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Energy efficiency and physical-layer security are crucial considerations in the advancement of mobile edge computing systems. This paper addresses the trade-off between secure-reliability and energy consumption in finite blocklength (FBL) communications. Specifically, we examine a three-node scenario involving a user, a legitimate edge computing server, and an eavesdropper, where the user offloads sensitive data to the edge server while facing potential eavesdropping threats. We propose an optimization framework aimed at minimizing energy consumption while ensuring secure-reliability by decomposing the problem into manageable subproblems. By demonstrating the convexity of the objective function concerning the variables, we establish the existence of an optimal parameter selection for the problem. This implies that practical optimization of parameters can significantly enhance system performance. Our numerical results demonstrate that the application of FBL regime and retransmission mechanism can effectively reduce the energy consumption of the system while ensuring secure-reliability. For the quantitative analyses, the retransmission mechanism is 33.1% better than no retransmission, and the FBL regime is 13.1% better than infinite blocklength (IBL) coding. [ABSTRACT FROM AUTHOR]

Abstract Energy efficiency and physical-layer security are crucial considerations in the advancement of mobile edge computing systems. This paper addresses the trade-off between secure-reliability and energy consumption in finite blocklength (FBL) communications. Specifically, we examine a three-node scenario involving a user, a legitimate edge computing server, and an eavesdropper, where the user offloads sensitive data to the edge server while facing potential eavesdropping threats. We propose an optimization framework aimed at minimizing energy consumption while ensuring secure-reliability by decomposing the problem into manageable subproblems. By demonstrating the convexity of the objective function concerning the variables, we establish the existence of an optimal parameter selection for the problem. This implies that practical optimization of parameters can significantly enhance system performance. Our numerical results demonstrate that the application of FBL regime and retransmission mechanism can effectively reduce the energy consumption of the system while ensuring secure-reliability. For the quantitative analyses, the retransmission mechanism is 33.1% better than no retransmission, and the FBL regime is 13.1% better than infinite blocklength (IBL) coding.

In this paper, we consider a low-latency Mobile Edge Computing (MEC) network where multiple User Equipment (UE) wirelessly reports to a decision-making edge server. At the same time, the transmissions are operated with Finite Blocklength (FBL) codes to achieve low-latency transmission. We introduce the task of Age upon Decision (AuD) aimed at the timeliness of tasks used for decision-making, which highlights the timeliness of the information at decision-making moments. For the case in which dynamic task generation and random fading channels are considered, we provide a task AuD minimization design by jointly selecting UE and allocating blocklength. In particular, to solve the task AuD minimization problem, we transform the optimization problem to a Markov Decision Process problem and propose an Error Probability-Controlled Action-Masked Proximal Policy Optimization (EMPPO) algorithm. Via simulation, we show that the proposed design achieves a lower AuD than baseline methods across various network conditions, especially in scenarios with significant channel Signal-to-Noise Ratio (SNR) differences and low average SNR, which shows the robustness of EMPPO and its potential for real-time applications. [ABSTRACT FROM AUTHOR]

In this paper, we consider a low-latency Mobile Edge Computing (MEC) network where multiple User Equipment (UE) wirelessly reports to a decision-making edge server. At the same time, the transmissions are operated with Finite Blocklength (FBL) codes to achieve low-latency transmission. We introduce the task of Age upon Decision (AuD) aimed at the timeliness of tasks used for decision-making, which highlights the timeliness of the information at decision-making moments. For the case in which dynamic task generation and random fading channels are considered, we provide a task AuD minimization design by jointly selecting UE and allocating blocklength. In particular, to solve the task AuD minimization problem, we transform the optimization problem to a Markov Decision Process problem and propose an Error Probability-Controlled Action-Masked Proximal Policy Optimization (EMPPO) algorithm. Via simulation, we show that the proposed design achieves a lower AuD than baseline methods across various network conditions, especially in scenarios with significant channel Signal-to-Noise Ratio (SNR) differences and low average SNR, which shows the robustness of EMPPO and its potential for real-time applications.

