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 decoder knows which of $K$ possible transmitters are active. In the proposed rateless coding strategy, decoding occurs at a time $n_t$ that depends on the decoder's estimate $t$ of the number of active transmitters $k$. Single-bit feedback from the decoder to all encoders at each potential decoding time $n_i$, $i \leq t$, informs the encoders when to stop transmitting. For this RAC model, the proposed code achieves the same first-, second-, and third-order performance as the best known result for the Gaussian MAC in operation.
Rate-Splitting Multiple Access (RSMA) is an emerging flexible and powerful multiple access for downlink multiantenna networks. In this paper, we introduce the concept of RSMA into short-packet downlink communications. We design optimal linear precoders that maximize the sum rate with Finite Blocklength (FBL) constraints. The relations between the sum rate and blocklength of RSMA are investigated for a wide range of network loads and user deployments. Numerical results demonstrate that RSMA can achieve the same transmission rate as Non-Orthogonal Multiple Access (NOMA) and Space Division Multip…
In this letter, we investigate Rate-Splitting Multiple Access (RSMA) for an uplink communication system with finite blocklength. Considering a two-user Single-Input Single-Output (SISO) Multiple Access Channel (MAC), we study the impact of Signal-to-Noise Ratio (SNR), blocklength, power allocation and target rate on the error probability performance of RSMA where one user message is split. We demonstrate that RSMA can improve the error probability performance significantly compared to Non-Orthogonal Multiple Access (NOMA) and RSMA can have a larger rate region than NOMA.
A converse for the Discrete Memoryless Multiple Access Channel is given. The result in [13] is refined, and the third order term is obtained. Moreover, our proof is much simpler than [13]. With little modification, the region can be further improved.
This paper considers the achievability and converse bounds on the maximal channel coding rate at a given blocklength and error probability over AWGN channels. The problem stems from covert communication with Gaussian codewords. By re-visiting [18], we first present new and more general achievability bounds for random coding schemes under maximal or average probability of error requirements. Such general bounds are then applied to covert communication in AWGN channels where codewords are generated from Gaussian distribution while meeting the maximal power constraint. Further comparison is made …
Future wireless access networks aim to simultaneously support a large number of devices with heterogeneous service requirements, including data rates, error rates, and latencies. While achievable rate and capacity results exist for Gaussian broadcast channels in the asymptotic blocklength regime, the characterization of second-order achievable rate regions for heterogeneous blocklength constraints is not available. Therefore, we investigate a two-user Gaussian broadcast channel (GBC) with heterogeneous blocklength constraints, specified according to users' channel output signal-to-noise ratios…
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…
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 work focuses on the performance analysis of short blocklength communication with application in smart grids. We use stochastic geometry to compute in closed form the success probability of a typical message transmission as a function of its size (i.e. blocklength), the number of information bits and the density of interferers. Two different scenarios are investigated: (i) dynamic spectrum access where the licensed and unlicensed users, share the uplink channel frequency band and (ii) local licensing approach using the so called micro operator, which holds an exclusive license of its own. …
This paper applies error-exponent and dispersion-style analyses to derive finite-blocklength achievability bounds for low-density parity-check (LDPC) codes over the point-to-point channel (PPC) and multiple access channel (MAC). The error-exponent analysis applies Gallager's error exponent to bound achievable symmetrical and asymmetrical rates in the MAC. The dispersion-style analysis begins with a generalization of the random coding union (RCU) bound from random code ensembles with i.i.d. codewords to random code ensembles in which codewords may be statistically dependent; this generalization…
Rate-Splitting Multiple Access (RSMA) has emerged as a flexible and powerful framework for wireless networks. In this paper, we investigate the user fairness of downlink multi-antenna RSMA in short-packet communications with/without cooperative (user-relaying) transmission. We design optimal time allocation and linear precoders that maximize the Max-Min Fairness (MMF) rate with Finite Blocklength (FBL) constraints. The relation between the MMF rate and blocklength of RSMA, as well as the impact of cooperative transmission are investigated for a wide range of network loads. Numerical results de…
Finite-Blocklength ISAC Multiple Access: A Source-Channel Coding Perspective
National Mobile Communications Research Laboratory, Southeast University（东南大学国家移动通信实验室）；School of Cyber Science and Engineering, Southeast University（东南大学网络空间安全学院）；Department of Electrical and Electronic Engineering, University of Manchester（曼彻斯特大学电气与电子工程系）
