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. Specifically, optimal transmission policy, blocklength, and code rates are jointly designed to maximize the secrecy throughput. Additionally, null-space artificial noise is employed to improve the secrecy throughput for the multi-antenna setup with the optimal power allocation derived.Various important insights are developed. In particular, 1) increasing blocklength benefits both reliability and secrecy under the proposed transmission policy; 2) secrecy throughput monotonically increases with blocklength; 3) secrecy throughput initially increases but then decreases as secrecy rate increases, and the optimal secrecy rate maximizing the secrecy throughput should be carefully chosen in order to strike a good balance between rate and decoding correctness. Numerical results are eventually presented to verify theoretical findings.
We investigate the maximal achievable rate for a given blocklength and error probability over quasi-static single-input multiple-output (SIMO) fading channels. Under mild conditions on the channel gains, it is shown that the channel dispersion is zero regardless of whether the fading realizations are available at the transmitter and/or the receiver. The result follows from computationally and analytically tractable converse and achievability bounds. Through numerical evaluation, we verify that, in some scenarios, zero dispersion indeed entails fast convergence to outage capacity as the blockle…
This paper investigates the maximal achievable rate for a given blocklength and error probability over quasi-static multiple-input multiple-output (MIMO) fading channels, with and without channel state information (CSI) at the transmitter and/or the receiver. The principal finding is that outage capacity, despite being an asymptotic quantity, is a sharp proxy for the finite-blocklength fundamental limits of slow-fading channels. Specifically, the channel dispersion is shown to be zero regardless of whether the fading realizations are available at both transmitter and receiver, at only one of t…
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.
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…
In many wireless systems, the channel state information at the transmitter (CSIT) can not be learned until after a transmission has taken place and is thereby outdated. In this paper, we study the benefits of delayed CSIT on a block-fading channel at finite blocklength. First, the achievable rates of a family of codes that allows the number of codewords to expand during transmission, based on delayed CSIT, are characterized. A fixed-length and a variable-length characterization of the rates are provided using the dependency testing bound and the variable-length setting introduced by Polyanskiy…
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 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…
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.
Motivated by the current interest in ultra-reliable, low-latency, machine-type communication systems, we investigate the tradeoff between reliability, throughput, and latency in the transmission of information over multiple-antenna Rayleigh block-fading channels. Specifically, we obtain finite-blocklength, finite-SNR upper and lower bounds on the maximum coding rate achievable over such channels for a given constraint on the packet error probability. Numerical evidence suggests that our bounds delimit tightly the maximum coding rate already for short blocklengths (packets of about 100 symbols)…
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…
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.
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…
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…
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 opti…
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…
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 we provide secrecy metrics applicable to physical-layer coding techniques with finite blocklengths over Gaussian and fading wiretap channel models. Our metrics go beyond some of the known practical secrecy measures, such as bit error rate and security gap, so as to make lower bound probabilistic guarantees on error rates over short blocklengths both preceding and following a secrecy decoder. Our techniques are especially useful in cases where application of traditional information-theoretic security measures is either impractical or simply not yet understood. The metrics can aid …
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…
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 …
We consider a block fading additive white Gaussian noise (AWGN) channel with perfect channel state information (CSI) at the transmitter and the receiver. First, for a given codeword length and non-vanishing average probability of error, we obtain lower and upper bounds on the maximum transmission rate. We derive bounds for three kinds of power constraints inherent to a wireless transmitter. These include the canonical peak power constraint and average power constraint. In addition, we consider a time varying peak power constraint imposed by an \emph{energy harvesting device}-a mechanism that p…
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…