In this work, we investigate a wireless powered communication network (WPCN) where multiple sources are jointly utilized for wireless power transfer (WPT). By consuming the energy harvested from the these WPT sources, a set of sensors are expected to accomplish reliable transmissions carried by finite blocklength (FBL) codes. This work proposes a fairness-aware resource allocation design with low-complexity in such a multi-source WPCN, where the practical nonlinear energy harvesting process is considered (including the effects of components nonlinearity in rectifier circuits and mutual interference between multiple radio frequency signals). In particular, a joint power and blocklength optimization problem minimizing the maximum reliability of all short packet transmissions is considered. To cope with the formulated extremely intractable nonconvex problem, we decompose it into two subproblems, i.e., a power allocation problem and a blocklength allocation problem, nevertheless, both of which are still nonconvex. To address the power allocation subproblem, auxiliary variables are introduced. Subsequently variable substitutions are performed to convert the problem into one being analytically tractable, and an efficient iterative approach is provided via applying the successive convex approximation technique. For the blocklength allocation problem, we for the first time verify the convexity of error probability with respect to blocklength under a harvested energy constraint, which is of great theoretical value and can be extended to numerous applications with energy limitations. Finally, by alternatingly addressing the two subproblems, an efficient sub-optimal solution to the original problem is achieved. We provide numerical results to validate and evaluate the proposed design, and a set of guidelines are provided for practical system designs.

In this paper, we study the age-oriented hybrid automatic repeat request (HARQ) protocol design in space-air-ground integrated networks (SAGINs) scenarios. A real-time communication system, where the updates are delivered from the remote nodes to terrestrial devices, is formulated. As the end-to-end latency $D$ is nontrivial, the traditional HARQ with frequent feedbacks is not always beneficial to timely transmission. Intuitively, there is a threshold $D^{*}$ of $D$ , only within which retransmission is advantageous to age. Inspired by this, we formulate an age-optimal redundancy allocation problem and derive the explicit expression of $D^{*}$ for advantageous retransmissions. Besides, to further increase the timeliness of the system, we propose a fast incremental redundancy hybrid ARQ protocol (fast IR-HARQ), where successive decoding and feedback operations are omitted based on channel estimation. Considering the shadowed Rician fading channel and finite blocklength regime, we derive expressions of the average age for the standard IR-HARQ and fast IR-HARQ setups. As expected, the proposed fast IR-HARQ scheme reduces the average age significantly compared with the IR-HARQ strategy. Further, we evaluate the influence of different parameters on the age performance of the fast IR-HARQ scheme. The results demonstrate the superiority of the proposed fast IR-HARQ protocol without loss of reliability. [ABSTRACT FROM AUTHOR]

In this paper, a decode-and-forward (DF) short-packet relaying model is developed to achieve timely status updates for intelligent monitoring within the Internet of Things (IoT), where the status updates generated at an IoT device are delivered to a remote server with the aid of a relay in both half-duplex (HD) and full-duplex (FD) modes. To characterise the data freshness of status updates, we exploit the age of information (AoI) as a metric, which is defined as the time elapsed since the generation of the latest successfully decoded status update. The average AoI is formulated and minimised for both HD-DF and FD-DF relaying IoT networks in finite blocklength regime. For the HD-DF relaying, we introduce a perfect approximation of the average AoI to solve the problem of average AoI minimisation with the optimal blocklengths in two phases. For the FD-DF relaying, we propose an iterative algorithm to solve the problem of average AoI minimisation by optimising the relay’s transmit power and the blocklength. Illustrative numerical results not only substantiate the validity of our proposed algorithms, but also provide useful references for the IoT monitoring network design, specifically for the transmit power thresholds at the IoT device and the relay. [ABSTRACT FROM AUTHOR]

Polarization-adjusted convolutional (PAC) codes were recently proposed and arouse the interest of the channel coding community because they were shown to approach theoretical bounds for the (128,64) code size. In this letter, we propose systematic PAC codes. Thanks to the systematic property, improvement in the bit-error rate of up to 0.2 dB is observed, while preserving the frame-error rate performance. Moreover, a genetic-algorithm-based construction method targeted to approach the theoretical bound is provided. It is then shown that using the proposed construction method systematic and non-systematic PAC codes can approach the theoretical bound even for higher code sizes such as (256,128). [ABSTRACT FROM AUTHOR]

