievability bounds are shown to be asymptotically tight up to the second order of the coding rate as $n$ goes to infinity with either constant or subexponentially decreasing $\epsilon $ in the case of Gallager parity check ensemble, and to imply that low density parity check (LDPC) codes be capacity-achieving in the case of LDPC ensembles. Numerically, they are also compared favorably, for finite $n$ and $\epsilon $ of practical interest, with existing nonasymptotic achievability bounds in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we formally define and analyze the class of noisy permutation channels. The noisy permutation channel model constitutes a standard discrete memoryless channel (DMC) followed by an independent random permutation that reorders the output codeword of the DMC. While coding theoretic aspects of this model have been studied extensively, particularly in the context of reliable communication in network settings where packets undergo transpositions, and closely related models of DNA based storage systems have also been analyzed recently, we initiate an information theoretic study of this model by defining an appropriate notion of noisy permutation channel capacity. Specifically, on the achievability front, we prove a lower bound on the noisy permutation channel capacity of any DMC in terms of the rank of the stochastic matrix of the DMC. On the converse front, we establish two upper bounds on the noisy permutation channel capacity of any DMC whose stochastic matrix is strictly positive (entry-wise). Together, these bounds yield coding theorems that characterize the noisy permutation channel capacities of every strictly positive and “full rank” DMC, and our achievability proof yields a conceptually simple, computationally efficient, and capacity achieving coding scheme for such DMCs. Furthermore, we also demonstrate the relation between the well-known output degradation preorder over channels and noisy permutation channel capacity. In fact, the proof of one of our converse bounds exploits a degradation result that constructs a symmetric channel for any DMC such that the DMC is a degraded version of the symmetric channel. Finally, we illustrate some examples such as the special cases of binary symmetric channels and (general) erasure channels. Somewhat surprisingly, our results suggest that noisy permutation channel capacities are generally quite agnostic to the parameters that define the DMCs. [ABSTRACT FROM AUTHOR]

The sphere packing bound, in the form given by Shannon, Gallager, and Berlekamp, was recently extended to classical-quantum channels, and it was shown that this creates a natural setting for combining probabilistic approaches with some combinatorial ones such as the Lovász theta function. In this paper, we extend the study to the case of constant-composition codes. We first extend the sphere packing bound for classical-quantum channels to this case, and we then show that the obtained result is related to a variation of the Lovász theta function studied by Marton. We then propose a further extension to the case of varying channels and codewords with a constant conditional composition given a particular sequence. This extension is finally applied to auxiliary channels to deduce a bound, which is useful in the low rate region and which can be interpreted as an extension of the Elias bound. [ABSTRACT FROM AUTHOR]

In this paper, we initiate a first information-theoretic study on multilevel NAND flash memory channels with intercell interference. More specifically, for a multilevel NAND flash memory channel under mild assumptions, we first prove that such a channel is indecomposable and it features asymptotic equipartition property; we then further prove that stationary processes achieve its information capacity, and consequently, as the order tends to infinity, its Markov capacity converges to its information capacity; eventually, we establish that its operational capacity is equal to its information capacity. Our results suggest that it is highly plausible to apply the ideas and techniques in the computation of the capacity of finite-state channels, which are relatively better explored, to that of the capacity of multilevel NAND flash memory channels. [ABSTRACT FROM AUTHOR]

This paper presents the first systematic study of the zero-error capacity regions of noisy networks. First, we consider two simple such networks, each consisting of a stationary memoryless multiple access channel with two binary inputs and one discrete output. There are two users in each network. Each of the two users transmits a message through the network, and the sink(s) of the network can decode both messages with zero error. A graph is used to represent the distinguishability of the inputs of the channel, and a graph set is used to represent the distinguishability of the inputs of the network. We show that for two networks represented by the same graph set, their zero-error capacity regions are the same. We list all the possible graph sets for the two networks and determine the zero-error capacity regions for some of these graph sets. Based on this result, we explore a relation between graph theory and set theory, and then redefine the cancellative pair of families of subsets. We further extend the problem formulation to a general network called the parallel network, which may consist of more than one channel with multiple inputs and multiple outputs. [ABSTRACT FROM AUTHOR]

This paper investigates the capacity of general multiple-input single-output (MISO) optical intensity channels (OICs) under per-antenna peak- and average-intensity constraints. We first consider the MISO equal-cost constrained OIC (EC-OIC), where, apart from the peak-intensity constraint, average intensities of inputs are equal to arbitrarily preassigned constants. The second model of our interest is the MISO bounded-cost constrained OIC (BC-OIC), where, as compared with the EC-OIC, average intensities of inputs are no larger than arbitrarily preassigned constants. By leveraging tools from quantile functions, stop-loss transform and convex ordering of nonnegative random variables, we prove two decomposition theorems for bounded and nonnegative random variables, based on which we equivalently transform both the EC-OIC and the BC-OIC into respective single-input single-output channels under a peak-intensity and several stop-loss mean constraints. Capacity lower and upper bounds for both channels are established, based on which the asymptotic capacity at high and low signal-to-noise-ratio are determined. [ABSTRACT FROM AUTHOR]

