In two-sampling testing, one observes two independent sequences of independent and identically distributed random variables distributed according to the distributions $P_1$ and $P_2$ and wishes to decide whether $P_1=P_2$ (null hypothesis) or $P_1\neq P_2$ (alternative hypothesis). The Gutman test for this problem compares the empirical distributions of the observed sequences and decides on the null hypothesis if the Jensen-Shannon (JS) divergence between these empirical distributions is below a given threshold. This paper proposes a generalization of the Gutman test, termed \emph{divergence test}, which replaces the JS divergence by an arbitrary divergence. For this test, the exponential decay of the type-II error probability for a fixed type-I error probability is studied. First, it is shown that the divergence test achieves the optimal first-order exponent, irrespective of the choice of divergence. Second, it is demonstrated that divergence tests with invariant divergences achieve the same second-order asymptotics as the Gutman test. In addition, a connection between two-sample testing and robust goodness-of-fit testing is established.

Quantum hypothesis testing concerns the discrimination between quantum states. This paper introduces a novel lower bound for asymmetric quantum hypothesis testing that is based on the Nussbaum-Szkoła mapping. The lower bound provides a unified recovery of converse results across all major asymptotic regimes, including large-, moderate-, and small-deviations. Unlike existing bounds, which either rely on technically involved information-spectrum arguments or suffer from fixed prefactors and limited applicability in the non-asymptotic regime, the proposed bound arises from a single expression and enables, in some cases, the direct use of classical results. It is further demonstrated that the proposed bound provides accurate approximations to the optimal quantum error trade-off function at small blocklengths. Numerical comparisons with existing bounds, including those based on fidelity and information spectrum methods, highlight its improved tightness.

This paper investigates the maximum coding rate at which data can be transmitted over a noncoherent, multiple-input, multiple-output (MIMO) Rayleigh block-fading channel using an error-correcting code of a given blocklength with a block-error probability not exceeding a given value. A high-SNR normal approximation is derived that becomes accurate as the signal-to-noise ratio (SNR) and the number of coherence intervals over which we code tend to infinity. The obtained normal approximation complements the nonasymptotic bounds that have appeared in the literature, but whose evaluation is computationally demanding. It further lays the theoretical foundation for an analytical analysis of the fundamental tradeoff between diversity, multiplexing, and channel-estimation cost at finite blocklength and finite SNR.

This paper studies the capacity of massive random-access networks modeled as a multiple-input multiple-output fading channel with infinitely many interfering users. The network is assumed to operate in a noncoherent regime, where transmitters and receivers know the fading statistics but not their realizations. Users access the network via random activation with a given probability. To characterize the symmetric sum rate, a random-coding argument is invoked together with the assumption that users and interferers draw their codebooks according to the same distribution. For this channel model, rigorous upper and lower bounds on the network capacity are derived. The behavior of these bounds depends critically on the spatial decay of the large-scale fading statistics from interfering users. In particular, if the large-scale fading coefficients of the interferers (ordered according to their distance to the receiver) decay exponentially or more slowly, then the capacity is bounded in the transmit power. This occurs because the aggregate interference scales with the transmit power, and reveals an inherent saturation effect in interference-limited networks. Moreover, in this regime, random user activity cannot fundamentally eliminate the resulting capacity ceiling. In contrast, if the large-scale fading coefficients of the interferers decay faster than double-exponentially, then the capacity becomes unbounded in the transmit power. Note that proving an unbounded capacity is nontrivial even if the number of interfering users is finite, since the condition that the users’ codebooks follow the same distribution prevents interference-avoiding strategies such as time-, frequency-, or code-division multiple access, and cooperation among users associated with different access nodes is not allowed. An unbounded coding rate is achieved by using bursty signaling together with treating interference as noise.

Consider a composite hypothesis testing problem where the test has access to the null hypothesisPbut not to the alternative hypothesisQ. The generalized likelihood-ratio test (GLRT) for this problem is the Hoeffding test, which acceptsPif the Kullback-Leibler (KL) divergence between the empirical distribution ofZnandPis below some threshold. This paper proposes a generalization of the Hoeffding test, termed divergence test, for which the KL divergence is replaced by an arbitrary divergence. For this test, the first and second-order terms of the type-II error probability for a fixed type-I error probability are characterized and compared with the error terms of the Neyman-Pearson test, which is the optimal test when bothPandQare known. It is demonstrated that, irrespective of the divergence, divergence tests achieve the first-order term of the Neyman-Pearson test. In contrast, the second-order term of divergence tests is strictly worse than that of the Neyman-Pearson test. It is further demonstrated that divergence tests with an invariant divergence achieve the same second-order term as the Hoeffding test, but divergence tests with a non-invariant divergence may outperform the Hoeffding test for some alternative hypothesesQ. This implies that the GLRT may have a second-order asymptotic performance that is strictly suboptimal.

