Effective Capacity (EC) indicates the maximum communication rate subject to a certain delay constraint while effective energy efficiency (EEE) denotes the ratio between EC and power consumption. In this paper, we analyze the EEE of ultra-reliable networks operating in the finite blocklength regime. We obtain a closed form approximation for the EEE in Rayleigh block fading channels as a function of power, error probability, and delay. We show the optimum power allocation strategy for maximizing the EEE in finite blocklength transmission which reveals that Shannon's model underestimates the optimum power when compared to the exact finite blocklength model. Furthermore, we characterize the buffer constrained EEE maximization problem for different power consumption models. The results show that accounting for empty buffer probability (EBP) and extending the maximum delay tolerance jointly enhance the EC and EEE.
In this paper, we examine the performance of the decode-and-forward (DF) relaying protocols with finite blocklength (FB). We provide the overall outage probability of three distinct DF relaying protocols, where the channels are assumed to be quasi static Rayleigh fading. More importantly, we derive the closed form expressions of the outage probability in the three relaying scenarios. We illustrate protocols where the cooperative communications outperform the direct transmission (DT). In addition, we compare the operating efficiency of the cooperative schemes in the ultra-reliable (UR) region.
We study the determination problem of the channel capacity for the discrete memoryless channels in the finite blocklength regime. We derive explicit lower and upper bounds of the capacity. We shall demonstrate that the information spectrum approach is quite useful for investigating this problem.
To support ultra-reliable and low-latency services for mission-critical applications, transmissions are usually carried via short blocklength codes, i.e., in the so-called finite blocklength (FBL) regime. Different from the infinite blocklength regime where transmissions are assumed to be arbitrarily reliable at the Shannon's capacity, the reliability and capacity performances of an FBL transmission are impacted by the coding blocklength. The relationship among reliability, coding rate, blocklength and channel quality has recently been characterized in the literature, considering the FBL perfo…
In this paper, wireless systems operating under queueing constraints in the form of limitations on the buffer violation probabilities are considered. The throughput under such constraints is captured by the effective capacity formulation. It is assumed that finite blocklength codes are employed for transmission. Under this assumption, a recent result on the channel coding rate in the finite blocklength regime is incorporated into the analysis and the throughput achieved with such codes in the presence of queueing constraints and decoding errors is identified. Performance of different transmiss…
In this paper, we study a quantized feedback scheme to maximize the goodput of a finite blocklength communication scenario over a quasi-static fading channel. It is assumed that the receiver has perfect channel state information (CSI) and sends back the CSI to the transmitter over a resolution-limited error-free feedback channel. With this partial CSI, the transmitter is supposed to select the optimum transmission rate, such that it maximizes the overall goodput of the communication system. This problem has been studied for the asymptotic blocklength regime, however, no solution has so far bee…
This paper studies the minimum achievable source coding rate as a function of blocklength $n$ and probability $ε$ 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 $R(d) + \sqrt{\frac{V(d)}{n}} Q^{-1}(ε)$, 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 $Q^{-1}(ε)$ …
Future autonomous systems require wireless connectivity able to support extremely stringent requirements on both latency and reliability. In this paper, we leverage recent developments in the field of finite-blocklength information theory to illustrate how to optimally design wireless systems in the presence of such stringent constraints. Focusing on a multi-antenna Rayleigh block-fading channel, we obtain bounds on the maximum number of bits that can be transmitted within given bandwidth, latency, and reliability constraints, using an orthogonal frequency-division multiplexing system similar …
Empirical coordination in the finite blocklength regime: an achievability result---Extended version
Univ. Rennes, CNRS, Inria, IRISA UMR 6074（雷恩大学、法国国家科学研究中心、法国国家信息与自动化研究所、IRISA联合研究实验室）；IMT Nord Europe, Institut Mines-Telecom, Centre for Digital Systems（欧洲北部高等矿业电信学院、矿业电信学院、数字系统中心）
Wyner's soft-handoff network is considered where transmitters simultaneously send messages of enhanced mobile broadband (eMBB) and ultra-reliable low-latency communication (URLLC) services. Due to the low-latency requirements, the URLLC messages are transmitted over fewer channel uses compared to the eMBB messages. To improve the reliability of the URLLC transmissions, we propose a coding scheme with finite blocklength codewords that exploits dirty-paper coding (DPC) to precancel the interference from eMBB transmissions. Rigorous bounds are derived for the error probabilities of eMBB and URLLC…
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-Verdu, and are investigated under parallel AWGN channels, the AWGN channels, 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 integr…
This paper studies physical-layer secure transmissions from a transmitter to a legitimate receiver against an eavesdropper over slow fading channels, taking into account the impact of finite blocklength secrecy coding. A comprehensive analysis and optimization framework is established to investigate secrecy throughput for both single- and multi-antenna transmitter scenarios. Both adaptive and non-adaptive design schemes are devised, in which the secrecy throughput is maximized by exploiting the instantaneous and statistical channel state information of the legitimate receiver, respectively. Sp…