In this paper, we propose capacity-achieving communication schemes for Gaussian finite-state Markov channels subject to an average channel input power constraint, under the assumption that the transmitters can have access to delayed noiseless output feedback as well as instantaneous or delayed channel state information. We show that the proposed schemes reveals connections between feedback communication and feedback control. [ABSTRACT FROM PUBLISHER]

The growing interest in action-dependent channels motivates us to extend the study of action-dependent settings, which until now focused on point-to-point models, to multiple-access channels (MACs). In this paper, we consider a two-user, state-dependent MAC, in which one of the encoders, called the informed (cognitive) encoder, is allowed to take an action that affects the formation of the channel states. Two independent messages are to be sent through the channel: 1) a common message known to both encoders and 2) a private message known only to the informed encoder. In addition, the informed encoder has access to the sequence of channel states in a noncausal manner. Our framework generalizes the previously evaluated settings of state-dependent point-to-point channels with actions and MACs with common messages. We derive a single letter characterization of the capacity region for this setting. Using this general result, we obtain and compute the capacity region for the Gaussian action-dependent MAC. The special methods used in solving the Gaussian case are then applied to obtain the capacity of the Gaussian action-dependent point-to-point channel, a problem left open and solved now. Finally, we establish some dualities between action-dependent channel coding and source coding problems. In particular, we obtain a duality equivalence between the considered MAC setting and the rate distortion model known as successive refinement with actions. This is done by developing a set of simple duality principles that enables us to successfully evaluate the outcome of one problem given the outcome of the other. [ABSTRACT FROM PUBLISHER]

This paper studies the transceiver design of the Gaussian two-pair two-way relay channel (TWRC), where two pairs of users exchange information through a common relay in a pairwise manner. Our main contribution is to show that the capacity of the Gaussian two-pair TWRC is achievable to within $\frac{1}{ 2}$ bit for arbitrary channel conditions. For the outer bound, we derive a genie-aided bound of the Gaussian two-pair TWRC, which is tighter than the cut-set bound. For the inner bound, we develop a hybrid coding scheme involving Gaussian random coding, nested lattice coding, superposition coding, and network-coded decoding. We further present a message-reassembling strategy to decouple the coding design for the user-to-relay and relay-to-user links, so as to provide flexibility to fully exploit the channel randomness. We show that judicious power allocation at the users and at the relay is necessary to approach the channel capacity under various channel conditions. [ABSTRACT FROM AUTHOR]

In this paper, we make use of channel symmetry properties to determine the capacity region of three types of two-way networks: 1) two-user memoryless two-way channels (TWCs); 2) two-user TWCs with memory; and 3) three-user multiaccess/degraded broadcast (MA/DB) TWCs. For each network, symmetry conditions under which a Shannon-type random coding inner bound (under independent non-adaptive inputs) is tight are given. For two-user memoryless TWCs, prior results are substantially generalized by viewing a TWC as two interacting state-dependent one-way channels. The capacity of symmetric TWCs with memory, whose outputs are functions of the inputs and independent stationary and ergodic noise processes, is also obtained. Moreover, various channel symmetry properties under which the Shannon-type inner bound is tight are identified for three-user MA/DB TWCs. The results not only enlarge the class of symmetric TWCs whose capacity region can be exactly determined but also imply that interactive adaptive coding, not improving capacity, is unnecessary for such channels. [ABSTRACT FROM AUTHOR]

For any prime power $q$ , Mori and Tanaka introduced a family of $q$ -ary polar codes based on the $q\,\,\times \,\,q$ Reed–Solomon polarization kernels. For transmission over a $q$ -ary erasure channel, they also derived a closed-form recursion for the erasure probability of each effective channel. In this paper, we use that expression to analyze the finite-length scaling of these codes on the $q$ -ary erasure channel with erasure probability $\epsilon \in (0,1)$. Our primary result is that for any $\gamma >0$ and $\delta >0$ , there is a $q_{0}$ , such that for all $q\geq q_{0}$ , the fraction of effective channels with erasure rate at most $N^{-\gamma }$ is at least $1-\epsilon -O(N^{-1/2+\delta })$ , where $N=q^{n}$ is the blocklength. Since this fraction cannot be larger than $1-\epsilon -O(N^{-1/2})$ , this establishes near-optimal finite-length scaling for this family of codes. Our approach can be seen as an extension of a similar analysis for binary polar codes by Hassani, Alishahi, and Urbanke. A similar analysis is also considered for $q$ -ary polar codes with $m \times m$ polarizing matrices. This separates the effect of the alphabet size from the effect of the matrix size. If the polarizing matrix at each stage is drawn independently and uniformly from the set of invertible $m \times m$ matrices, then the linear operator associated with the Lyapunov function analysis can be written in the closed form. To prove near-optimal scaling for polar codes with fixed $q$ as $m$ increases, however, two technical obstacles remain. Thus, we conclude by stating two concrete mathematical conjectures that, if proven, would imply near-optimal scaling for fixed $q$. [ABSTRACT FROM AUTHOR]