We consider a binary statistical hypothesis testing problem, where n independent and identically distributed random variables Znare either distributed according to the null hypothesis P or the alternate hypothesis Q, and only P is known. For this problem, a well-known test is the Hoeffding test, which accepts P if the Kullback-Leibler (KL) divergence between the empirical distribution of Znand P is below some threshold. In this paper, we consider Hoeffding-like tests, where the KL divergence is replaced by other divergences, and characterize, for a large class of divergences, the first and second-order terms of the type-II error for a fixed type-I error. Since the considered class includes the KL divergence, we obtain the second-order term of the Hoeffding test as a special case.

This paper considers a Gaussian multiple-access channel with random user activity where the total number of users$\ell _{n}$and the average number of active users$k_{n}$may grow with the blocklength$n$. For this channel, it studies the maximum number of bits that can be transmitted reliably per unit-energy as a function of$\ell _{n}$and$k_{n}$. When all users are active with probability one, i.e.,$\ell _{n} = k_{n}$, it is demonstrated that, if$k_{n}$is of an order strictly below$n/\log n$, then each user can achieve the single-user capacity per unit-energy$(\log e)/N_{0}$(where$N_{0}/ 2$is the noise power) by using an orthogonal-access scheme. In contrast, if$k_{n}$is of an order strictly above$n/\log n$, then the users cannot achieve any positive rate per unit-energy. Consequently, there is a sharp transition between orders of growth where interference-free communication is feasible and orders of growth where reliable communication at a positive rate per unit-energy is infeasible. It is further demonstrated that orthogonal-access schemes in combination with orthogonal codebooks, which achieve the capacity per unit-energy when the number of users is bounded, can be strictly suboptimal. When the user activity is random, i.e., when$\ell _{n}$and$k_{n}$are different, it is demonstrated that, if$k_{n}\log \ell _{n}$is sublinear in$n$, then each user can achieve the single-user capacity per unit-energy$(\log e)/N_{0}$. Conversely, if$k_{n}\log \ell _{n}$is superlinear in$n$, then the users cannot achieve any positive rate per unit-energy. Consequently, there is again a sharp transition between orders of growth where interference-free communication is feasible and orders of growth where reliable communication at a positive rate is infeasible that depends on the asymptotic behaviors of both$\ell _{n}$and$k_{n}$. It is further demonstrated that orthogonal-access schemes, which are optimal when all users are active with probability one, can be strictly suboptimal in general.

This paper concerns the maximum coding rate at which a code of given blocklength can be transmitted with a given block-error probability over a non-coherent Rayleigh block-fading channel with multiple transmit and receive antennas (MIMO). In particular, a high-SNR normal approximation of the maximum coding rate is presented, which is proved to become accurate as the signal-to-noise ratio (SNR) and the number of coherence intervals L tend to infinity.

We consider a Gaussian multiple-access channel with random user activity where the total number of users ℓnand the average number of active users knmay be unbounded. For this channel, we characterize the maximum number of bits that can be transmitted reliably per unit-energy in terms of ℓnand kn. We show that if knlog ℓnis sublinear in n, then each user can achieve the single-user capacity per unit-energy. Conversely, if knlog ℓnis superlinear in n, then the capacity per unit-energy is zero. We further demonstrate that orthogonal-access schemes, which are optimal when all users are active with probability one, can be strictly suboptimal.

This article concerns the maximum coding rate at which data can be transmitted over a noncoherent, single-antenna, Rayleigh block-fading channel using an error-correcting code of a given blocklength with a block-error probability not exceeding a given value. A high-SNR normal approximation of the maximum coding rate is presented that becomes accurate as the signal-to-noise ratio (SNR) and the number of coherence intervals L over which we code tend to infinity. Numerical analyses suggest that the approximation is accurate at SNR values above 15dB and when the number of coherence intervals is 10 or more.

In recent years, the derivation of nonasymptotic converse and achievability bounds on the maximum coding rate as a function of the error probability and blocklength has gained attention in the information theory literature. While these bounds are accurate for many scenarios of interest, they need to be evaluated numerically for most wireless channels of practical interest, and their evaluation is computationally demanding. This paper presents saddlepoint approximations of state-of-the-art converse and achievability bounds for noncoherent, single-antenna, Rayleigh block-fading channels. These approximations can be calculated efficiently and are shown to be accurate for SNR values as small as 0 dB and blocklengths of 168 channel uses or more.