The design of block codes for short information blocks (e.g., a thousand or less information bits) is an open research problem that is gaining relevance thanks to emerging applications in wireless communication networks. In this paper, we review some of the most promising code constructions targeting the short block regime, and we compare them with both finite-length performance bounds and classical error-correction coding schemes. The work addresses the use of both binary and high-order modulations over the additive white Gaussian noise channel. We will illustrate how to effectively approach …
This paper analyzes the effective capacity (EC) of delay constrained machine type communication (MTC) networks operating in the finite blocklength (FB) regime. First, we derive a closed-form mathematical approximation for the EC in Rayleigh block fading channels. We characterize the optimum error probability to maximize the concave EC function and study the effect of SINR variations for different delay constraints. Our analysis reveals that SINR variations have less impact on EC for strict delay constrained networks. We present an exemplary scenario for massive MTC access to analyze the interf…
We prove new strong converse results in a variety of group testing settings, generalizing a result of Baldassini, Johnson and Aldridge. These results are proved by two distinct approaches, corresponding to the non-adaptive and adaptive cases. In the non-adaptive case, we mimic the hypothesis testing argument introduced in the finite blocklength channel coding regime by Polyanskiy, Poor and Verdú. In the adaptive case, we combine a formulation based on directed information theory with ideas of Kemperman, Kesten and Wolfowitz from the problem of channel coding with feedback. In both cases, we pr…
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 non-asymptotic 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 $ε$ that the distortion exceeds a given threshold $d$. For memoryless sources and channels, it is demonstrated that the parameters of the best joint source…
In this paper, we investigate the latency performance of non-orthogonal multiple access (NOMA) and orthogonal multiple access (OMA) technologies in finite blocklength regime. In the comparative study, we derive the achievable effective capacity of two-user NOMA and its OMA counterpart under delay quality-of-service constraints. We then obtain closed-form expressions for the achievable effective capacity of the weak and strong users in both scenarios considering transmissions over Rayleigh fading channels. Numerical results are provided. In particular, it is shown that at low signal-to-noise ra…
This paper presents a new technique for providing the analysis and comparison of wiretap codes in the small blocklength regime over the binary erasure wiretap channel. A major result is the development of Monte Carlo strategies for quantifying a code's equivocation, which mirrors techniques used to analyze normal error correcting codes. For this paper, we limit our analysis to coset-based wiretap codes, and make several comparisons of different code families at small and medium blocklengths. Our results indicate that there are security advantages to using specific codes when using small to med…
Under the assumption of outdated channel state information (CSI) at the source, we consider the finite blocklength (FBL) throughput of a two-hop relaying system. Previous work has considered this setting so far only for the infinite blocklength case, where decoding can be arbitrarily reliable as long as operating below the Shannon limit. In contrast, in the FBL regime residual decoding errors can not be avoided even when transmitting below the Shannon limit. This makes the scheduling problem at the source more vulnerable to transmission errors, where we investigate the trade-off between the ch…
A finite blocklenth analysis of the diversity-multiplexing tradeoff is presented, based on nonasymptotic bounds on the maximum channel coding rate of multiple-antenna block-memoryless Rayleigh-fading channels.The bounds in this paper allow one to numerically assess for which packet size, number of antennas, and degree of channel selectivity, diversity-exploiting schemes are close to optimal, and when instead the available spatial degrees of freedom should be used to provide spatial multiplexing. This finite blocklength view on the diversity-multiplexing tradeoff provides insights on the design…
Motivated by the demand of reliable and low latency communications, we employ tools from information theory, stochastic processes and queueing theory, in order to provide a comprehensive framework regarding the analysis of a Time Division Multiple Access (TDMA) network with bursty traffic, in the finite blocklength regime. Specifically, we re-examine the stability conditions of a noncooperative TDMA multiple access channel, evaluate the optimal throughput, and identify the optimal trade-off between data packet size and latency. The evaluation is performed both numerically and via the proposed …
This paper presents finite-blocklength achievability bounds for the Gaussian multiple access channel (MAC) and random access channel (RAC) under average-error and maximal-power constraints. Using random codewords uniformly distributed on a sphere and a maximum likelihood decoder, the derived MAC bound on each transmitter's rate matches the MolavianJazi-Laneman bound (2015) in its first- and second-order terms, improving the remaining terms to $\frac12\frac{\log n}{n}+O \left(\frac 1 n \right)$ bits per channel use. The result then extends to a RAC model in which neither the encoders nor the de…
We consider Additive White Gaussian Noise channels and Discrete Memoryless channels when the transmitter harvests energy from the environment. These can model wireless sensor networks as well as Internet of Things. By providing a unifying framework that works for any energy harvesting channel, we study these channels assuming an infinite energy buffer and provide the corresponding achievability and converse bounds on the channel capacity in the finite blocklength regime. We additionally provide moderate deviation asymptotic bounds as well.
