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Upper and lower bounds to estimate the random coding exponent for a peak-power-limited channel

IEEE TRANSACTIONS ON COMMUNICATIONS 2002年第1期50卷 16-20页

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

In this paper, we consider the estimation of Gallager's random coding exponent (RCE) for a peak power constraint at the transmitter for the two-dimensional fading channel with additive white Gaussian noise (AWGN) and with perfect channel estimation at the receiver. Despite the fact that many wireless channels are peak-power-limited, the RCE for such channels has not been considered previously in the literature. Such a problem has only been partially solved for the AWGN case due to the difficulty in finding an input signal distribution that yields the RCE. In this paper, we adopt a different approach in which we develop upper and lower bounds to the RCE with the hope of trapping it in a narrow region. Our quest is successful as we can estimate the RCE to an error of only 0.72 bit per modulation symbol. Furthermore, we find that the RCE for the peak-power-limited channel does not represent a severe degradation relative to that attained for the average-power-limited channel. Thus, good modulation and coding schemes at reasonable complexity should exist for a peak-power-constrained fading channel.

关键词： channel capacity fading channels peak and average power random coding exponent reliability function

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Extremality Properties for Gallager's random coding exponent

Extremality Properties for Gallager's Random Coding Exponent

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IEEE International Symposium on Information Theory

作者： Alsan, Mine Ecole Polytech Fed Lausanne LTHI I&C CH-1015 Lausanne Switzerland

ISBN: (纸本)9781467325790

We describe certain extremality properties for Gallager's reliability function E-0 for binary input symmetric DMCs. In particular, we show that amongst such DMC's whose E-0(rho(1)) has a given value for a given rho(1), the BEC and BSC have the largest and smallest value of the derivative of E-0(rho(2)) for any rho(2) >= rho(1). As the random coding exponent is obtained by tracing the map rho -> (E-0'(rho), E-0(rho) - rho E-0'(rho)) this conclusion includes as a special case the results of [1]. Furthermore, we show that amongst channels W with a given value of E-0(rho) for a given rho the BEC and BSC are the most and least polarizing under Arikan's polar transformations in the sense that their polar transforms W+ and W- has the largest and smallest difference in their E-0 values.

关键词： Channel reliability function random coding exponent channel polarization

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General random coding bounds: AWGN channels to MIMO fading channels

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ANNALS OF TELECOMMUNICATIONS 2010年第1-2期65卷 87-99页

作者： Lee, Heung-No Zhang, Jingqiao Choi, Cheon Won GIST Kwangju South Korea Amazon Com Seattle WA USA Dankook Univ Yongin South Korea

random coding bounds are obtained for multiple-input multiple-output (MIMO) fading channels. To derive the result in a compact and easy-to-evaluate form, a series of combinatorial codeword enumeration problems are solved for input-constrained MIMO fading channels. The bounds obtained in this paper are shown useful as performance prediction measures for MIMO systems which employ turbo-like block codes as the outer code to derive the space-time inner code. The error exponents for MIMO channels are also derived from the bounds, and then compared with the classical Gallager error exponents as well as the channel capacities. The random coding bounds associated with the maximum likelihood receiver exhibit good match with the extensive system simulation results obtained with a turbo-iterative receiver.

关键词： Union bound random coding exponent MIMO capacity

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random coding error exponents for two-dimensional flat fading channels with complete channel state information

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IEEE TRANSACTIONS ON INFORMATION THEORY 1999年第4期45卷 1338-1346页

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

In this correspondence, we consider the random coding error exponent for nondispersive two-dimensional (2-D) (quadrature) fading channels for which the channel state information (CSI) is perfectly known at the receiver and the input to the transmitter is constrained in its average power. Also, the effect of space diversity on improving the performance is demonstrated. The results obtained in this correspondence shed light on the effect of fading on communications reliability as well as the amount of coding complexity required to achieve a certain decoding error rate. A treatment for the random coding error exponent for time-correlated flat fading channels with Rayleigh fading and Bessel function correlation (the Jake's model) is also provided.