This paper presents saddlepoint approximations of state-of-the-art converse and achievability bounds for noncoherent, single-antenna, Rayleigh block-fading channels. These approximations can be calculated efficiently and are shown to be accurate for SNR values as small as 0 dB, blocklengths of 168 channel uses or more, and when the channel's coherence interval is not smaller than two. It is demonstrated that the derived approximations recover both the normal approximation and the reliability function of the channel.

We consider a Gaussian multiple-access channel where the number of transmitters grows with the blocklength n. For this setup, the maximum number of bits that can be transmitted reliably per unit-energy is analyzed. We show that if the number of users is of an order strictly above n/log n, then the users cannot achieve any positive rate per unit-energy. In contrast, if the number of users is of order strictly below n/log n, then each user can achieve the single-user capacity per unit-energy (log e)/N0(where N0/2 is the noise power) by using an orthogonal access scheme such as time division multiple access. We further demonstrate that orthogonal codebooks, which achieve the capacity per unit-energy when the number of users is bounded, can be strictly suboptimal.

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

In this paper, we analyze the tradeoff between coding rate and asymptotic performance of a class of generalized low-density parity-check (GLDPC) codes constructed by including a certain fraction of generalized constraint (GC) nodes in the graph. The rate of the GLDPC ensemble is bounded using classical results on linear block codes, namely, Hamming bound and Varshamov bound. We also study the impact of the decoding method used at GC nodes. To incorporate both bounded-distance (BD) and maximum likelihood (ML) decoding at GC nodes into our analysis without resorting on multi-edge type of degree distributions (DDs), we propose the probabilistic peeling decoding (P-PD) algorithm, which models the decoding step at every GC node as an instance of a Bernoulli random variable with a successful decoding probability that depends on both the GC block code and its decoding algorithm. The P-PD asymptotic performance over the BEC can be efficiently predicted using standard techniques for LDPC codes such as density evolution (DE) or the differential equation method. Furthermore, for a class of GLDPC ensembles, we demonstrate that the simulated P-PD performance accurately predicts the actual performance of the GLPDC code under ML decoding at GC nodes. We illustrate our analysis for GLDPC code ensembles with regular and irregular DDs. In all cases, we show that a large fraction of GC nodes is required to reduce the original gap to capacity, but the optimal fraction is strictly smaller than one. We then consider techniques to further reduce the gap to capacity by means of random puncturing, and the inclusion of a certain fraction of generalized variable nodes in the graph.

The capacity-achieving input distribution of the complex Gaussian channel with both average- and peak-power constraint is known to have a discrete amplitude and a continuous, uniformly-distributed, phase. Practical considerations, however, render the continuous phase inapplicable. This work studies the backoff from capacity induced by discretizing the phase of the input signal. A sufficient condition on the total number of quantization points that guarantees an arbitrarily small backoff is derived, and constellations that attain this guaranteed performance are proposed.

We propose a saddlepoint approximation of the error probability of a binary hypothesis test between two i.i.d. distributions. The approximation is accurate, simple to compute, and yields a unified analysis in different asymptotic regimes. The proposed formulation is used to efficiently compute the meta-converse lower bound for moderate block-lengths in several cases of interest.

The nonnegativity of relative entropy implies that the differential entropy of a random vector X with probability density function (pdf) f is upper bounded by -E[log g(X)] for any arbitrary pdf g. Using this inequality with a cleverly chosen g, we derive a lower bound on the asymptotic excess rate of entropy-constrained vector quantization for d-dimensional sources and rth-power distortion, where the asymptotic excess rate is defined as the difference between the smallest output entropy of a vector quantizer satisfying the distortion constraint and the rate-distortion function in the limit as the distortion tends to zero. Specialized to the one-dimensional case, this lower bound coincides with the asymptotic excess rate achieved by a uniform quantizer, thereby recovering the result by Gish and Pierce that uniform quantizers are asymptotically optimal as the allowed distortion tends to zero. Furthermore, in the one-dimensional case, the derivation of the lower bound reveals a necessary condition for a sequence of quantizers to be asymptotically optimal. This condition implies that any sequence of asymptotically optimal almost-regular quantizers must converge to a uniform quantizer as the distortion tends to zero. While the obtained lower bound itself is not novel, to the best of our knowledge, we present the first rigorous derivation that follows the direct approach by Gish and Pierce without resorting to heuristic high-resolution approximations commonly found in the quantization literature. Furthermore, our derivation holds for all d-dimensional sources having finite differential entropy and whose integer part has finite entropy. In contrast to Gish and Pierce, we do not require additional constraints on the continuity or decay of the source pdf.