We consider the concatenation of a convolutional code (CC) with an optimized cyclic redundancy check (CRC) code as a promising paradigm for good short blocklength codes. The resulting CRC-aided convolutional code naturally permits the use of serial list Viterbi decoding (SLVD) to achieve maximum-likelihood decoding. The convolutional encoder of interest is of rate-$1/ω$ and the convolutional code is either zero-terminated (ZT) or tail-biting (TB). The resulting CRC-aided convolutional code is called a CRC-ZTCC or a CRC-TBCC. To design a good CRC-aided convolutional code, we propose the distanc…
Fundamental Tradeoffs for ISAC Multiple Access in Finite-Blocklength Regime
National Mobile Communications Research Laboratory, Southeast University（国家移动通信重点实验室，东南大学）；Frontiers Science Center for Mobile Information Communication and Security, Southeast University（移动信息通信与安全前沿科学中心，东南大学）；Purple Mountain Laboratories（紫金山实验室）；Department of Electronic and Electrical Engineering, University College London（电子与电气工程系，伦敦大学学院）；Yonsei Frontier Lab., Yonsei University（延世前沿实验室，延世大学）；Department of Electrical and Electronic Engineering, University of Manchester（电气与电子工程系，曼彻斯特大学）；Chair of Information Theory and Machine Learning, Technische Universität Dresden（信息理论与机器学习讲席，德累斯顿工业大学）
In this work, we obtain lower and upper bounds on the maximal transmission rate at a given codeword length $n$, average probability of error $ε$ and power constraint $\bar{P}$, over a finite valued, block fading additive white Gaussian noise (AWGN) channel with channel state information (CSI) at the transmitter and the receiver. These bounds characterize deviation of the finite blocklength coding rates from the channel capacity which is in turn achieved by the water filling power allocation across time. The bounds obtained also characterize the rate enhancement possible due to the CSI at the t…
Fano's inequality reveals the relation between the conditional entropy and the probability of error . It has been the key tool in proving the converse of coding theorems in the past sixty years. In this paper, an extended Fano's inequality is proposed, which is tighter and more applicable for codings in the finite blocklength regime. Lower bounds on the mutual information and an upper bound on the codebook size are also given, which are shown to be tighter than the original Fano's inequality. Especially, the extended Fano's inequality is tight for some symmetric channels such as the $q$-ary sy…
As an emerging metric for the timeliness of information delivery, Age-of-Information (AoI) raises a special interest in the research area of tolerance-critical communications, wherein sufficiently short blocklength is usually adopted as an essential requirement. However, the interplay between AoI and finite blocklength is scantly treated. This paper studies the occurrence of high AoI, i.e., AoI outage, in TDMA systems with respect to the blocklength allocation among users. A Markov Decision Process model is set up for the problem, which enables a static state analysis, and therewith a policy i…
Successive relaying can improve the transmission rate by allowing the source and relays to transmit messages simultaneously, but it may cause severe inter-relay interference (IRI). IRI cancellation schemes have been proposed to mitigate IRI. However, interference cancellation methods have a high risk of error propagation, resulting in a severe transmission rate loss in finite blocklength regimes. Thus, jointly decoding for successive relaying with finite-blocklength coding (FBC) remains a challenge. In this paper, we present an optimized channel-aware ordered successive relaying protocol with …
Considering a short frame length, which is typical in Ultra-Reliable Low-Latency and massive Machine Type Communications, a trade-off exists between improving the performance of frame synchronization (FS) and improving the performance of information throughput. In this paper, we consider the case of continuous transmission over AWGN channels where the synchronization sequence is superimposed to the data symbols, as opposed to being added as a frame header. The advantage of this superposition is that the synchronization length is as long as the frame length. On the other hand, its power has to …
