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random coding error exponent for Dual-Hop Nakagami-m Fading Channels with Amplify-and-Forward Relaying

IEEE COMMUNICATIONS LETTERS 2009年第11期13卷 823-825页

作者： Ngo, Hien Quoc Quek, Tony Q. S. Shin, Hyundong Kyung Hee Univ Sch Elect & Informat Yongin 446701 Gyeonggi Do South Korea Inst Infocomm Res Singapore 138632 Singapore

We derive the random coding error exponent for dual-hop transmission over Nakagami-m fading channels with amplify-and-forward relaying. This information-theoretic measure allows us to determine the capacity and cutoff rate as well as to gain valuable insight into the inherent tradeoff between the communication reliability and transmission rate in such channels.

关键词： Amplify-and-forward relay Nakagami-m fading random coding error exponent

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Achievable Rate Analysis of Millimeter Wave Channels with random coding error exponent

Achievable Rate Analysis of Millimeter Wave Channels with Ra...

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IEEE International Conference on Communications (IEEE ICC)

作者： Huang, Shaocheng Xiao, Ming Royal Inst Technol KTH Sch Elect Engn & Comp Sci S-10044 Stockholm Sweden

ISBN: (纸本)9781538680889

Millimeter Wave (mmWave) communication has attracted massive attentions, since the abundant available bandwidth can potentially provide reliable communication with orders of magnitude capacity improvements relative to microwave. However, the achievable rate of mmWave channels under latency and reliability constraints is still not quite clear. We investigate the achievable rates of mmWave channels by random coding error exponent (RCEE) with finite blocklength. With imperfect channel state information at the receiver, the exact and approximate analytical expressions of the training based maximum achievable rate are derived to capture the relationship among rate-latency-reliability. Additionally, the relationship between the training based maximum achievable rate and bandwidth is investigated. We show that there exists critical bandwidth to maximize the training based maximum achievable rale for the non-line-of-sight (NLoS) propagation. Numerical results show that the approximate expression of the training based maximum achievable rate are tight and can capture the tendency at low SNRs. In addition, results show that for a given rate, one can reduce both packet duration and decoding error probability by increasing bandwidth. Results also suggest that in some mmWave bands, e.g. 57 - 64 GHz band, the performance, i.e., Gallager function, is significantly affected by frequency selective power absorption.

关键词： millimeter Wave random coding error exponent achievable rate latency reliability finite blocklength

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Physical-layer Network coding: A random coding error exponent Perspective

Physical-layer Network Coding: A Random Coding Error Exponen...

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2017 IEEE Information Theory Workshop (ITW)

作者： Ullah, Shakeel Salamat Liva, Gianluigi Liew, Soung Chang Chinese Univ Hong Kong Dept Informat Engn Hong Kong Hong Kong Peoples R China German Aerosp Ctr DLR Inst Commun & Networking Cologne Germany

ISBN: (纸本)9781509030972

In this work, we derive the random coding error exponent for the uplink phase of a two-way relay system where physical layer network coding (PNC) is employed. The error exponent is derived for the practical (yet sub-optimum) XOR channel decoding setting. We show that the random coding error exponent under optimum (i.e., maximum likelihood) PNC channel decoding can be achieved even under the sub-optimal XOR channel decoding. The derived achievability bounds provide us with valuable insight and can be used as a benchmark for the performance of practical channel-coded PNC systems employing low complexity decoders when finite-length codewords are used.

关键词： random coding bound random coding error exponent degraded channel XOR channel decoding physicallayer network coding

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random coding error exponents for flat fading channels with realistic channel estimation

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IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS 2000年第3期18卷 369-379页

作者： Ahmed, WKM McLane, PJ Lucent Technol Bell Labs Holmdel NJ 07733 USA Queens Univ Dept Elect & Comp Engn Kingston ON K7L 3N6 Canada

Recently, there has been a considerable interest in determining the limits to communications over multipath fading channels. However, most studies have assumed that the channel is perfectly known at the receiver. In this paper, the random coding error exponent for flat fading channels with realisitic channel state information (CSI) is studied. It is assumed that the CSI is obtained via some practical technique which utilizes a linear estimation scheme. Two commonly used techniques for channel estimation are considered in this paper, namely pilot tone extraction and pilot symbol transmission. The degradation in the achievable performance due to partial CSI is assessed and comparison of the different channel estimation methods is made. The focus of this paper is on the Jake's mobile Rayleigh flat fading model. Although Jake's model does not have a Markov property, such as that found in the commonly used exponential correlation model, which is usually attractive from the mathematical tractability point of view, Jake's model has a physical basis. Also, this model is considered herein from the standpoint of the random coding exponent. The results in this paper shed light on the amount of degradation in the achievable performance that is expected when the receiver has partial CSI, Finally, the sensitivity of the loss in achievable performance for the various channel estimation techniques with respect to channel parameters, such as Doppler spread and signal-to-noise ratio (SNR), is studied.

