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IEEE Global Communications Conference (GLOBECOM)

作者： Gultekin, Yunus Can Willems, Frans M. J. Alvarado, Alex Eindhoven Univ Technol Informat & Commun Theory Lab Eindhoven Netherlands

ISBN: (纸本)9781665435406

Probabilistic amplitude shaping (PAS) is on track to become the de facto coded modulation standard for communication systems aiming to operate close to channel capacity at high transmission rates. The essential component of PAS that breeds this widespread interest is the amplitude shaping block, through which the channel input distribution is controlled. This block is responsible for converting bit strings into amplitude sequences with certain properties, e.g., fixed composition, limited energy, limited energy variation, etc. Recently, band-trellis enumerative sphere shaping (B-ESS) was introduced as an amplitude shaping technique that achieves limited energy variations which is useful in optical communication scenarios. B-ESS operates based on a trellis diagram in which sequences with high energy variations are pruned. In this work, we study the implementation of B-ESS. We first show that thanks to the trellis structure obtained by this pruning, B-ESS can be implemented with very low storage complexity. The trellis computation is shown to be reduced to a set of recursive multiplications with a scalar factor. Then we show that this scalar factor can be adjusted such that the trellis computation is further simplified and realized with only binary shifts. This shift-based B-ESS (1) can be implemented for arbitrarily long blocklengths without incurring an increase in complexity, and (2) can operate in a streaming mode similar to convolutional coding.

关键词： Probabilistic Amplitude Shaping enumerative coding Streaming Encoder

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New extremal binary self-dual codes of length 58 as R₃-lifts from the shortened binary Hamming code

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JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS 2012年第9期349卷 2824-2833页

作者： Karadeniz, Suat Kaya, Abidin Fatih Univ Dept Math TR-34500 Istanbul Turkey

In this correspondence, a lift of the shortened binary [8,4,4] Hamming code to the ring R-3 is described. Using this lift, a family of self-dual codes over R-3 of length 7 are obtained. By taking the binary images of these codes and applying the extension method given in [15], 11 new extremal binary self-dual [58,29,10] codes with new weight enumerators are found which were not previously known to exist. (c) 2012 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

关键词： coding theory EXTREMAL problems (Mathematics) BINARY system (Mathematics) MATHEMATICAL analysis DUAL-coding hypothesis enumerative coding

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A New Joint Source-Channel coding for Short-Packet Communications

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IEEE TRANSACTIONS ON COMMUNICATIONS 2024年第1期72卷 28-37页

作者： Wang, Qianfan Chen, Yanzhi Liang, Jifan Ma, Xiao Sun Yat Sen Univ Sch Comp Sci & Engn Guangzhou 510006 Peoples R China Sun Yat Sen Univ Guangdong Key Lab Informat Secur Technol Guangzhou 510006 Peoples R China

In this paper, we propose a new joint source-channel coding (JSCC) for short-packet communications, especially for the uplink from the sensor to the base station. At the transmitter, the sensing information is first encoded by a two-stage description, referred to as classified enumerative (CE) coding, and then encoded by a random multiple-rate code. The two-stage CE coding describes a binary sequence by its type class indicator and its rank in the associated type class, which can approach the entropy for biased sources. The random multiple rate coding transforms the variable-length output of the CE coding into a fixed-length channel input, allocating lower energy to lower-rate component codes. At the receiver, the sensing information can be recovered by a trial-and-error (for type classes) decoding either serially or parallelly. The serial decoding has a low implementation complexity, while the parallel decoding has a low decoding delay. To alleviate the mis-correction probability and stop the decoding earlier, we turn to the cyclic redundancy check (CRC) coding. To predict the performance of the proposed JSCC scheme, we present the weighted random-coding union (RCU) bounds based on the conventional RCU bound. The proposed JSCC scheme is universal in the sense that it does not require knowledge of source statistics. Simulation results show that the performance matches well with the presented bounds, validating our analysis. Simulation results also show that the proposed JSCC scheme can outperform the double polar JSCC scheme (exhibiting a coding gain of up to 0.3 dB) and can approach the JSCC bounds (exhibiting a gap of less than 0.5 dB).