Jalali and Poor (“Universal compressed sensing,” arXiv:1406.7807v3, Jan. 2016) have recently proposed a generalization of Rényi's information dimension to stationary stochastic processes by defining the information dimension of the stochastic process as the information dimension of k samples divided by k in the limit as k →∞ to. This paper proposes an alternative definition of information dimension as the entropy rate of the uniformly-quantized stochastic process divided by minus the logarithm of the quantizer step size 1/m in the limit as m →∞ to. It is demonstrated that both definitions are equivalent for stochastic processes that are ψ*-mixing, but that they may differ in general. In particular, it is shown that for Gaussian processes with essentially-bounded power spectral density (PSD), the proposed information dimension equals the Lebesgue measure of the PSD's support. This is in stark contrast to the information dimension proposed by Jalali and Poor, which is 1 if the process's PSD is positive on a set of positive Lebesgue measure, irrespective of its support size.

This paper concerns the maximal achievable rate at which data can be transmitted over a non-coherent, single-antenna, Rayleigh block-fading channel using an error-correcting code of a given blocklength with a block-error probability not exceeding a given value. In particular, a high-SNR normal approximation of the maximal achievable rate is presented that becomes accurate as the signal-to-noise ratio (SNR) and the number of coherence intervals L over which we code tend to infinity. Numerical analyses suggest that the approximation is accurate already at SNR values of 15 dB.

In this paper, we analyze the tradeoff between coding rate and asymptotic performance of a class of generalized low-density parity-check (GLDPC) codes constructed by including a certain fraction of generalized constraint (GC) nodes in the graph. The rate of the GLDPC ensemble is bounded using classical results on linear block codes, namely Hamming bound and Varshamov bound. We also study the impact of the decoding method used at GC nodes. To incorporate both bounded-distance (BD) and Maximum Likelihood (ML) decoding at GC nodes into our analysis without having to resort on multi-edge type of degree distributions (DDs), we propose the probabilistic peeling decoder (P-PD) algorithm, which models the decoding step at every GC node as an instance of a Bernoulli random variable with a success probability that depends on the GC block code and its decoding algorithm. The P-PD asymptotic performance over the BEC can be efficiently predicted using standard techniques for LDPC codes such as density evolution (DE) or the differential equation method. Furthermore, for a class of GLDPC ensembles, we demonstrate that the simulated P-PD performance accurately predicts the actual performance of the GLPDC code. We illustrate our analysis for GLDPC code ensembles using (2, 6) and (2,15) base DDs. In all cases, we show that a large fraction of GC nodes is required to reduce the original gap to capacity.

We derive a lower bound on the smallest output entropy that can be achieved via scalar quantization of a source with given expected quadratic distortion. As the allowed distortion tends to zero, the bound converges to the output entropy achieved by a uniform quantizer, thereby recovering the result by Gish and Pierce that uniform quantizers are asymptotically optimal. The proposed derivation applies for any memoryless source that has a probability density function (pdf), a finite differential entropy, and whose integer part has a finite entropy. In contrast to Gish and Pierce, we do not require any additional constraints on the continuity or decay of the source pdf.

The channel capacity of wireless networks is often studied under the assumption that the communicating nodes have perfect channel-state information (CSI) in the sense that they have access to the fading coefficients in the network. To the best of our knowledge, one of the few works that studies wireless networks without this assumption is by Lozano, Heath, and Andrews. Inter alia, Lozano et al. show that in the absence of perfect CSI, and if the channel inputs are given by the square-root of the transmit power times a power-independent random variable, then the achievable information rate is bounded in the signal-to-noise ratio (SNR). However, such inputs do not necessarily achieve capacity, so one may argue that the information rate is bounded in the SNR because of the suboptimal input distribution. In this paper, it is demonstrated that if the nodes do not cooperate and they all use the same codebook, then the achievable information rate remains bounded in the SNR even if the input distribution is allowed to change arbitrarily with the transmit power.