A technique for bounding the capacities of networks of independent channels is introduced. Parts I and II treat point-to-point and multiterminal channels, respectively. Bounds are derived using a new tool called a bounding model. Channel 1 is an upper (lower) bounding model for channel 2 if replacing channel 2 by channel 1 in any network yields a new network whose capacity region is a superset (subset) of the capacity region of the original network. This paper derives bounding models from noiseless links, with lower bounding models corresponding to points in the channel's capacity region and upper bounding models corresponding to points in a new channel characterization called an emulation region. Replacing all channels in a network by their noiseless upper (lower) bounding models yields a network of lossless links whose capacity region is a superset (subset) of the capacity region for the original network. This converts a general (often stochastic) network into a network coding instance, enabling the application of tools and results derived in that domain. A channel's upper and lower bounding models differ when the channel can carry more information in some networks than in others. Bounding the difference between upper and lower bounding models bounds both the accuracy of the technique and the price of separating source-network coding from channel coding. [ABSTRACT FROM AUTHOR]

Energy harvesting sensor nodes are gaining popularity due to their ability to improve the network life time and are becoming a preferred choice supporting green communication. In this paper, we focus on communicating reliably over an additive white Gaussian noise channel using such an energy harvesting sensor node. An important part of this paper involves appropriate modeling of energy harvesting, as done via various practical architectures. Our main result is the characterization of the Shannon capacity of the communication system. The key technical challenge involves dealing with the dynamic (and stochastic) nature of the (quadratic) cost of the input to the channel. As a corollary, we find close connections between the capacity achieving energy management policies and the queueing theoretic throughput optimal policies. [ABSTRACT FROM AUTHOR]

In many wireless communication systems, radios are subject to a duty cycle constraint, that is, a radio can only actively transmit signals over a fraction of the time. For example, it is desirable to have a small duty cycle in some low power systems; a half-duplex radio cannot keep transmitting if it wishes to receive useful signals; and a cognitive radio needs to listen and detect primary users frequently. This paper studies the capacity of point-to-point scalar discrete-time Gaussian channels subject to a duty cycle constraint as well as an average transmit power constraint. An idealized duty cycle constraint is first studied, which can be regarded as a requirement on the minimum fraction of nontransmissions or zero symbols in each codeword. Independent input with a unique discrete distribution is shown to achieve the channel capacity. In many situations, numerically optimized on-off signaling can achieve much higher rate than Gaussian signaling over a deterministic transmission schedule. This is in part because the positions of nontransmissions in a codeword can convey information. A more realistic duty cycle constraint is also studied, where the extra cost of transitions between transmissions and nontransmissions due to pulse shaping is accounted for. The capacity-achieving input is correlated over time and is hard to compute. A lower bound of the achievable rate as a function of the input distribution is shown to be maximized by a first-order Markov input process, whose stationary distribution is also discrete and can be computed efficiently. The results in this paper suggest that, under various duty cycle constraints, departing from the usual paradigm of intermittent packet transmissions may yield substantial gain. [ABSTRACT FROM AUTHOR]

In this paper, we study the problem of simulating a discrete memoryless channel (DMC) from another DMC under an average-case and an exact model. We present several achievability and infeasibility results, with tight characterizations in special cases. In particular, for the exact model, we fully characterize when a binary symmetric channel can be simulated from a binary erasure channel when there is no shared randomness. We also provide infeasibility and achievability results for the simulation of a binary channel from another binary channel in the case of no shared randomness. To do this, we use the properties of Rényi capacity of a given order. We also introduce a notion of “channel diameter” which is shown to be additive and satisfy a data processing inequality. [ABSTRACT FROM PUBLISHER]

Current deterministic algorithms for the construction of polar codes can only be argued to be practical for channels with small input alphabet sizes. In this paper, we show that any construction algorithm for channels with moderate input alphabet size, which follows the paradigm of “degrading after each polarization step,” will inherently be impractical with respect to a certain “hard” underlying channel. This result also sheds light on why the construction of low-density parity-check codes using density evolution is impractical for channels with moderate-sized input alphabets. [ABSTRACT FROM PUBLISHER]

Transmissions across asynchronous communication channels are subject to delay injection attacks, which can cause an arbitrary number of skews. That is, such attacks can cause an arbitrary number of transmitted signals to arrive after the first signal of the next transmission has arrived. The (common) assumption that despite the delays, all signals from the $i$ th transmission arrive at the decoder before any signal from the (i+2){\text{nd}} transmission arrives is called a no switch assumption. This paper presents a self-synchronizing, zero-latency, zero-error coding scheme that requires no acknowledge and can decode transmissions distorted by an arbitrary number of skews that obey this no switch assumption. The rate associated with the coding scheme provides a lower bound of 0.6942 for the (zero-error) capacity of such a channel. It is further shown that zero-error channel capacity of the channel is upper bounded by 0.7248. Finally, this paper presents bounds on the (zero-error) capacity of a channel for which the number of transmissions that can mix with one another is large. [ABSTRACT FROM AUTHOR]