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 symmetric channels (QSC).
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 …
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…
We present nonasymptotic bounds on the maximum coding rate achievable over a Rician block-fading channel for a fixed packet size and a fixed packet error probability. Our bounds, which apply to the scenario where no a priori channel state information is available at the receiver, allow one to quantify the tradeoff between the rate gains resulting from the exploitation of time-frequency diversity and the rate loss resulting from fast channel variations and pilot-symbol overhead.
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 …
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…
In this paper, the wireless hierarchical federated learning (HFL) is revisited by considering physical layer security (PLS). First, we establish a framework for this new problem. Then, we propose a practical finite blocklength (FBL) coding scheme for the wireless HFL in the presence of PLS, which is self-secure when the coding blocklength is lager than a certain threshold. Finally, the study of this paper is further explained via numerical examples and simulation results.
A new finite blocklength converse for the Slepian- Wolf coding problem is presented which significantly improves on the best known converse for this problem, due to Miyake and Kanaya [2]. To obtain this converse, an extension of the linear programming (LP) based framework for finite blocklength point- to-point coding problems from [3] is employed. However, a direct application of this framework demands a complicated analysis for the Slepian-Wolf problem. An analytically simpler approach is presented wherein LP-based finite blocklength converses for this problem are synthesized from point-to-po…
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）
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 …
In this work, lossy distributed compression of pairs of correlated sources is considered. Conventionally, Shannon's random coding arguments -- using randomly generated unstructured codebooks whose blocklength is taken to be asymptotically large -- are used to derive achievability results. However, it was recently observed that in various multi-terminal communications scenarios, using random codes with constant finite blocklength may lead to improved achievable regions compared to the conventional approach. In other words, in some network communication scenarios, there is a finite optimal value…
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 relaxati…
A tight converse bound to channel coding rate in the finite block-length regime and under AWGN conditions was recently proposed by Polyanskiy, Poor, and Verdu (PPV). The bound is a generalization of a number of other classical results, and it was also claimed to be equivalent to Shannon's 1959 cone packing bound. Unfortunately, its numerical evaluation is troublesome even for not too large values of the block-length n. In this paper we tackle the numerical evaluation by compactly expressing the PPV converse bound in terms of non-central chi-squared distributions, and by evaluating those throug…
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…
We consider universal variable-to-fixed length compression of memoryless sources with a fidelity criterion. We design a dictionary codebook over the reproduction alphabet which is used to parse the source stream. Once a source subsequence is within a specified distortion of a dictionary codeword, the index of the codeword is emitted as the reproduced string. Our proposed dictionary consists of coverings of type classes in the boundary of transition from low to high empirical lossy rate. We derive the asymptotics of the ε-coding rate (up to the third-order term) of our coding scheme for large e…
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.
This paper concerns the maximum coding rate at which data can be transmitted over a noncoherent, single-antenna, Rayleigh block-fading channel using an error-correcting code of a given blocklength with a block-error probability not exceeding a given value. A high-SNR normal approximation of the maximum coding rate is presented that becomes accurate as the signal-to-noise ratio (SNR) and the number of coherence intervals $L$ over which we code tend to infinity. Numerical analyses suggest that the approximation is accurate at SNR values above 15dB and when the number of coherence intervals is 10…
In this paper we consider a channel model that is often used to describe the mobile wireless scenario: multiple-antenna additive white Gaussian noise channels subject to random (fading) gain with full channel state information at the receiver. Dynamics of the fading process are approximated by a piecewise-constant process (frequency non-selective isotropic block fading). This work addresses the finite blocklength fundamental limits of this channel model. Specifically, we give a formula for the channel dispersion -- a quantity governing the delay required to achieve capacity. Multiplicative nat…