Most of the recent advances in the design of high-speed wireless systems are based on information-theoretic principles that demonstrate how to efficiently transmit long data packets. However, the upcoming wireless systems, notably the fifth-generation (5G) system, will need to support novel traffic types that use short packets. For example, short packets represent the most common form of traffic generated by sensors and other devices involved in machine-to-machine (M2M) communications. Furthermore, there are emerging applications in which small packets are expected to carry critical information that should be received with low latency and ultrahigh reliability. Current wireless systems are not designed to support short-packet transmissions. For example, the design of current systems relies on the assumption that the metadata (control information) is of negligible size compared to the actual information payload. Hence, transmitting metadata using heuristic methods does not affect the overall system performance. However, when the packets are short, metadata may be of the same size as the payload, and the conventional methods to transmit it may be highly suboptimal. In this paper, we review recent advances in information theory, which provide the theoretical principles that govern the transmission of short packets. We then apply these principles to three exemplary scenarios (the two-way channel, the downlink broadcast channel, and the uplink random access channel), thereby illustrating how the transmission of control information can be optimized when the packets are short. The insights brought by these examples suggest that new principles are needed for the design of wireless protocols supporting short packets. These principles will have a direct impact on the system design.

Motivated by the current interest in ultra-reliable, low-latency, machine-type communication systems, we investigate the tradeoff between reliability, throughput, and latency in the transmission of information over multiple-antenna Rayleigh block-fading channels. Specifically, we obtain finite-blocklength, finite-SNR upper and lower bounds on the maximum coding rate achievable over such channels for a given constraint on the packet error probability. Numerical evidence suggests that our bounds delimit tightly the maximum coding rate already for short blocklengths (packets of about 100 symbols). Furthermore, our bounds reveal the existence of a tradeoff between the rate gain obtainable by spreading each codeword over all available time-frequency-spatial degrees of freedom, and the rate loss caused by the need of estimating the fading coefficients over these degrees of freedom. In particular, our bounds allow us to determine the optimal number of transmit antennas and the optimal number of time-frequency diversity branches that maximize the rate. Finally, we show that infinite-blocklength performance metrics such as the ergodic capacity and the outage capacity yield inaccurate throughput estimates.

The Shannon lower bound is one of the few lower bounds on the rate-distortion function that holds for a large class of sources. In this paper, which considers exclusively norm-based difference distortion measures, it is demonstrated that its gap to the rate-distortion function vanishes as the allowed distortion tends to zero for all sources having finite differential entropy and whose integer part has finite entropy. Conversely, it is demonstrated that if the integer part of the source has infinite entropy, then its rate-distortion function is infinite for every finite distortion level. Thus, the Shannon lower bound provides an asymptotically tight bound on the rate-distortion function if, and only if, the integer part of the source has finite entropy.

We study the capacity of the peak-and-average-power-limited Gaussian channel when its output is quantized using a dithered, infinite-level, uniform quantizer of step size Δ. We focus on the low signal-to-noise-ratio (SNR) regime, where communication at low spectral efficiencies takes place. We show that, when the peak-power constraint is absent, the low-SNR asymptotic capacity is equal to that of the unquantized channel irrespective of Δ. We further derive an expression for the low-SNR asymptotic capacity for finite peak-to-average-power ratios and evaluate it in the low- and high-resolution limit. We demonstrate that, in this case, the low-SNR asymptotic capacity converges to that of the unquantized channel when Δ tends to zero, and it tends to zero when Δ tends to infinity.

This paper analyzes the channel dispersion of quasi-static multiple-input multiple-output fading channels with no channel state information at the transmitter. We show that the channel dispersion is zero under mild conditions on the fading distribution. The proof of our result is based on Stokes' theorem, which deals with the integration of differential forms on manifolds with boundary.

Asymptotic expressions of the mutual information between any discrete input and the corresponding output of the scalar additive white Gaussian noise channel are presented in the limit as the signal-to-noise ratio (SNR) tends to infinity. Asymptotic expressions of the symbol-error probability (SEP) and the minimum mean-square error (MMSE) achieved by estimating the channel input given the channel output are also developed. It is shown that for any input distribution, the conditional entropy of the channel input given the output, MMSE, and SEP have an asymptotic behavior proportional to the Gaussian Q-function. The argument of the Q-function depends only on the minimum Euclidean distance (MED) of the constellation and the SNR, and the proportionality constants are functions of the MED and the probabilities of the pairs of constellation points at MED. The developed expressions are then generalized to study the high-SNR behavior of the generalized mutual information (GMI) for bit-interleaved coded modulation (BICM). By means of these asymptotic expressions, the long-standing conjecture that Gray codes are the binary labelings that maximize the BICM-GMI at high SNR is proven. It is further shown that for any equally spaced constellation whose size is a power of two, there always exists an anti-Gray code giving the lowest BICM-GMI at high SNR.

This paper studies the random-coding exponent of joint source-channel coding for a scheme where source messages are assigned to disjoint subsets (referred to as classes), and codewords are independently generated according to a distribution that depends on the class index of the source message. For discrete memoryless systems, two optimally chosen classes and product distributions are found to be sufficient to attain the sphere-packing exponent in those cases where it is tight.