关键词： average power constraints channel capacity channel state information (CSI) channels with side information coding complexity fading channels random coding error exponent reliability function Rician fading model

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Achievable Rate Analysis of Millimeter Wave Channels Using random coding error exponents

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IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS 2022年第1期21卷 250-263页

作者： Huang, Shaocheng Xiao, Ming Poor, H. Vincent Natl Key Lab Sci & Technol Blind Signal Proc Chengdu 610041 Peoples R China KTH Royal Inst Technol Div Informat Sci & Engn S-10044 Stockholm Sweden Princeton Univ Dept Elect & Comp Engn Princeton NJ 08544 USA

With emerging applications, e.g., factory automation, autonomous driving and augmented/virtual reality, there have been increasing technical challenges regarding reliability, latency and data rates for existing communication systems. Owing to abundant available bandwidth, millimeter Wave (mmWave) communications can potentially provide reliable communication with an order of magnitude capacity improvement relative to microwave, e.g., sub 6 GHz communications. Though there are many research results showing improved throughputs, the latency and reliability performance of mmWave communications is still not quite clear, especially for finite blocklength regimes. In this paper, we investigate achievable rates of mmWave channels using random coding error exponents. Under the assumption of perfect and imperfect channel state information at the receiver (CSIR), exact and approximate analytical expressions of achievable rates are derived to capture the relationships among rate, latency and reliability. Furthermore, we show that the achievable rate always increases as the bandwidth increases with perfect CSIR. However, there exists a critical bandwidth that maximizes the achievable rate for non-line-of-sight mmWave signals with imperfect CSIR, beyond which the achievable rate will decrease with increasing bandwidth. For imperfect CSIR, the training symbol length and power allocation factor for maximizing the achievable rate at the training phase are investigated and closed-form expressions for special cases are derived.

关键词： Bandwidth Reliability Fading channels Millimeter wave communication MIMO communication Training Encoding Millimeter wave random coding error exponent achievable rate reliability latency

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Amplify-and-Forward Two-Way Relay Networks: error exponents and Resource Allocation

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IEEE TRANSACTIONS ON COMMUNICATIONS 2010年第9期58卷 2653-2666页

作者： Ngo, Hien Quoc Quek, Tony Q. S. Shin, Hyundong Kyung Hee Univ Dept Elect & Radio Engn Yonginsi 446701 Gyeonggi Do South Korea ASTAR Inst Infocomm Res Singapore 138632 Singapore

In a two-way relay network, two terminals exchange information over a shared wireless half-duplex channel with the help of a relay. Due to its fundamental and practical importance, there has been an increasing interest in this channel. However, there has been little work that characterizes the fundamental tradeoff between the communication reliability and transmission rate across all signal-to-noise ratios. In this paper, we consider amplify-and-forward (AF) two-way relaying due to its simplicity. We first derive the random coding error exponent for the link in each direction. From the exponent expression, the capacity and cutoff rate for each link are also deduced. We then put forth the notion of bottleneck error exponent, which is the worst exponent decay between the two links, to give us insight into the fundamental tradeoff between the rate pair and information-exchange reliability in the two-way relay network. As applications of the error exponent analysis to design a reliable AF two-way relay network, we present two optimization framework to maximize the bottleneck error exponent, namely: i) the optimal rate allocation under a sum-rate constraint and its closed-form quasi-optimal solution that requires only knowledge of the capacity and cutoff rate of each link;and ii) the optimal power allocation under a total power constraint and perfect global channel state information, which is shown equivalently to a quasi-convex optimization problem. Numerical results verify our analysis and the effectiveness of the optimal rate and power allocations in maximizing the bottleneck error exponent, i.e. the network information-exchange reliability.

关键词： Amplify-and-forward relaying bidirectional communication quasi-convex optimization random coding error exponent resource allocation two-way relay network

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Gallager's exponent for MIMO Channels: A Reliability-Rate Tradeoff

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IEEE TRANSACTIONS ON COMMUNICATIONS 2009年第4期57卷 972-985页

作者： Shin, Hyundong Win, Moe Z. MIT LIDS Cambridge MA 02139 USA

In this paper, we derive Gallager's random coding error exponent for multiple-input multiple-output (MIMO) Rayleigh block-fading channels, assuming no channel-state information (CSI) at the transmitter and perfect CSI at the receiver. This measure gives insight into a fundamental tradeoff between the communication reliability and information rate of MIMO channels, enabling to determine the required codeword length to achieve a prescribed error probability at a given rate below the channel capacity. We quantify the effects of the number of antennas, channel coherence time, and spatial fading correlation on the MIMO exponent. In addition, the general formulae for the ergodic capacity and the cutoff rate in the presence of spatial correlation are deduced from the exponent expressions. These formulae are applicable to arbitrary structures of transmit and receive correlation, encompassing all the previously known results as special cases of our expressions.