Consider a random access communication scenario over a channel whose operation is defined for any number of possible transmitters. As in the model recently introduced by Polyanskiy for the Multiple Access Channel (MAC) with a fixed, known number of transmitters, the channel is assumed to be invariant to permutations on its inputs, and all active transmitters employ identical encoders. Unlike the Polyanskiy model, in the proposed scenario, neither the transmitters nor the receiver knows which transmitters are active. We refer to this agnostic communication setup as the Random Access Channel (RAC). Scheduled feedback of a finite number of bits is used to synchronize the transmitters. The decoder is tasked with determining from the channel output the number of active transmitters, $k$ , and their messages but not which transmitter sent which message. The decoding procedure occurs at a time ${n}_{t}$ depending on the decoder’s estimate, $t$ , of the number of active transmitters, $k$ , thereby achieving a rate that varies with the number of active transmitters. Single-bit feedback at each time ${n}_{i}, {i} \leq {t}$ , enables all transmitters to determine the end of one coding epoch and the start of the next. The central result of this work demonstrates the achievability on a RAC of performance that is first-order optimal for the MAC in operation during each coding epoch. While prior multiple access schemes for a fixed number of transmitters require $2^{k} - 1$ simultaneous threshold rules, the proposed scheme uses a single threshold rule and achieves the same dispersion. [ABSTRACT FROM AUTHOR]

This study investigates a power allocation algorithm using blocklength estimation by the finite blocklength (FBL) regime in a multicarrier downlink nonorthogonal multiple access (NOMA) system for ultrareliable low latency communication (URLLC) that is one of the services in 5G networks, requiring exceedingly high reliability and low latency. As NOMA systems can boost the capacity and increase the spectrum efficiency, it can be considered as a solution for URLLC. A multicarrier downlink NOMA system using blocklength estimation based on the FBL regime is proposed for effective resource allocation in this study. The FBL is used to derive the equation for dynamic blocklength estimation for an efficient power allocation algorithm in multicarrier downlink NOMA systems. The proposed power allocation algorithm is compared with other power allocation methods in terms of blocklength, missed deadlines, and energy efficiency; it performed the best compared with the other methods. [ABSTRACT FROM AUTHOR]

The Gauss–Markov source produces $U_{i} = aU_{i-1} + Z_{i}$ for $i\geq 1$ , where $U_{0} = 0$ , $|a|< 1$ and $Z_{i}\sim \mathcal {N}(0, \sigma ^{2})$ are i.i.d. Gaussian random variables. We consider lossy compression of a block of $n$ samples of the Gauss–Markov source under squared error distortion. We obtain the Gaussian approximation for the Gauss–Markov source with excess-distortion criterion for any distortion $d>0$ , and we show that the dispersion has a reverse waterfilling representation. This is the first finite blocklength result for lossy compression of sources with memory. We prove that the finite blocklength rate-distortion function $R(n,d,\epsilon)$ approaches the rate-distortion function $\mathbb {R}(d)$ as $R(n,d,\epsilon) = \mathbb {R}(d) + \sqrt {\frac {V(d)}{n}}Q^{-1}(\epsilon) + o\left ({\frac {1}{\sqrt {n}}}\right)$ , where $V(d)$ is the dispersion, $\epsilon \in (0,1)$ is the excess-distortion probability, and $Q^{-1}$ is the inverse $Q$ -function. We give a reverse waterfilling integral representation for the dispersion $V(d)$ , which parallels that of the rate-distortion functions for Gaussian processes. Remarkably, for all $0 < d\leq \frac {\sigma ^{2}}{(1+|a|)^{2}}$ , $R(n,d,\epsilon)$ of the Gauss–Markov source coincides with that of $Z_{i}$ , the i.i.d. Gaussian noise driving the process, up to the second-order term. Among novel technical tools developed in this paper is a sharp approximation of the eigenvalues of the covariance matrix of $n$ samples of the Gauss–Markov source, and a construction of a typical set using the maximum likelihood estimate of the parameter $a$ based on $n$ observations. [ABSTRACT FROM AUTHOR]

We study a multi-node Internet of Things system supporting low-latency high-reliability communication to a destination node. The rest of the nodes are potential relays in which the best single relay (BSR) is selected to assist the transmission to the destination. The system operates with finite blocklength (FBL) codes to satisfy the low-latency requirement. The scope of this work is to derive and improve the FBL performance of the considered BSR system. On the one hand, we extend Polyanskiy's FBL model of a single-hop scenario to the considered relaying system and derive the corresponding achievable reliability. On the other hand, by employing a practical FBL coding scheme, namely polar codes (PCs), an FBL performance bound attainable by a low-complexity coding scheme is presented. In particular, we provide a reliability bound of a dynamic-length PC scheme. Addressing a source-driven BSR strategy, as well as a relay-driven BSR strategy, we investigate two viable strategies for relay selection in the FBL regime, while the corresponding performance under an infinite blocklength (IBL) assumption serves as a reference. We prove that the two BSR strategies have the same performance in the IBL regime, while the relay-driven strategy is significantly more reliable than the source-driven one when considering the FBL regime. Furthermore, following the derived FBL performance model, we provide an optimal design to minimize the overall error probability via blocklength allocation. Through simulation and numerical investigations, we show the appropriateness of the proposed analytical model. Moreover, we evaluate both the achievable performance with FBLs and the performance of PCs in the considered scenarios while comparing the source-driven and relay-driven strategies. [ABSTRACT FROM AUTHOR]