As shown by Médard, the capacity of fading channels with imperfect channel-state information can be lower-bounded by assuming a Gaussian channel input X with power P and by upper-bounding the conditional entropy h(X|Y, Ĥ) by the entropy of a Gaussian random variable with variance equal to the linear minimum mean-square error in estimating X from (Y, Ĥ). We demonstrate that, using a rate-splitting approach, this lower bound can be sharpened: by expressing the Gaussian input X as the sum of two independent Gaussian variables X1and X2and by applying Médard's lower bound first to bound the mutual information between X1and Y while treating X2as noise, and by applying it a second time to the mutual information between X2and Y while assuming X1to be known, we obtain a capacity lower bound that is strictly larger than Médard's lower bound. We then generalize this approach to an arbitrary number L of layers, where X is expressed as the sum of L independent Gaussian random variables of respective variances Pℓ, ℓ = 1, ... , L summing up to P. Among all such rate-splitting bounds, we determine the supremum over power allocations Pℓand total number of layers L. This supremum is achieved for L →∞ and gives rise to an analytically expressible capacity lower bound. For Gaussian fading, this novel bound is shown to converge to the Gaussian-input mutual information as the signal-to-noise ratio (SNR) grows, provided that the variance of the channel estimation error H - Ĥ tends to zero as the SNR tends to infinity.

This paper investigates the maximal achievable rate for a given blocklength and error probability over quasi-static multiple-input multiple-output fading channels, with and without channel state information at the transmitter and/or the receiver. The principal finding is that outage capacity, despite being an asymptotic quantity, is a sharp proxy for the finite-blocklength fundamental limits of slow-fading channels. Specifically, the channel dispersion is shown to be zero regardless of whether the fading realizations are available at both transmitter and receiver, at only one of them, or at neither of them. These results follow from analytically tractable converse and achievability bounds. Numerical evaluation of these bounds verifies that zero dispersion may indeed imply fast convergence to the outage capacity as the blocklength increases. In the example of a particular 1 × 2 single-input multiple-output Rician fading channel, the blocklength required to achieve 90% of capacity is about an order of magnitude smaller compared with the blocklength required for an AWGN channel with the same capacity. For this specific scenario, the coding/decoding schemes adopted in the LTE-Advanced standard are benchmarked against the finite-blocklength achievability and converse bounds.

We consider a multiple-input multiple-output (MIMO) AWGN channel affected by phase noise. Focusing on the 2 × 2 case, we show that no MIMO multiplexing gain is to be expected when the phase-noise processes at each antenna are independent, memoryless in time, and with uniform marginal distribution over [0, 2π] (strong phase noise), and when the transmit signal is isotropically distributed on the real plane. The scenario of independent phase-noise processes across antennas is relevant for microwave backhaul links operating in the 20-40 GHz range.

The asymptotic behavior of the mutual information (MI) at high signal-to-noise ratio (SNR) for discrete constellations over the scalar additive white Gaussian noise channel is studied. Exact asymptotic expressions for the MI for arbitrary one-dimensional constellations and input distributions are presented in the limit as the SNR tends to infinity. Asymptotics of the minimum mean-square error (MMSE) are also developed. It is shown that for any input distribution, the MI and the MMSE have an asymptotic behavior proportional to a Gaussian Q-function, whose argument depends on the minimum Euclidean distance of the constellation and the SNR. Closed-form expressions for the coefficients of these Q-functions are calculated.

We investigate the maximal achievable rate for a given blocklength and error probability over quasi-static single-input multiple-output (SIMO) fading channels. Under mild conditions on the channel gains, it is shown that the channel dispersion is zero regardless of whether the fading realizations are available at the transmitter and/or the receiver. The result follows from computationally and analytically tractable converse and achievability bounds. Through numerical evaluation, we verify that, in some scenarios, zero dispersion indeed entails fast convergence to outage capacity as the blocklength increases. In the example of a particular 1×2 SIMO Rician channel, the blocklength required to achieve 90% of capacity is about an order of magnitude smaller compared to the blocklength required for an AWGN channel with the same capacity.

The capacity of noncoherent regular-fading relay channels is studied where all terminals are aware of the fading statistics but not of their realizations. It is shown that if the fading coefficient of the channel between the transmitter and the receiver can be predicted more accurately from its infinite past than the fading coefficient of the channel between the relay and the receiver, then at high signal-to-noise ratio (SNR), the relay does not increase capacity. It is further shown that if the fading coefficient of the channel between the transmitter and the relay can be predicted more accurately from its infinite past than the fading coefficient of the channel between the relay and the receiver, then at high SNR, one can achieve communication rates that are within one bit of the capacity of the multiple-input single-output fading channel that results when the transmitter and the relay can cooperate.