We investigate novel inner and outer bounds on the rate region of a 2-user Gaussian broadcast channel with finite, heterogeneous blocklength constraints (HB-GBC). In particular, we introduce a new, modified Sato-type outer bound that can be applied in the finite blocklength regime and which does not require the same marginal property. We then develop and analyze composite shell codes, which are suitable for the HB-GBC. Especially, to achieve a lower decoding latency for the user with a shorter blocklength constraint when successive interference cancellation is used, we derive the number of sym…
Confusions and Erasures of Error-Bounded Block Decoders with Finite Blocklength
RPTU University Kaiserslautern-Landau（凯泽斯劳滕-兰道理工大学）；RWTH Aachen University（亚琛工业大学）；TU Dresden（德累斯顿工业大学）；TU Berlin（柏林工业大学）；Princeton University（普林斯顿大学）；German Research Center for Artificial Intelligence (DFKI GmbH)（德国人工智能研究中心）
To realize ultra-reliable low latency communications with high spectral efficiency and security, we investigate a joint optimization problem for downlink communications with multiple users and eavesdroppers in the finite blocklength (FBL) regime. We formulate a multi-objective optimization problem to maximize a sum secrecy rate by developing a secure precoder and to minimize a maximum error probability and information leakage rate. The main challenges arise from the complicated multi-objective problem, non-tractable back-off factors from the FBL assumption, non-convexity and non-smoothness of …
Wirelessly powered communications will entail short packets due to naturally small payloads, low-latency requirements and/or insufficient energy resources to support longer transmissions. In this paper, a wirelessly powered communication system is investigated where an energy harvesting transmitter, charged by one or more power beacons via wireless energy transfer, attempts to communicate with a receiver over a noisy channel. Under a save-then-transmit protocol, the system performance is characterized using metrics such as the energy supply probability at the transmitter, and the achievable ra…
This paper considers the downlink of an ultra-reliable low-latency communication (URLLC) system in which a base station (BS) serves multiple single-antenna users in the short (finite) blocklength (FBL) regime with the assistance of a reconfigurable intelligent surface (RIS). In the FBL regime, the users' achievable rates are complex functions of the beamforming vectors and of the RIS's programmable reflecting elements (PREs). We propose the joint design of the transmit beamformers and PREs, the problem of maximizing the geometric mean (GM) of these rates (GM-rate) and show that this aforementi…
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 th…
This paper investigates the energy efficiency of massive unsourced random access~(URA) in multiple-input multiple-output quasi-static Rayleigh fading channels. Specifically, we derive achievability and converse bounds on the minimum required energy-per-bit under the per-user probability of error constraint, where the converse bounds contain two parts: one is general and the other is a weaker ensemble bound. Numerical evaluation shows that the gap between our achievability and converse bounds is less than $5$~dB in the considered regime. Some practical schemes are energy-inefficient compared wi…
We consider a dual-hop wireless network where an energy constrained relay node first harvests energy through the received radio-frequency signal from the source, and then uses the harvested energy to forward the source's information to the destination node. The throughput and delay metrics are investigated for a decode-and-forward relaying mechanism at finite blocklength regime and delay-limited transmission mode. We consider ultra-reliable communication scenarios under discussion for the next fifth-generation of wireless systems, with error and latency constraints. The impact on these metrics…
Finite-blocklength Fluid Antenna Systems With Spatial Block-Correlation Channel Model
National Mobile Communications Research Laboratory, Southeast University（东南大学国家移动通信重点实验室）；School of Artificial Intelligence, Nanjing University of Information Science and Technology（南京信息工程大学人工智能学院）；Department of Electronic and Electrical Engineering, University College London（伦敦大学学院电子电气工程系）；Yonsei Frontier Lab., Yonsei University（延世大学延世前沿实验室）；Department of Signal Theory, Networking and Communications, University of Granada（格拉纳达大学信号理论与网络通信系）；Telecommunications Research Institute (TELMA), University of Malaga（马拉加大学电信研究所（TELMA））；School of Integrated Technology, Yonsei University（延世大学综合技术学院）