This paper investigates the fundamental limits of communication over a noisy discrete memoryless channel that wears out, in the sense of signal-dependent catastrophic failure. In particular, we consider a channel that starts as a memoryless binary-input channel and when the number of transmitted ones causes a sufficient amount of damage, the channel ceases to convey signals. Constant composition codes are adopted to obtain an achievability bound, and the left-concave right-convex inequality is then refined to obtain a converse bound on the log-volume throughput for channels that wear out. Since infinite blocklength codes will always wear out the channel for any finite threshold of failure, and therefore cannot convey information at positive rates, we analyze the performance of finite blocklength codes to determine the maximum expected transmission volume at a given level of average error probability. We show that this maximization problem has a recursive form and can be solved by dynamic programming. Numerical results demonstrate that a sequence of block codes is preferred to a single block code for streaming sources. [ABSTRACT FROM AUTHOR]

We use stochastic network calculus to investigate the delay performance of a multiuser MISO system with zero-forcing beamforming. First, we consider ideal assumptions with long codewords and perfect CSI at the transmitter, where we observe a strong channel hardening effect that results in very high reliability with respect to the maximum delay of the application. We then study the system under more realistic assumptions with imperfect CSI and finite blocklength channel coding. These effects lead to interference and to transmission errors, and we derive closed-form approximations for the resulting error probability. Compared to the ideal case, imperfect CSI and finite length coding cause massive degradations in the average transmission rate. Surprisingly, the system nevertheless maintains the same qualitative behavior as in the ideal case: as long as the average transmission rate is higher than the arrival rate, the system can still achieve very high reliability with respect to the maximum delay. [ABSTRACT FROM AUTHOR]

With the rise of critical machine-to-machine applications, next generation wireless communication systems must meet challenging requirements with respect to latency and reliability. A key question in this context relates to channel state estimation, which allows the transmitter to adapt the code rate to the channel state. In this paper, we characterize the tradeoff between the training sequence length and data codeword length: shorter channel estimation leaves more time for the payload transmission but reduces the estimation accuracy and causes more decoding errors. Using lower coding rates can mitigate this effect, but may result in a higher backlog of data at the transmitter. In order to optimize the training sequence length and the rate adaptation scheme with respect to the delay performance, we employ queuing analysis on top of accurate models of the physical layer. We obtain an analytically tractable solution to the problem by deriving a closed-form approximation for the decoding error probability due to imperfect channel knowledge and finite-blocklength channel coding. The optimized training sequence length and rate adaptation strategy can reduce the delay violation probability by an order of magnitude, compared with suboptimal strategies that do not consider the delay constraints. [ABSTRACT FROM AUTHOR]

We investigate the maximum coding rate achievable on a two-user broadcast channel for the case where a common message is transmitted with feedback using either fixed-blocklength codes or variable-length codes. For the fixed-blocklength-code setup, we establish nonasymptotic converse and achievability bounds. An asymptotic analysis of these bounds reveals that feedback improves the second-order term compared to the no-feedback case. In particular, for a certain class of antisymmetric broadcast channels, we show that the dispersion is halved. For the variable-length-code setup, we demonstrate that the channel dispersion is zero. [ABSTRACT FROM AUTHOR]