We study the capacity of the discrete-time Gaussian channel when its output is quantized with a 1-bit quantizer. We focus on the low signal-to-noise ratio (SNR) regime, where communication at very low spectral efficiencies takes place. In this regime, a symmetric threshold quantizer is known to reduce channel capacity by a factor of 2/π, i.e., to cause an asymptotic power loss of approximately 2 dB. Here, it is shown that this power loss can be avoided by using asymmetric threshold quantizers and asymmetric signaling constellations. To avoid this power loss, flash-signaling input distributions are essential. Consequently, 1-bit output quantization of the Gaussian channel reduces spectral efficiency. Threshold quantizers are not only asymptotically optimal: at every fixed SNR, a threshold quantizer maximizes capacity among all 1-bit output quantizers. The picture changes on the Rayleigh-fading channel. In the noncoherent case, a 1-bit output quantizer causes an unavoidable low-SNR asymptotic power loss. In the coherent case, however, this power loss is avoidable provided that we allow the quantizer to depend on the fading level.

We derive a random-coding upper bound on the average probability of error of joint source-channel coding that recovers Csiszár's error exponent when used with product distributions over the channel inputs. Our proof technique for the error probability analysis employs a code construction for which source messages are assigned to subsets and codewords are generated with a distribution that depends on the subset.

We determine the loss in capacity incurred by using signal constellations with a bounded support over general complex-valued additive-noise channels for suitably high signal-to-noise ratio. Our expression for the capacity loss recovers the power loss of 1.53dB for square signal constellations.

We study the maximal achievable rate R*(n, ∈) for a given block-length n and block error probability o over Rayleigh block-fading channels in the noncoherent setting and in the finite block-length regime. Our results show that for a given block-length and error probability, R*(n, ∈) is not monotonic in the channel's coherence time, but there exists a rate maximizing coherence time that optimally trades between diversity and cost of estimating the channel.

We study the information rates of non-coherent, stationary, Gaussian, multiple-input multiple-output (MIMO) flat-fading channels that are achievable with nearest neighbour decoding and pilot-aided channel estimation. In particular, we analyse the behaviour of these achievable rates in the limit as the signal-to-noise ratio (SNR) tends to infinity. We demonstrate that nearest neighbour decoding and pilot-aided channel estimation achieves the capacity pre-log-which is defined as the limiting ratio of the capacity to the logarithm of SNR as the SNR tends to infinity-of non-coherent multiple-input single-output (MISO) flat-fading channels, and it achieves the best so far known lower bound on the capacity pre-log of non-coherent MIMO flat-fading channels.

We study the behavior of channel capacity when a one-bit quantizer is employed at the output of the discrete-time average-power-limited Gaussian channel. We focus on the low signal-to-noise ratio regime, where communication at very low spectral efficiencies takes place, as in Spread-Spectrum and Ultra-Wideband communications. It is well known that, in this regime, a symmetric one-bit quantizer reduces capacity by 2/π, which translates to a power loss of approximately two decibels. Here we show that if an asymmetric one-bit quantizer is employed, and if asymmetric signal constellations are used, then these two decibels can be recovered in full.

The capacity of peak-power limited, single-antenna, noncoherent, flat-fading channels with memory is considered. The emphasis is on the capacity pre-log, i.e., on the limiting ratio of channel capacity to the logarithm of the signal-to-noise ratio (SNR), as the SNR tends to infinity. It is shown that, among all stationary and ergodic fading processes of a given spectral distribution function and whose law has no mass point at zero, the Gaussian process gives rise to the smallest pre-log. The assumption that the law of the fading process has no mass point at zero is essential in the sense that there exist stationary and ergodic fading processes whose law has a mass point at zero and that give rise to a smaller pre-log than the Gaussian process of equal spectral distribution function. An extension of these results to multiple-input single-output (MISO) fading channels with memory is also presented.

A noncoherent multipath fading channel is considered, where neither the transmitter nor the receiver is cognizant of the realization of the path gains, but both are cognizant of their statistics. It is shown that if the delay spread is large in the sense that the variances of the path gains decay exponentially or slower, then capacity is bounded in the signal-to-noise ratio (SNR). For such channels, capacity does not tend to infinity as the SNR tends to infinity. In contrast, if the variances of the path gains decay faster than exponentially, then capacity is unbounded in the SNR. It is further demonstrated that if the number of paths is finite, then at high SNR capacity grows double-logarithmically with the SNR, and the capacity pre-loglog-defined as the limiting ratio of capacity to loglog(SNR) as the SNR tends to infinity-is 1 irrespective of the number of paths. The results demonstrate that at high SNR multipath fading channels with an infinite number of paths cannot be approximated by multipath fading channels with only a finite number of paths. The number of paths that are needed to approximate a multipath fading channel typically depends on the SNR and may grow to infinity as the SNR tends to infinity.