关键词： average and peak-power constraints coding complexity fading channels mobile fading model Nakagami fading model random coding exponent space diversity time-correlated fading

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Error exponent for Gaussian Channels With Partial Sequential Feedback

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IEEE TRANSACTIONS ON INFORMATION THEORY 2013年第8期59卷 4757-4766页

作者： Agarwal, Manish Guo, Dongning Honig, Michael L. Northwestern Univ Dept Elect Engn & Comp Sci Evanston IL 60208 USA

This paper studies the error exponent of block coding over an additive white Gaussian noise channel where a fraction (f) of the channel output symbols are revealed to the transmitter through noiseless feedback. If the code rate exceeds fC, where C is the channel capacity, then the probability of decoding error cannot decay faster than exponentially with block length. However, if the code rate is below fC, the error probability can decrease faster than exponentially with the block length, as with full feedback (f = 1). This is achieved by combining a feedback code and a forward error control code, and jointly decoding them at the receiver. This scheme can attain higher reliability than rate splitting in which feedback and forward codes independently encode separate source messages.

关键词： Error exponent feedback random coding exponent Schalkwijk-Kailath (SK) coding

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Exact exponent for Soft Covering

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IEEE TRANSACTIONS ON INFORMATION THEORY 2019年第10期65卷 6234-6262页

作者： Yagli, Semih Cuff, Paul Princeton Univ Dept Elect Engn Princeton NJ 08544 USA Renaissance Technol LLC Long Isl City NY 11733 USA

This paper establishes the exact exponents for the soft-covering phenomenon of a memoryless channel under the total variation metric when random (i.i.d. and constant-composition) channel codes are used. The exponents, established herein, are strict improvements in both directions on bounds found in the literature. This complements the recent literature establishing the exact exponents under the relative entropy metric;however, the proof techniques have significant differences, and thus, neither result trivially implies the other. The found exponents imply new and improved bounds for various problems that use soft-covering as their achievability argument, including new lower bounds for the resolvability exponent and the secrecy exponent in the wiretap channel.

关键词： Soft-covering lemma total variation distance channel resolvability random coding exponent random i.i.d. coding ensemble random constant-composition coding ensemble

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Exact Correct-Decoding exponent of the Wiretap Channel Decoder

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IEEE TRANSACTIONS ON INFORMATION THEORY 2014年第12期60卷 7606-7615页

作者： Merhav, Neri Technion Israel Inst Technol Dept Elect Engn IL-32000 Haifa Israel

The performance of the achievability scheme for Wyner's wiretap channel model is examined from the perspective of the probability of correct decoding, P-c, at the wiretap channel decoder. In particular, for finite-alphabet memoryless channels, the exact random coding exponent of P-c is derived as a function of the total coding rate R-1 and the rate of each subcode R-2. Two different representations are given for this function and its basic properties are provided. We also characterize the region of pairs of rates (R-1, R-2) of full security in the sense of the random coding exponent of P-c, in other words, the region where the exponent of this achievability scheme is the same as that of blind guessing at the eavesdropper side. Finally, an analogous derivation of the correct-decoding exponent is outlined for the case of the Gaussian channel.

关键词： Wiretap channel random coding exponent information-theoretic security secrecy

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Gallager's exponent Analysis of STBC MIMO Systems over η-μ and κ-μ Fading Channels

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IEEE TRANSACTIONS ON COMMUNICATIONS 2013年第3期61卷 1028-1039页

作者： Zhang, Jiayi Matthaiou, Michail Karagiannidis, George K. Wang, Haibo Tan, Zhenhui Beijing Jiaotong Univ Inst Broadband Wireless Mobile Commun Beijing 100044 Peoples R China Beijing Jiaotong Univ State Key Lab Rail Traff Control & Safety Beijing 100044 Peoples R China Chalmers Univ Technol Dept Signals & Syst SE-41296 Gothenburg Sweden Aristotle Univ Thessaloniki Dept Elect & Comp Engn Thessaloniki 54124 Greece Beijing Jiaotong Univ Inst Broadband Wireless Mobile Commun Sch Elect & Informat Engn Beijing 100044 Peoples R China