We investigate the maximum coding rate for a given average blocklength and error probability over a $K$ -user discrete memoryless broadcast channel for the scenario where a common message is transmitted using variable-length stop-feedback codes. For the point-to-point case, Polyanskiyet al.(2011) demonstrated that variable-length coding combined with stop-feedback significantly increases the speed of convergence of the maximum coding rate to capacity. This speed-up manifests itself in the absence of a square-root penalty in the asymptotic expansion of the maximum coding rate for large blocklengths, i.e.,zero dispersion. In this paper, we present nonasymptotic achievability and converse bounds on the maximum coding rate of the common-message $K$ -user discrete memoryless broadcast channel, which strengthen and generalize the ones reported in Trillingsgaardet al.(2015) for the two-user case. An asymptotic analysis of these bounds reveals that zero dispersion cannot be achieved for certain common-message broadcast channels (e.g., the binary symmetric broadcast channel). Furthermore, we identify conditions under which our converse and achievability bounds are tight up to the second order. Through numerical evaluations, we illustrate that our second-order expansions approximate accurately the maximum coding rate and that the speed of convergence to capacity is indeed slower than for the point-to-point case. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Thanks to the autonomy of unmanned aerial vehicle (UAV), UAV-enabled data collection in Internet of Things (IoT) networks has become a key application for the next generation communication network. In this paper, we consider a scenario where an UAV is responsible for collecting data from sensor equipments (SEs) one by one and finally carrying the collected data to the computation center for processing. Different from the commonly used assumption that SEs always generate data at the beginning of each time slot, it is assumed that SEs can generate data at any instant during one time slot, which is more practical. Since SEs are energy limited, they upload data to the UAV by adopting backscatter communication technology to reduce energy consumption. Meanwhile, the updated information usually contains a small number of information bits but requires low latency and high reliability, thus the finite blocklength regime in ultra-reliable and low-latency communication is adopted for SEs' data transmission to the UAV. To keep the freshness of the updated information, a joint resource allocation problem including data collection time allocation, transmission power and trajectory design of the UAV is formulated as an optimization problem to minimize the average age of information (AoI) of all SEs. The formulated problem mixes discrete and continuous variables, which makes it difficult to solve. Thereby, we decompose the optimization problem into data collection time minimization subproblem and UAV trajectory design subproblem, which are solved by the successive convex approximation method, and the backtracking algorithm and the genetic algorithm, respectively. Numerical results show that the backtracking-based algorithm that can obtain the optimal trajectory of the UAV gains the minimal average AoI, and the genetic-based algorithm achieves sub-optimal average AoI with much lower computational complexity. The results also demonstrate that the average AoI of the backtracking-based algorithm and the genetic-based algorithm is reduced by up to 54% and 46% compared with the greedy-based benchmark algorithm, respectively. [ABSTRACT FROM AUTHOR]

A linear programming (LP)-based framework is presented for obtaining converses for finite blocklength lossy joint source-channel coding problems. The framework applies for any loss criterion, generalizes certain previously known converses, and also extends to multi-terminal settings. The finite blocklength problem is posed equivalently as a nonconvex optimization problem and using a lift-and-project-like method, a close but tractable LP relaxation of this problem is derived. Lower bounds on the original problem are obtained by the construction of feasible points for the dual of the LP relaxation. A particular application of this approach leads to new converses, which recover and improve on the converses of Kostina and Verdú for finite blocklength lossy joint source-channel coding and lossy source coding. For finite blocklength channel coding, the LP relaxation recovers the converse of Polyanskiy, Poor and Verdú and leads to a new improvement on the converse of Wolfowitz, showing thereby that our LP relaxation is asymptotically tight with increasing blocklengths for channel coding, lossless source coding, and joint source-channel coding with the excess distortion probability as the loss criterion. Using a duality-based argument, a new converse is derived for finite blocklength joint source-channel coding for a class of source-channel pairs. Employing this converse, the LP relaxation is also shown to be tight for all blocklengths for the minimization of the expected average symbolwise Hamming distortion of a $q$ -ary uniform source over a q$ -ary symmetric memoryless channel for any q\in {\mathbb {N}} . The optimization formulation and the lift-and-project method are extended to networked settings and demonstrated by obtaining an improvement on a converse of Zhou et al. for the successive refinement problem for successively refinable source-distortion measure triplets. [ABSTRACT FROM PUBLISHER]