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 present finite-blocklength achievability bounds for the unsourced A-channel. In this multiple-access channel, users noiselessly transmit codewords picked from a common codebook with entries generated from a $q$-ary alphabet. At each channel use, the receiver observes the set of different transmitted symbols but not their multiplicity. We show that the A-channel finds applications in unsourced random-access (URA) and group testing. Leveraging the insights provided by the finite-blocklength bounds and the connection between URA and non-adaptive group testing through the A-channel, we propose …
Motivated by the growing application of wireless multi-access networks with stringent delay constraints, we investigate the Gaussian multiple access channel (MAC) in the finite blocklength regime. Building upon information spectrum concepts, we develop several non-asymptotic inner bounds on channel coding rates over the Gaussian MAC with a given finite blocklength, positive average error probability, and maximal power constraints. Employing Central Limit Theorem (CLT) approximations, we also obtain achievable second-order coding rates for the Gaussian MAC based on an explicit expression for it…
This paper investigates the maximal secrecy rate over a wiretap channel subject to reliability and secrecy constraints at a given blocklength. New achievability and converse bounds are derived, which are shown to be tighter than existing bounds. The bounds also lead to the tightest second-order coding rate for discrete memoryless and Gaussian wiretap channels.
We consider an additive White Gaussian channel where the transmitter is powered by an energy harvesting source. For such a system, we provide a lower bound on the maximal code book at finite code lengths that improves upon previously known bounds.
Consider a problem of forward error-correction for the additive white Gaussian noise (AWGN) channel. For finite blocklength codes the backoff from the channel capacity is inversely proportional to the square root of the blocklength. In this paper it is shown that codes achieving this tradeoff must necessarily have peak-to-average power ratio (PAPR) proportional to logarithm of the blocklength. This is extended to codes approaching capacity slower, and to PAPR measured at the output of an OFDM modulator. As a by-product the convergence of (Smith's) amplitude-constrained AWGN capacity to Shannon…
In this paper, we present a finite-block-length comparison between the orthogonal multiple access (OMA) scheme and the non-orthogonal multiple access (NOMA) for the uplink channel. First, we consider the Gaussian channel, and derive the closed form expressions for the rate and outage probability. Then, we extend our results to the quasi-static Rayleigh fading channel. Our analysis is based on the recent results on the characterization of the maximum coding rate at finite block-length and finite block-error probability. The overall system throughput is evaluated as a function of the number of i…
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.
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 $Q^{-1}(ε)$ …
This work introduces downlink non-orthogonal multiple access (NOMA) into short-packet communications. NOMA has great potential to improve fairness and spectral efficiency with respect to orthogonal multiple access (OMA) for low-latency downlink transmission, thus making it attractive for the emerging Internet of Things. We consider a two-user downlink NOMA system with finite blocklength constraints, in which the transmission rates and power allocation are optimized. To this end, we investigate the trade-off among the transmission rate, decoding error probability, and the transmission latency m…
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）
Classical multiuser information theory studies the fundamental limits of models with a fixed (often small) number of users as the coding blocklength goes to infinity. This work proposes a new paradigm, referred to as {\em many-user information theory}, where the number of users is allowed to grow with the blocklength. This paradigm is motivated by emerging systems with a massive number of users in an area, such as machine-to-machine communication systems and sensor networks. The focus of the current paper is the {\em many-access} channel model, which consists of a single receiver and many tran…
This paper investigates the performance of a two-user downlink non-orthogonal multiple access (NOMA) system using hybrid automatic repeat request with chase combining (HARQ-CC) in finite blocklength. First, an analytical framework is developed by deriving closed-form approximations for the individual average block error rate (BLER) of the near and the far user. Based upon that, the performance of NOMA is discussed in comparison to orthogonal multiple access (OMA), which draws the conclusion that NOMA outperforms OMA in terms of user fairness. Further, an algorithm is devised to determine the r…
Classical multiuser information theory studies the fundamental limits of models with a fixed (often small) number of users as the coding blocklength goes to infinity. This work proposes a new paradigm, referred to as many-user information theory, where the number of users is allowed to grow with the blocklength. This paradigm is motivated by emerging systems with a massive number of users in an area, such as machine-to-machine communication systems and sensor networks. The focus of the current paper is the many-access channel model, which consists of a single receiver and many transmitters, wh…