This paper investigates an energy-efficient non-orthogonal transmission design problem for two downlink receivers that have strict reliability and finite blocklength (latency) constraints. The Shannon capacity formula widely used in traditional designs needs the assumption of infinite blocklength and thus is no longer appropriate. We adopt the newly finite blocklength coding capacity formula for explicitly specifying the trade-off between reliability and code blocklength. However, conventional successive interference cancellation (SIC) may become infeasible due to heterogeneous blocklengths. W…
It is well known that the mutual information between two random variables can be expressed as the difference of two relative entropies that depend on an auxiliary distribution, a relation sometimes referred to as the golden formula. This paper is concerned with a finite-blocklength extension of this relation. This extension consists of two elements: 1) a finite-blocklength channel-coding converse bound by Polyanskiy and Verdú (2014), which involves the ratio of two Neyman-Pearson $β$ functions (beta-beta converse bound); and 2) a novel beta-beta channel-coding achievability bound, expressed ag…
Finite blocklength and second-order (dispersion) results are presented for the arbitrarily-varying channel (AVC), a classical model wherein an adversary can transmit arbitrary signals into the channel. A novel finite blocklength achievability bound is presented, roughly analogous to the random coding union bound for non-adversarial channels. This finite blocklength bound, along with a known converse bound, is used to derive bounds on the dispersion of discrete memoryless AVCs without shared randomness, and with cost constraints on the input and the state. These bounds are tight for many channe…
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 studies the coherent and non-coherent multiuser multiple-input multiple-output (MU-MIMO) uplink system in the finite blocklength regime. The i.i.d. Gaussian codebook is assumed for each user. To be more specific, the BS first uses two popular linear processing schemes to combine the signals transmitted from all users, namely, MRC and ZF. Following it, the matched maximum-likelihood (ML) and mismatched nearest-neighbour (NN) decoding metric for the coherent and non-coherent cases are respectively employed at the BS. Under these conditions, the refined third-order achievable coding ra…
Motivated by applications in the security of cyber-physical systems, we pose the finite blocklength communication problem in the presence of a jammer as a zero-sum game between the encoder-decoder team and the jammer, by allowing the communicating team as well as the jammer only locally randomized strategies. The communicating team's problem is non-convex under locally randomized codes, and hence, in general, a minimax theorem need not hold for this game. However, we show that approximate minimax theorems hold in the sense that the minimax and maximin values of the game approach each other asy…
Homophonic coding is a framework to reversibly convert a message into a sequence with some target distribution. This is a promising tool to generate a codeword with a biased code-symbol distribution, which is required for capacity-achieving communication by asymmetric channels. It is known that asymptotically optimal homophonic coding can be realized by a Fixed-to-Variable (FV) length code using an interval algorithm similar to a random number generator. However, FV codes are not preferable as a component of channel codes since a decoding error propagates to all subsequent codewords. As a solu…
In this work, we address the question of the largest rate of linear subcodes of Reed-Muller (RM) codes, all of whose codewords respect a runlength-limited (RLL) constraint. Our interest is in the $(d,\infty)$-RLL constraint, which mandates that every pair of successive $1$s be separated by at least $d$ $0$s. Consider any sequence $\{{\mathcal{C}_m}\}_{m\geq 1}$ of RM codes with increasing blocklength, whose rates approach $R$, in the limit as the blocklength goes to infinity. We show that for any linear $(d,\infty)$-RLL subcode, $\hat{\mathcal{C}}_m$, of the code $\mathcal{C}_m$, it holds that…
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 paper analyzes the maximal achievable rate for a given blocklength and error probability over a multiple-antenna ambient backscatter channel with perfect channel state information at the receiver. The result consists of a finite blocklength channel coding achievability bound and a converse bound based on the Neyman-Pearson test and the normal approximation based on the Berry- Esseen Theorem. Numerical evaluation of these bounds shows fast convergence to the channel capacity as the blocklength increases and also proves that the channel dispersion is an accurate measure of the backoff from …
The maximum rate at which classical information can be reliably transmitted per use of a quantum channel strictly increases in general with $N$, the number of channel outputs that are detected jointly by the quantum joint-detection receiver (JDR). This phenomenon is known as superadditivity of the maximum achievable information rate over a quantum channel. We study this phenomenon for a pure-state classical-quantum (cq) channel and provide a lower bound on $C_N/N$, the maximum information rate when the JDR is restricted to making joint measurements over no more than $N$ quantum channel outputs…