This paper considers lossy source coding of $n$ -dimensional memoryless sources and shows an explicit approximation to the minimum source coding rate required to sustain the probability of exceeding distortion $d$ no greater than $\epsilon $ , which is simpler than known dispersion-based approximations. Our approach takes inspiration in the celebrated classical result stating that the Shannon lower bound to rate-distortion function becomes tight in the limit $d \to 0$ . We formulate an abstract version of the Shannon lower bound that recovers both the classical Shannon lower bound and the rate-distortion function itself as special cases. Likewise, we show that a nonasymptotic version of the abstract Shannon lower bound recovers all previously known nonasymptotic converses. A necessary and sufficient condition for the Shannon lower bound to be attained exactly is presented. It is demonstrated that whenever that condition is met, the rate-dispersion function is given simply by the varentropy of the source. Remarkably, all finite alphabet sources with balanced distortion measures satisfy that condition in the range of low distortions. Most continuous sources violate that condition. Still, we show that lattice quantizers closely approach the nonasymptotic Shannon lower bound, provided that the source density is smooth enough and the distortion is low. This implies that fine multidimensional lattice coverings are nearly optimal in the rate-distortion sense even at finite $n$ . The achievability proof technique is based on a new bound on the output entropy of lattice quantizers in terms of the differential entropy of the source, the lattice cell size, and a smoothness parameter of the source density. The technique avoids both the usual random coding argument and the simplifying assumption of the presence of a dither signal. [ABSTRACT FROM PUBLISHER]

In this paper, we consider single- and multi-user Gaussian channels with feedback under expected power constraints and with non-vanishing error probabilities. In the first of two contributions, we study asymptotic expansions for the additive white Gaussian noise (AWGN) channel with feedback under the average error probability formalism. By drawing ideas from Gallager and Nakiboğlu’s work for the direct part and the meta-converse for the converse part, we establish the \varepsilon -capacity and show that it depends on \varepsilon in general and so the strong converse fails to hold. Furthermore, we provide bounds on the second-order term in the asymptotic expansion. We show that for any positive integer L , the second-order term is bounded between a term proportional to (where \ln _{(L)}(\cdot ) is the L -fold nested logarithm function) and a term proportional to +(n\ln n)^1/2 , where n is the blocklength. The lower bound on the second-order term shows that feedback does provide an improvement in the maximal achievable rate over the case where no feedback is available. In our second contribution, we establish the $ \varepsilon $ -capacity region for the AWGN multiple access channel with feedback under the expected power constraint by combining ideas from hypothesis testing, information spectrum analysis, Ozarow’s coding scheme, and power control. [ABSTRACT FROM PUBLISHER]

In this paper, we provide new compact integral expressions and associated simple asymptotic approximations for converse and achievability bounds in the finite blocklength regime. The chosen converse and random coding union bounds were taken from the recent work of Polyanskyi–Poor–Verdù, and are investigated under parallel AWGN channels, the AWGN channel, the BI-AWGN channel, and the BSC. The technique we use, which is a generalization of some recent results available from the literature, is to map the probabilities of interest into a Laplace integral, and then solve (or approximate) the integral by use of a steepest descent technique. The proposed results are particularly useful for short packet lengths, where the normal approximation may provide unreliable results. [ABSTRACT FROM PUBLISHER]

This paper investigates the information-theoretic limits of energy-harvesting (EH) channels in the finite blocklength regime. The EH process is characterized by a sequence of i.i.d. random variables with finite variances. We use the save-and-transmit strategy proposed by Ozel and Ulukus (2012) together with Shannon’s non-asymptotic achievability bound to obtain lower bounds on the achievable rates for both additive white Gaussian noise channels and discrete memoryless channels under EH constraints. The first-order terms of the lower bounds of the achievable rates are equal to C and the second-order (backoff from capacity) terms are proportional to -\sqrt { \frac {\log n}{n}} , where n$ denotes the blocklength and $C$ denotes the capacity of the EH channel, which is the same as the capacity without the EH constraints. The constant of proportionality of the backoff term is found and qualitative interpretations are provided. [ABSTRACT FROM AUTHOR]

This paper shows new general nonasymptotic achievability and converse bounds and performs their dispersion analysis for the lossy compression problem in which the compressor observes the source through a noisy channel. While this problem is asymptotically equivalent to a noiseless lossy source coding problem with a modified distortion function, nonasymptotically there is a noticeable gap in how fast their minimum achievable coding rates approach the common rate-distortion function, as evidenced both by the refined asymptotic analysis (dispersion) and the numerical results. The size of the gap between the dispersions of the noisy problem and the asymptotically equivalent noiseless problem depends on the stochastic variability of the channel through which the compressor observes the source. [ABSTRACT FROM PUBLISHER]

In this paper, relaying performance is studied under the finite-blocklength regime. The overall error probability of relaying is derived. Moreover, we investigate the blocklength-limited capacity (BL-capacity) of relaying. We prove that the BL-capacity of relaying is quasiconcave in the overall error probability. Therefore, the BL-capacity has a global maximum value, which can be achieved by choosing an appropriate error probability. Through numerical investigations, we validate our analytical model and compare the performance of relaying under the finite-blocklength regime versus the Shannon capacity regime. [ABSTRACT FROM AUTHOR]