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…
This work focuses on the performance of multi-terminal wireless industrial networks, where the transmissions of all terminals are required to be scheduled within a tight deadline. The transmissions thus share a fixed amount of resources, i.e., symbols, while facing short blocklengths due to the low-latency requirement. We investigate two distinct relaying strategies, namely best relay selection among the participating terminals and best antenna selection at the access point of the network. In both schemes, we incorporate the cost of acquiring instantaneous Channel State Information (CSI) at th…
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 (RA…
This paper considers the single antenna, static Gaussian broadcast channel in the finite blocklength regime. Second order achievable and converse rate regions are presented. Both a global reliability requirement and per-user reliability requirements are considered. The two-user case is analyzed in detail, and generalizations to the $K$-user case are also discussed. The largest second order achievable region presented here requires both superposition and rate splitting in the code construction, as opposed to the (infinite blocklength, first order) capacity region which does not require rate spl…
We design short blocklength codes for the Gaussian wiretap channel under information-theoretic security guarantees. Our approach consists in decoupling the reliability and secrecy constraints in our code design. Specifically, we handle the reliability constraint via an autoencoder, and handle the secrecy constraint with hash functions. For blocklengths smaller than or equal to 128, we evaluate through simulations the probability of error at the legitimate receiver and the leakage at the eavesdropper for our code construction. This leakage is defined as the mutual information between the confid…
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 studies the performance of block coding on an additive white Gaussian noise channel under different power limitations at the transmitter. Lower bounds are presented for the minimum error probability of codes satisfying maximal and average power constraints. These bounds are tighter than previous results in the finite blocklength regime, and yield a better understanding on the structure of good codes under an average power limitation. Evaluation of these bounds for short and moderate blocklengths is also discussed.
This paper considers the massive random access problem in MIMO quasi-static Rayleigh fading channels. Specifically, we derive achievability and converse bounds on the minimum energy-per-bit required for each active user to transmit $J$ bits with blocklength $n$ and power $P$ under a per-user probability of error (PUPE) constraint, in the cases with and without \emph{a priori} channel state information at the receiver (CSIR and no-CSI). In the case of no-CSI, we consider both the settings with and without knowing the number $K_a$ of active users. The achievability bounds rely on the design of t…
Classical multiuser information theory studies the fundamental limits of models with a fixed (often small) number of users as the coding blocklength goes to infinity. Motivated by emerging systems with a massive number of users, this paper studies the new {\em many-user paradigm}, where the number of users is allowed to grow with the blocklength. The focus of this paper is the degraded many-broadcast channel model, whose number of users may grow as fast as linearly with the blocklength. A notion of capacity in terms of message length is defined and an example of Gaussian degraded many-broadcas…
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 …
The work at hand presents a finite-blocklength analysis of the multiple access channel (MAC) sum-rate under the cooperation facilitator (CF) model. The CF model, in which independent encoders coordinate through an intermediary node, is known to show significant rate benefits, even when the rate of cooperation is limited. We continue this line of study for cooperation rates which are sub-linear in the blocklength $n$. Roughly speaking, our results show that if the facilitator transmits $\log{K}$ bits, there is a sum-rate benefit of order $\sqrt{\log{K}/n}$. This result extends across a wide ran…
Channel Knowledge Empowered Finite-Blocklength Rate-Splitting Transmission for High-Mobility Autonomous Driving
College of Information Science and Technology, Jinan University（暨南大学信息科学技术学院）；School of Information Science and Technology, ShanghaiTech University（上海科技大学信息科学与技术学院）；School of Computer Science, Beijing University of Posts and Telecommunications（北京邮电大学计算机学院）；National Key Laboratory of Science and Technology on Communications, University of Electronic Science and Technology of China（电子科技大学通信科学与技术国家重点实验室）
This paper investigates the maximal channel coding rate achievable at a given blocklength $n$ and error probability $ε$, when the codewords are subject to a long-term (i.e., averaged-over-all-codeword) power constraint. The second-order term in the large-$n$ expansion of the maximal channel coding rate is characterized both for additive white Gaussian noise (AWGN) channels and for quasi-static fading channels with perfect channel state information available at both the transmitter and the receiver. It is shown that in both cases the second-order term is proportional to $\sqrt{n^{-1}\ln n}$. Fo…
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…
