Variable-Length Coding with Cost Allowing Non-Vanishing Error Probability

Regular cost functions have been introduced recently as an extension to the notion of regular languages with counting capabilities. The specificity of cost functions is that exact values are not considered, but only estimated. In this paper, we study the strict subclass of regular temporal cost functions. In such cost functions, it is only allowed to count the number of occurrences of consecutive events. For this reason, this model intends to measure the length of intervals, i.e., a discrete notion of time. We provide various equivalent representations for functions in this class, using automata, and 'clock based' reduction to regular languages. We show that the conversions are much simpler to obtain, and much more efficient than in the general case of regular cost functions. Our second aim in this paper is to use temporal cost function as a test-case for exploring the algebraic nature of regular cost functions. Following the seminal ideas of Schutzenberger, this results in a decidable algebraic characterization of regular temporal cost functions inside the class of regular cost functions.

The variable-length source coding problem allowing the error probability up to some constant is considered for general sources. In this problem, the optimum mean codeword length of variable-length codes has already been determined. On the other hand, in this paper, we focus on the overflow (or excess codeword length) probability instead of the mean codeword length. The infimum of overflow thresholds under the constraint that both of the error probability and the overflow probability are smaller than or equal to some constant is called the optimum overflow threshold. In this paper, we first derive finite-length upper and lower bounds on these probabilities so as to analyze the optimum overflow thresholds. Then, by using these bounds, we determine the general formula of the optimum overflow thresholds in both of the first-order and second-order forms. Next, we consider another expression of the derived general formula so as to reveal the relationship with the optimum coding rate in the fixed-length source coding problem. Finally, we apply the general formula derived in this paper to the case of stationary memoryless sources.

A setup involving zero-delay sequential transmission of a vector Markov source over a burst erasure channel is studied. A sequence of source vectors is compressed in a causal fashion at the encoder, and the resulting output is transmitted over a burst erasure channel. The destination is required to reconstruct each source vector with zero-delay, but those source sequences that are observed either during the burst erasure, or in the interval of length W following the burst erasure need not be reconstructed. The minimum achievable compression rate is called the rate-recovery function. We assume that each source vector is independent identically distributed (i.i.d.) across the spatial dimension and is sampled from a stationary, first-order Markov process across the temporal dimension. For discrete sources, the case of lossless recovery is considered, and upper and lower bounds on the rate-recovery function are established. Both these bounds can be expressed as the rate for predictive coding, plus a term that decreases at least inversely with the recovery window length W. For Gauss-Markov sources and a quadratic distortion measure, upper and lower bounds on the minimum rate are established when W = 0. These bounds are shown to coincide in the high resolution limit. Finally, another setup involving i.i.d. Gaussian sources is studied and the raterecovery function is completely characterized in this case.

We address the optimization of joint source-channel coding schemes for iterative source-channel decoding (ISCD) of first-order Markov sources. The optimization requires source encoders, providing code words with a minimum Hamming distance dmin ges 2. Usually, specifically designed variable- length codes (VLCs) are applied for this purpose, leading, however, to an increased complexity of the decoder. In this paper, we propose a novel concept: a single parity-check code is employed for mapping the quantized source symbols to a binary representation. The additional redundancy introduced by this mapping is afterwards compensated by an inner channel code with rate R > 1. Simulation results for the AWGN channel show that the proposed scheme is superior to VLC- based approaches, while leading to a significantly reduced complexity at the same time.

This paper considers a relay-assisted massive multiple-input multiple-output (MIMO) downlink system in which a base station (BS) communicates with all terminals via a relay node enabled simultaneous wireless information and power transfer (SWIPT). Both time-switching (TS) and energy-splitting (PS) protocols are respectively considered at the relay node for coordinating energy harvesting and information decoding. The quality-of-service (QoS) fairness problem among terminals is investigated in the considered systems. In detail, the power allocation coefficients and energy harvesting time duration for TS based SWIPT, and the power allocation coefficients and PS ratio for PS based SWIPT are jointly optimised, aiming at seeking to maximise the minimum achievable rate over all terminals. As the formulated problems are non-convex and non-linear, and hard to solve directly, suboptimal heuristic algorithms are proposed for solving them. Additionally, the convergence and complexity of the proposed algorithms are also analysed. Finally, the performance of the proposed algorithms is demonstrated by extensive computer simulations. Results manifest that the proposed algorithms can provide uniformly great QoS for every terminal by resource allocation.

This paper deals with a parallel machine scheduling problem whose objective is to minimize a regular step total cost function. A real world application of the problem is presented, and Mixed Integer Linear Programming models are described for the cases with and without release dates, as well as a dedicated constraint generation procedure. Experimental results are reported and discussed to evaluate the relevance of the different approaches on well-known special cases and the general case.