This paper shows the strong converse and the dispersion of memoryless channels with cost constraints and performs a refined analysis of the third-order term in the asymptotic expansion of the maximum achievable channel coding rate, showing that it is equal to (1/ 2)((\log n)/n) in most cases of interest. The analysis is based on a nonasymptotic converse bound expressed in terms of the distribution of a random variable termed the $\mathsf b$ -tilted information density, which plays a role similar to that of the $\mathsf d$ -tilted information in lossy source coding. We also analyze the fundamental limits of lossy joint-source-channel coding over channels with cost constraints. [ABSTRACT FROM AUTHOR]

This paper finds new tight finite-blocklength bounds for the best achievable lossy joint source-channel code rate, and demonstrates that joint source-channel code design brings considerable performance advantage over a separate one in the nonasymptotic regime. A joint source-channel code maps a block of k source symbols onto a length-n channel codeword, and the fidelity of reproduction at the receiver end is measured by the probability \epsilon that the distortion exceeds a given threshold d. For memoryless sources and channels, it is demonstrated that the parameters of the best joint source-channel code must satisfy nC - kR(d) \approx \sqrt nV + k \cal V(d) Q^-1\left(\epsilon \right), where C and V are the channel capacity and channel dispersion, respectively; R(d) and \cal V(d) are the source rate-distortion and rate-dispersion functions; and Q is the standard Gaussian complementary cumulative distribution function. Symbol-by-symbol (uncoded) transmission is known to achieve the Shannon limit when the source and channel satisfy a certain probabilistic matching condition. In this paper, we show that even when this condition is not satisfied, symbol-by-symbol transmission is, in some cases, the best known strategy in the nonasymptotic regime. [ABSTRACT FROM PUBLISHER]

Given the possibility of communication systems failing catastrophically, we investigate limits to communicating over channels that fail at random times. These channels are finite-state semi-Markov channels. We show that communication with arbitrarily small probability of error is not possible. Making use of results in finite blocklength channel coding, we determine sequences of blocklengths that optimize transmission volume communicated at fixed maximum message error probabilities. We provide a partial ordering of communication channels. A dynamic programming formulation is used to show the structural result that channel state feedback does not improve performance. [ABSTRACT FROM AUTHOR]

This paper studies the minimum achievable source coding rate as a function of blocklength n and probability \epsilon that the distortion exceeds a given level d. Tight general achievability and converse bounds are derived that hold at arbitrary fixed blocklength. For stationary memoryless sources with separable distortion, the minimum rate achievable is shown to be closely approximated by R(d) + \sqrt V(d) \over n Q^-1\left(\epsilon \right), where R(d) is the rate-distortion function, V(d) is the rate dispersion, a characteristic of the source which measures its stochastic variability, and Q^-1\left(\cdot \right) is the inverse of the standard Gaussian complementary cumulative distribution function. [ABSTRACT FROM PUBLISHER]

Channel dispersion plays a fundamental role in assessing the backoff from capacity due to finite blocklength. This paper analyzes the channel dispersion for a simple channel with memory: the Gilbert-Elliott communication model in which the crossover probability of a binary symmetric channel evolves as a binary symmetric Markov chain, with and without side information at the receiver about the channel state. With side information, dispersion is equal to the average of the dispersions of the individual binary symmetric channels plus a term that depends on the Markov chain dynamics, which do not affect the channel capacity. Without side information, dispersion is equal to the spectral density at zero of a certain stationary process, whose mean is the capacity. In addition, the finite blocklength behavior is analyzed in the non-ergodic case, in which the chain remains in the initial state forever. [ABSTRACT FROM AUTHOR]

This paper investigates the maximal channel coding rate achievable at a given blocklength and error probability. For general classes of channels new achievability and converse bounds are given, which are tighter than existing bounds for wide ranges of parameters of interest, and lead to tight approximations of the maximal achievable rate for blocklengths n as short as 100. It is also shown analytically that the maximal rate achievable with error probability V is closely approximated by C - √V/n Q-1(ε) where C is the capacity, ε is a characteristic of the channel referred to as channel dispersion, and Q is the complementary Gaussian cumulative distribution function. [ABSTRACT FROM AUTHOR]