In this paper, the blocklength-limited performance of a relaying system is studied, where channels are assumed to experience quasi-static Rayleigh fading while at the same time only the average channel state information (CSI) is available at the source. Both the physical-layer performance (blocklength-limited throughput) and the link-layer performance (effective capacity) of the relaying system are investigated. We propose a simple system operation by introducing a factor based on which we weight the average CSI and let the source determine the coding rate accordingly. In particular, we prove …
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…
The use of channel output feedback to improve the reliability of fading channels has received scant attention in the literature. In most work on feedback for fading channels, only channel state information (CSI) feedback has been exploited for coding at the transmitter. In this work, the design of a coding scheme for multiple-input multiple-output (MIMO) fading systems with channel output and channel state feedback at the transmitter is considered. Under the assumption of additive white Gaussian noise and an independent and identically distributed fading process, a simple linear coding strateg…
We analyze a wireless communication system with finite block length and finite battery energy, under quasi-static Nakagami-m fading. Wireless energy transfer is carried out in the downlink while information transfer occurs in the uplink. Transmission strategies for scenarios with/without energy accumulation between transmission rounds are characterized in terms of error probability and energy consumption. A power control protocol for the energy accumulation scenario is proposed and results show the enormous impact on improving the system performance, in terms of error probability and energy co…
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…
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…
Ensuring the physical layer security (PHY-security) of millimeter wave (mmWave) communications is one of the key factors for the success of 5G. Recent field measurements show that conventional fading models cannot accurately model the random fluctuations of mmWave signals. To tackle this challenge, the fluctuating two-ray (FTR) fading model has been proposed. In this correspondence, we comprehensively analyze the PHY-security in mmWave communications over FTR fading channels. More specifically, we derive analytical expressions for significant PHY-security metrics, such as average secrecy capac…
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 considers an energy-efficient packet scheduling problem over quasi-static block fading channels. The goal is to minimize the total energy for transmitting a sequence of data packets under the first-in-first-out rule and strict delay constraints. Conventionally, such design problem is studied under the assumption that the packet transmission rate can be characterized by the classical Shannon capacity formula, which, however, may provide inaccurate energy consumption estimation, especially when the code blocklength is finite. In this paper, we formulate a new energy-efficient packet s…
In this letter, the performance analysis of physical layer security over Fisher-Snedecor $\mathcal{F}$ fading channels is investigated. In particular, the average secrecy capacity (ASC), the secure outage probability (SOP), the lower bound of the SOP (SOP$^L$), and the strictly positive secure capacity (SPSC) are derived in exact closed-from expressions. The Fisher-Snedecor $\mathcal{F}$ fading channel is a composite of multipath/shadowed fading that are represented by the Nakagami-$m$ distribution. Moreover, it provides close results to the practical measurements than the generalised $K$ ($K_…
A bit error rate (BER)-based physical layer security approach is proposed for finite blocklength. For secure communication in the sense of high BER, the information-theoretic strong converse is combined with cryptographic error amplification achieved by substitution permutation networks (SPNs) based on confusion and diffusion. For discrete memoryless channels (DMCs), an analytical framework is provided showing the tradeoffs among finite blocklength, maximum/minimum possible transmission rates, and BER requirements for the legitimate receiver and the eavesdropper. Also, the security gap is anal…
In this paper, we investigate the impact of side information (SI) on the performance of physical layer security (PLS) under correlated fading channels. By considering non-causally known SI at the transmitter and exploiting the copula technique to describe the fading correlation, we derive closed-from expressions for the average secrecy capacity (ASC) and secrecy outage probability (SOP) under positive/negative dependence conditions. We indicate that considering such knowledge at the transmitter is beneficial for system performance and ensures reliable communication with higher rates, as it imp…
VLSF Decoding with Reliability Guarantees over Correlated Noncoherent Fading Channels
Inria（法国国家信息与自动化研究所）；Université de la Polynésie française（法属波利尼西亚大学）；Princeton University（普林斯顿大学）；Univ. Rennes, INSA, CNRS, IETR UMR 6164（雷恩大学、国立应用科学学院、法国国家科学研究中心、信息电子工程研究所）；Inria, INSA Lyon, CITI Laboratory（法国国家信息与自动化研究所、里昂国立应用科学学院、信息与通信技术创新实验室）
This paper analyzes the effective capacity of delay constrained machine type communication (MTC) networks operating in the finite blocklength regime. First, we derive a closed-form mathematical approximation for the effective capacity in quasi-static Rayleigh fading channels. We characterize the optimum error probability to maximize the concave effective capacity function with reliability constraint and study the effect of signal-to-interference-plus-noise ratio (SINR) variations for different delay constraints. The trade off between reliability and effective capacity maximization reveals that…