We characterize the fundamental limits of transmission of information over a Gaussian multiple access channel (MAC) with the use of variable-length feedback codes and under a non-vanishing error probability formalism. We develop new achievability and converse techniques to handle the continuous nature of the channel and the presence of expected power constraints. We establish the $\varepsilon $ -capacity regions and bounds on the second-order asymptotics of the Gaussian MAC with variable-length feedback with termination codes and stop-feedback codes. We show that the former outperforms the latter significantly. Due to the multi-terminal nature of the channel model, we leverage tools from renewal theory developed by Lai and Siegmund to bound the asymptotic behavior of the maximum of a finite number of stopping times.

Reconfigurable surfaces (RS) have recently emerged as an enabler for smart radio environments where they are used to actively tailor/control the radio propagation (e.g., to support users under adverse channel conditions). If multiple RSs are deployed (e.g., coated on various buildings) to support different groups of users, it is critical to jointly optimize the phase-shifts of all the RSs to mitigate interference amongst them as well as to leverage the secondary reflections amongst them. Motivated by these considerations, this paper considers the uplink transmissions of multiple users that are grouped and supported by multiple RSs to communicate with a multi-antenna base station (BS). We first formulate two optimization problems: the weighted sum-rate maximization and the minimum achievable rate (from all users) maximization. Unlike existing works that considered single user or single RS or multiple RSs without inter-RS reflections, the considered problems require the joint optimization of the phase-shifts of all RS elements and all beamformers at the multi-antenna BS. The two problems turn out to be non-convex and thus are difficult to be solved in general. Moreover, the inter-RS reflections give rise to the coupling of the phase-shifts amongst the RSs, making the optimization problems even more challenging to solve. To tackle them, we design alternating optimization algorithms that provably converge to locally optimal solutions. Simulation results reveal that by effectively mitigating interference and leveraging the secondary reflections amongst the RSs, there is a great benefit of deploying more RSs to support different groups of users so as to achieve a higher rate per user. This gain is even more significant with a larger number of elements per RS. Without properly dealing with the secondary reflections, by contrast, increasing the number of RSs can adversely impact the network throughput, especially for high transmit power.

This work studies the problem of designing computer-generated holograms using phase-shifting masks limited to represent only a small number of discrete phase levels. This problem has various applications, notably in the emerging field of optogenetics and lithography. A novel regularized cost function is proposed for the problem at hand that penalizes the unfeasible phase levels. Since the proposed cost function is non-smooth, we derive proper proximal gradient algorithms for its minimization. Simulation results, considering an optogenetics application, demonstrate that the proposed proximal gradient algorithm yields better performance as compared to other algorithms proposed in the literature.

We revisit the Wyner-Ahlswede-Körner network, focusing especially on the converse part of the dispersion analysis, which is known to be challenging. Using the functional-entropic duality and the reverse hypercontractivity of the transposition semigroup, we lower bound the error probability for each joint type. Then by averaging the error probability over types, we lower bound the c-dispersion (which characterizes the second-order behavior of the weighted sum of the rates of the two compressors when a nonvanishing error probability is small) as the variance of the gradient of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\inf _{ {P}_{ {U}| {X}}}\{{ { cH}}( {Y}| {U})+ {I}( {U}; {X})\}$ </tex-math></inline-formula> with respect to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$ {Q}_{{{ XY}}}$ </tex-math></inline-formula> , the per-letter side information and source distribution. In comparison, using standard achievability arguments based on the method of types, we upper-bound the c-dispersion as the variance of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$ {c}\imath _{ {Y}| {U}}( {Y}| {U})+\imath _{ {U}; {X}}( {U}; {X})$ </tex-math></inline-formula> , which improves the existing upper bounds but has a gap to the aforementioned lower bound. Our converse analysis should be immediately extendable to other distributed source-type problems, such as distributed source coding, common randomness generation, and hypothesis testing with communication constraints. We further present improved bounds for the general image-size problem via our semigroup technique.

Due to its high speed and low latency, D2D communication plays an important role in providing proximity data services in 5G systems, which may contain privacy sensitive data. Covert communication is useful to protect the privacy of user data against adversaries. In a D2D underlaying cellular network, an antenna array can be used at a base station (BS) to transmit artificial noise to confuse adversaries that try to detect D2D covert signals. Based on the numbers of antennas at BS, two covert schemes are presented in this work and their performances are evaluated in terms of D2D covert throughput, i.e., maximum achievable D2D data rate with the given covertness requirements. As only channel distribution information (CDI) of adversary links is known to the BS, the average minimum error probability (AMEP) is used as a metric to measure the covertness performance. In the proposed schemes, closed-form expressions of the minimum AMEP and achievable D2D data rate are derived. It is shown that the derivation of minimum AMEP can be simplified if either one or massive antennas are allocated for sending artificial noise. The analytical results are compared to Monte-Carlo simulation results to verify the feasibility of the proposed schemes. It is also revealed that covert throughput can be further improved by setting system parameters properly, e.g., the number of antennas at BS and artificial noise transmit power.