关键词： Block fading channel capacity cutoff rate multiple-input multiple-output (MIMO) system random coding error exponent spatial fading correlation

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error exponents analysis of dual-hop η-μ and κ-μ fading channel with amplify-and-forward relaying

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IET COMMUNICATIONS 2015年第11期9卷 1367-1379页

作者： Zhang, Yunhan Xue, Jiang Ratnarajah, Tharmalingam Zhong, Caijun Univ Edinburgh Inst Digital Commun Sch Engn Edinburgh EH9 3JL Midlothian Scotland Zhejiang Univ Inst Informat & Commun Engn Hangzhou Zhejiang Peoples R China Southeast Univ Natl Mobile Commun Res Lab Nanjing 210018 Jiangsu Peoples R China

In this study, the authors investigate the Gallager's error exponents of dual-hop amplify-and-forward systems over generalised eta-mu and kappa-mu fading channels, two versatile channel models which encompass a number of popular fading channels such as Rayleigh, Rician, Nakagami-m, Hoyt and one-sided Gaussian fading channels. The authors present new analytical expressions for the probability density function of the end-to-end signal-to-noise-ratio (SNR) of the system. These analytical expressions are then applied to analyse the system performance through the study of Gallager's exponents, which are classical tight bounds of error exponents and present the tradeoff between practical information rate and the reliability of communication. Two types of Gallager's exponents, namely, random coding error exponent and expurgated error exponent, are studied. Based on the newly derived analytical expressions, the authors provide an efficient method to compute the required codeword length to achieve a predefined upper bound of error probability. In addition, the analytical expressions are derived for the cutoff rate and ergodic capacity of the system. Moreover, simplified expressions are presented at the high SNR regime. All the analytical results are verified via Monte-Carlo simulations.

关键词： error analysis Rayleigh channels Rician channels Nakagami channels error statistics Monte Carlo methods error exponents analysis dual-hop η-μ and κ-μ fading channel dual-hop amplify-and-forward system amplify-and-forward relaying Rayleigh channel Rician channel Nakagami-m channel Hoyt channel one-sided Gaussian fading channel Gallager's exponents random coding error exponent expurgated error exponent error probability ergodic capacity Monte Carlo simulation

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Linear Multihop Amplify-and-Forward Relay Channels: error exponent and Optimal Number of Hops

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IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS 2011年第11期10卷 3834-3842页

作者： Hien Quoc Ngo Larsson, Erik G. Linkoping Univ Dept Elect Engn S-58183 Linkoping Sweden

We compute the random coding error exponent for linear multihop amplify-and-forward (AF) relay channels. Instead of considering only the achievable rate or the error probability as a performance measure separately, the error exponent results can give us insight into the fundamental tradeoff between the information rate and communication reliability in these channels. This measure enables us to determine what codeword length that is required to achieve a given level of communication reliability at a rate below the channel capacity. We first derive a general formula for the random coding exponent of general multihop AF relay channels. Then we present a closed-form expression of a tight upper bound on the random coding error exponent for the case of Rayleigh fading. From the exponent expression, the capacity of these channels is also deduced. The effect of the number of hops on the performance of linear multihop AF relay channels from the error exponent point of view is studied. As an application of the random coding error exponent analysis, we then find the optimal number of hops which maximizes the communication reliability (i.e., the random coding error exponent) for a given data rate. Numerical results verify our analysis, and show the tightness of the proposed bound.

关键词： Amplify-and-forward multihop relaying linear multihop relay channel random coding error exponent

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On the error exponent of Amplify and Forward Relay Networks

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IEEE COMMUNICATIONS LETTERS 2011年第10期15卷 1047-1049页

作者： Barua, Bappi Abolhasan, Mehran Safaei, Farzad Franklin, Daniel R. Univ Technol Sydney Fac Engn & IT Ultimo NSW 2007 Australia Univ Wollongong Fac Informat Wollongong NSW 2522 Australia

In this letter we derive the exact random coding error exponent of a dual hop amplify and forward (AF) relay network with channel state information (CSI) assisted ideal relay gain. Numerical results have been presented, which provide insight about the performance tradeoff between the error exponent and the data rate of the network. Finally we present the capacity analysis of this relay network.

关键词： random coding error exponent amplify and forward ergodic capacity

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