In this paper, we analytically investigate Gallager's exponent for space-time block codes over multiple-input multiple-output block-fading channels with Gaussian input distribution. As a suitable metric of the fundamental tradeoff between communication reliability and information rate, Gallager's exponent can be used to determine the required codeword length to achieve a prescribed error probability at a given rate below the channel capacity. We assume that the receiver has full channel state information (CSI), while the transmitter has no CSI and performs equal power allocation across all transmit antennas. In the following, novel exact expressions for Gallager's exponent are derived for two well-known channel fading models, namely eta-mu and k-mu fading models. More importantly, the implications of fading parameters and channel coherence time on Gallager's exponent are investigated. In addition, we present new expressions for the Shannon capacity, cutoff rate and expurgated exponent for the above mentioned fading models, while in the high signal-to-noise ratio regime, simplified closed-form expressions are also derived. Finally, we highlight the fact that the presented analysis encompasses all previously known results on Nakagami-m, Rician, Rayleigh and Hoyt fading channels, as special cases.

关键词： Capacity cutoff rate expurgated exponent MIMO fading channels random coding exponent

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The Generalized Stochastic Likelihood Decoder: random coding and Expurgated Bounds

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IEEE TRANSACTIONS ON INFORMATION THEORY 2017年第8期63卷 5039-5051页

作者： Merhav, Neri Technion Israel Inst Technol Dept Elect Engn IL-32000 Haifa Israel

The likelihood decoder is a stochastic decoder that selects the decoded message at random, using the posterior distribution of the true underlying message given the channel output. In this paper, we study a generalized version of this decoder, where the posterior is proportional to a general function that depends only on the joint empirical distribution of the output vector and the code word. This framework allows both mismatched versions and universal versions of the likelihood decoder, as well as the corresponding ordinary deterministic decoders, among many others. We provide a direct analysis method that yields the exact random coding exponent (as opposed to separate upper bounds and lower bounds that turn out to be compatible, which were derived earlier by Scarlett et al.). We also extend the result from pure channel coding to combined source and channel coding (random binning followed by random channel coding) with side information available to the decoder. Finally, returning to pure channel coding, we derive also an expurgated exponent for the stochastic likelihood decoder, which turns out to be at least as tight (and in some cases, strictly so) as the classical expurgated exponent of the maximum likelihood decoder, even though the stochastic likelihood decoder is suboptimal.

关键词： Stochastic decoder likelihood decoder random coding exponent expurgated exponent random binning source-channel coding

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ON coding WITHOUT RESTRICTIONS FOR THE AWGN CHANNEL

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IEEE TRANSACTIONS ON INFORMATION THEORY 1994年第2期40卷 409-417页

作者： POLYTREV, G Department of Electrical Engineering Tel-Aviv University Tel-Aviv Israel

Many coded modulation constructions, such as lattice codes, are visualized as restricted subsets of an infinite constellation (IC) of points in the n-dimensional Eudidean space. We shall regard an IC as a code without restrictions employed for the AWGN channel. For an IC the concept of coding rate is meaningless and we shall use, instead of coding rate, the normalized logarithmic density (NLD). The maximum value C(infinity) such that, for any NLD less than C(infinity), it is possible to construct an IC with arbitrarily small decoding error probability, will be called the generalized capacity of the AWGN channel without restrictions. We derive exponential upper and lower bounds for the decoding error probability of an IC, expressed in terms of the NLD. The upper bound is obtained by means of a random coding method and ft is very similar to the usual random coding bound for the AWGN channel. The exponents of these upper and lower bounds coincide for high values of the NLD, thereby enabling derivation of the generalized capacity of the AWGN channel without restrictions. It is also shown that the exponent of the random coding bound can be attained by linear IC's (lattices), implying that lattices play the same role with respect to the AWGN channel as linear codes do with respect to a discrete symmetric channel.

关键词： INFINITE CONSTELLATION LATTICE ERROR PROBABILITY random coding exponent AWGN CHANNEL

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