This paper investigates the achievable rates of an additive white Gaussian noise energy-harvesting (EH) channel with an infinite battery. The EH process is characterized by a sequence of blocks of harvested energy, which is known causally at the source. The harvested energy remains constant within a block while the harvested energy across different blocks is characterized by a sequence of independent and identically distributed random variables. The blocks have length $L$ , which can be interpreted as the coherence time of the energy-arrival process. If $L$ is a constant or grows sublinearly in the blocklength $n$ , we fully characterize the first-order term in the asymptotic expansion of the maximum transmission rate subject to a fixed tolerable error probability $\varepsilon $ . The first-order term is known as the $\varepsilon $ -capacity. In addition, we obtain lower and upper bounds on the second-order term in the asymptotic expansion, which reveal that the second order term is proportional to $-({L/{n}})^{1/2}$ for any $\varepsilon $ less than 1/2. The lower bound is obtained through analyzing the save-and-transmit strategy. If $L$ grows linearly in $n$ , we obtain lower and upper bounds on the $\varepsilon $ -capacity, which coincide whenever the cumulative distribution function of the EH random variable is continuous and strictly increasing. In order to achieve the lower bound, we have proposed a novel adaptive save-and-transmit strategy, which chooses different save-and-transmit codes across different blocks according to the energy variation across the blocks.

Joint source-channel decoding of variable length codes (VLC) for image and video streaming transmission over unreliable links, such as wireless networks, is a subject of increasing interest. Much more residual source redundancy can be exploited when both types of correlation: (i) the correlation between bits inside a VLC codeword as well as; (ii) the correlation between VLC codewords of a VLC sequence unit (e.g. corresponding to one image block), are taken into account. The paper (Hang Nguyen et al, IEEE Int. Conf. on Acoustics, Speech, and Sigpro., 2004) proposes an optimum maximum likelihood (ML) decoder of VLC sequences which can exploit these two kinds of correlation and outperforms the existing VLC decoders. This paper proposes a reduced complexity version of this optimal VLC decoder. Simulation results show that the complexity is reduced by 5 in terms of number of possible candidates, while the performance is only slightly sub-optimal compared with the optimal version of the Hang Nguyen paper.

We consider a communication scenario in which the channel undergoes two different classes of attacks at the same time: a passive eavesdropper and an active jammer. This scenario is modelled by the concept of arbitrarily varying wiretap channels (AVWCs). In this paper, we derive a full characterization of the list secrecy capacity of the AVWC, showing that the list secrecy capacity is equivalent to the correlated random secrecy capacity if the list size L is greater than the order of symmetrizability of the AVC between the transmitter and the legitimate receiver. Otherwise, it is zero. Our result indicates that for a sufficiently large list size L, list codes can overcome the drawbacks of correlated and uncorrelated codes and provide a stable secrecy capacity for AVWCs. Furthermore, we investigate the effect of relaxing the reliability and secrecy constraints by allowing a non-vanishing error probability and information leakage on the list size L. We found that we can construct a list code whose rate is close to the correlated secrecy capacity using a finite list size L that only depends on the average error probability requested. Finally, we point out that our capacity characterization is an important step in investigating the analytical properties of the capacity function such as: the continuity behavior, Turing computability and super-activation of parallel AVWCs.

In this paper, an intelligent reflective surface (IRS)-aided multi-way communication system is investigated. The full-duplex reflective properties of the IRS are exploited to enable full-mutual data exchange among multiple users within a single channel-use. A max-min fairness-based achievable rate optimization problem is formulated to control the phase-shift matrix at the IRS. To this end, a minorization-maximization based iterative IRS phase-shift optimization algorithm is used to maximize the minimum achievable system-wide user rate. The simulation/numerical results are presented to validate the convergence of the proposed IRS phase-shift optimization algorithm and to investigate the system performance. Thereby, it is revealed that the proposed system mitigates the adverse near-far effects by ensuring a common system-wide achievable user rate while accomplishing full-mutual data exchange via intelligently controlling the phase-shifts at the IRS. Our numerical results reveal that the proposed system outperforms the current state-of-the-art multi-way communication system based on multiple-input multiple-output (MIMO) relays in terms of the achievable sum rate in the moderate-to-large IRS element regime.