This paper studies the performance of delay-constrained hybrid automatic repeat request HARQ protocols. Particularly, we propose a fast HARQ protocol where, to increase the end-to-end throughput, some HARQ feedback signals and successive message decodings are omitted. Considering quasi-static channels and a bursty communication model, we derive closed-form expressions for the message decoding probabilities as well as the throughput, the expected delay and the error probability of the HARQ setups. The analysis is based on recent results on the achievable rates of finite-length codes and shows t…
Leveraging recent results in finite-blocklength information theory, we investigate the problem of designing a control channel in a 5G system. The setup involves the transmission, under stringent latency and reliability constraints, of a short data packet containing a small information payload, over a propagation channel that offers limited frequency diversity and no time diversity. We present an achievability bound, built upon the random-coding union bound with parameter $s$ (Martinez & Guillén i Fàbregas, 2011), which relies on quadrature phase-shift keying modulation, pilot-assisted transmis…
Theoretical studies on physical layer security often adopt the secrecy outage probability as the performance metric for wireless communications over quasi-static fading channels. The secrecy outage probability has two limitations from a practical point of view: a) it does not give any insight into the eavesdropper's decodability of confidential messages; b) it cannot characterize the amount of information leakage to the eavesdropper when an outage occurs. Motivated by the limitations of the secrecy outage probability, we propose three new secrecy metrics for secure transmissions over quasi-sta…
Most of the well-known fading distributions, if not all of them, could be encompassed by Fox's $H$-function fading. Consequently, we investigate the exact and asymptotic behavior of physical layer security (PLS) over Fox's $H$-function fading wiretap channels. In particular, closed-form expressions are derived for secrecy outage probability (SOP), probability of non-zero secrecy capacity (PNZ), and average secrecy capacity (ASC). These expressions are given in terms of either univariate or bivariate Fox's $H$-function. In order to show the comprehensive effectiveness of our derivations, three …
This paper investigates the effective capacity of a point-to-point ultra-reliable low latency communication (URLLC) transmission over multiple parallel sub-channels at finite blocklength (FBL) with imperfect channel state information (CSI). Based on reasonable assumptions and approximations, we derive the effective capacity as a function of the pilot length, decoding error probability, transmit power and the sub-channel number. Then we reveal significant impact of the above parameters on the effective capacity. A closed-form lower bound of the effective capacity is derived and an alternating o…
In this paper, we investigate the effectiveness of the hybrid automatic repeat request (HARQ) technique in providing high-reliability and low-latency in the finite blocklength (FBL) regime in a single user uplink scenario. We characterize the packet error rate (PER), throughput, and delay performance of chase combining HARQ (CC-HARQ) and incremental redundancy HARQ (IR-HARQ) in AWGN and Rayleigh fading channel with $m$ retransmissions. Furthermore, we consider a quasi-static fading channel model, which is more accurate than the over-simplified i.i.d. block fading or same channel assumption ove…
The existing investigations on artificial noise (AN) security systems assumed that only null spaces is used to send AN signals, and all eigen-subchannels should be used to transmit messages. Our previous work proposed an AN scheme that allocates some of eigen-subchannels to transmit AN signals for improving secrecy rates. Nevertheless, our previous work considered only uncorrelated MIMO Rayleigh fading channels. In fact, the correlations among antennas exist in realistic scattering channel environments. In this paper, we extend our previous AN scheme to spatially correlated Rayleigh fading cha…
Through ordinary transmissions over wireless multicast networks are greatly hampered due to the simultaneous presence of fading and shadowing of wireless channels, secure transmissions can be enhanced by properly exploiting random attributes of the propagation medium. This study focuses on the utilization of those attributes to enhance the physical layer security (PLS) performance of a dual-hop wireless multicast network over kappa-mu shadow-fading channel under the wiretapping attempts of multiple eavesdroppers. In order to improve the secrecy level, the best relay selection strategy among mu…
The secrecy capacity of the type II wiretap channel (WTC II) with a noisy main channel is currently an open problem. Herein its secrecy-capacity is derived and shown to be equal to its semantic-security (SS) capacity. In this setting, the legitimate users communicate via a discrete-memoryless (DM) channel in the presence of an eavesdropper that has perfect access to a subset of its choosing of the transmitted symbols, constrained to a fixed fraction of the blocklength. The secrecy criterion is achieved simultaneously for all possible eavesdropper subset choices. The SS criterion demands neglig…