This paper considers an additive noise channel where the time-A; noise variance is a weighted sum of the squared magnitudes of the previous channel inputs plus a constant. This channel model accounts for the dependence of the intrinsic thermal noise on the data due to the heat dissipation associated with the transmission of data in electronic circuits: the data determine the transmitted signal, which in turn heats up the circuit and thus influences the power of the thermal noise. The capacity of this channel (both with and without feedback) is studied at low transmit powers and at high transmit powers. At low transmit powers, the slope of the capacity-versus-power curve at zero is computed and it is shown that the heating-up effect is beneficial. At high transmit powers, conditions are determined under which the capacity is bounded, i.e., under which the capacity does not grow to infinity as the allowed average power tends to infinity.

This paper studies the capacity of discrete-time multipath fading channels. It is assumed that the number of paths is finite, i.e., that the channel output is influenced by the present and by the L previous channel inputs. A noncoherent channel model is considered where neither transmitter nor receiver are cognizant of the fading's realization, but both are aware of its statistic. The focus is on capacity at high signal-to-noise ratios (SNR). In particular, the capacity pre-loglog-defined as the limiting ratio of the capacity to loglog(SNR) as SNR tends to infinity-is studied. It is shown that, irrespective of the number of paths L, the capacity pre-loglog is 1.

The capacity of discrete-time, non-coherent, multi-path fading channels is considered. It is shown that if the delay spread is large in the sense that the variances of the path gains do not decay faster than geometrically, then capacity is bounded in the signal-to-noise ratio.

Motivated by on-chip communication, a channel model is proposed where the variance of the additive noise depends on the weighted sum of the past channel input powers. For this channel, an expression for the capacity per unit cost is derived, and it is shown that the expression holds also in the presence of feedback.

The capacity of pear-power limited, single-antenna, non-coherent, flat-fading channels with memory is considered. The emphasis is on the capacity pre-log, i.e., on the limiting ratio of channel capacity to the logarithm of the signal-to-noise ratio (SNR), as the SNR tends to infinity. It is shown that, among all stationary and ergodic fading processes of given spectral distribution function whose law has no mass point at zero, the Gaussian process gives rise to the smallest pre-log

It has been observed that a linear-feedback shift-register (LFSR) sequence can be synchronized by feeding the modulated sequence into a "soft" (or "analog") version of the LFSR. In this correspondence, the "soft LFSR" is derived as forward-only message passing in the corresponding factor graph. A continous-time analog (suitable for realization as a clockless electronic circuit) is then given of both the LFSR and the soft LFSR. A connection is thus established between statistical state estimation and the phenomenon of entrainment of dynamical systems, which opens the prospect of deriving dynamical systems (such as electronic circuits) with strong entrainment capabilities from more powerful message passing algorithms

The capacity of additive white Gaussian noise relay channels under Gaussian fading is investigated. The transmitter, the relay, and the receiver are all considered to be ignorant of the fading realizations. Capacity upper and lower bounds are derived with focus on the capacity pre-log, i.e., the limiting ratio of the capacity to the logarithm of the signal-to-noise ratio. Conditions are presented under which the upper and lower bounds on the capacity pre-log coincide

New non-asymptotic upper bounds on the capacity of non-coherent multiple-input multiple-output (MIMO) Gaussian fading channels with memory are proposed. These upper bounds are used to derive upper bounds on the fading number of regular Gaussian fading channels and on the pre-log of nonregular ones. The resulting bounds are tight in the multiple-input single-output (MISO) spatially independent Gaussian case when the entries in the fading vector are either zero-mean or possess the same spectral distribution function. A new approach is proposed for the derivation of lower bounds on the fading number of MIMO channels. This approach is applied to derive a lower bound on the fading number of spatially IID zero-mean Gaussian fading channels. The new upper and lower bounds on the fading number demonstrate that when the number of receive antennas does not exceed the number of transmit antennas, the fading number of zero-mean spatially IID slowly varying Gaussian MIMO channels is proportional to the number of degrees of freedom, i.e., to the minimum of the number of transmit and receive antennas. We conjecture that the same is true also when the number of receive antennas exceeds the number of transmit antennas. The single-input multiple-output case that was recently solved by Lapidoth & Moser supports this conjecture