关键词： Encoding Codes Sensors Maximum likelihood decoding Receivers Uplink Transmitters enumerative coding joint source-channel coding (JSCC) locally constrained ordered statistic decoding (LC-OSD) random codes short-packet communications weighted random-coding union (RCU) bounds

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Optimal block codes for M-ary Runlength-constrained channels

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IEEE TRANSACTIONS ON INFORMATION THEORY 2001年第5期47卷 2069-2078页

作者： Datta, S McLaughlin, SW Georgia Inst Technol Sch Elect & Comp Engn Atlanta GA 30332 USA

In this work, we consider the analysis and design of optimal block-decodable M-ary runlength-limited (RLL) codes. We present two general construction methods: one based on permutation codes due to Datta and McLaughlin, and the other, a nonbinary generalization of the binary enumeration methods of Patrovics and Immink, and Gu and Fuja, The construction based on permutation codes is simple and asymptotically (in block length) optimal, while the other construction is optimal in the sense that the resulting codes have the highest rate among all block-decodable codes for any block length. In the process, we shall also extend a result due to Zehavi and Wolf on the capacity of binary (d, k) constraints to M-ary channels, Finally, we present examples of template codes: remarkably low-complexity (M, d, k) block codes which achieve the optimal rate without the use of enumeration.

关键词： enumerative coding nonbinary optical recording permutation codes runlength-limited (RLL) codes template codes

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A Novel Representation for Permutations

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IEEE TRANSACTIONS ON INFORMATION THEORY 2021年第3期67卷 1920-1927页

作者： Ri, Won-Ho Song, Ok-Hyon Kim Il Sung Univ Fac Math Pyongyang North Korea

In this paper, we present a variable-length binary code for permutations of degree n, where n is a power of 2. The Lehmer code and its variants provide a bijection between permutations and the indexes in lexicographic ordering. They provide compression of permutations approaching Shannon bound at the expense of structural information. The variable-length code proposed in this paper has asymptotically optimal compression capability while preserving structural information of permutations. In other words, the code encodes the way a permutation is organized, and is optimal in the sense that the ratio of average codeword length and the entropy of permutations approaches 1 as n tends to infinity. The encoding and decoding are efficient. Like the Lehmer code and other enumerative codes, it is not necessary to construct look-up tables. The code is complete and satisfies the prefix condition. Furthermore, the codeword length indicates how "well shuffled" a permutation is. Permutations with longer codewords seem more "random." An enumeration method of the variable-length code is also given by using T. Cover's enumerative coding scheme and Schalkwijk code. This gives a different indexing from the Lehmer code. This work can be extended to the case of arbitrary n in a straightforward way.

关键词： Variable-length code permutation code enumerative coding source coding

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Nonblock coding of Binary Sources by Probabilistic Enumeration

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IEEE TRANSACTIONS ON INFORMATION THEORY 2011年第9期57卷 6170-6179页

作者： Teuhola, Jukka Univ Turku Dept Informat Technol SF-20500 Turku Finland

A simple and efficient nonblock coding scheme for binary sources is suggested. It uses a probability model to map any source string to a unique integer, and thereby defines an enumeration of all possible strings. Contrary to normal enumerative coding, the new method is noncombinatorial and operates sequentially, incrementing the code value symbol by symbol, by simple arithmetic. It is akin to arithmetic coding but does not use intervals. For memoryless sources, the redundancy per symbol is shown to be asymptotically less than p(3) bits, where p is the smaller of symbol probabilities. Especially, for integer-valued 1/p, the code is asymptotically optimal. These results are confirmed by both analysis and experiments with arbitrary-precision arithmetic. In a practical implementation, the source is partitioned into substrings enabling restricted-precision arithmetic. Thanks to subtle implicit coding, the additional redundancy is marginal. The source model can be also context-based, and even adaptivity can be incorporated. A peculiarity of the method is that decoding is done backwards (LIFO). Hence, for higher-order models, the string suffix, not prefix, is used as the context domain. The speed of the practical version is close to that of binary arithmetic coders.

关键词： Arithmetic coding binary source enumerative coding nonblock coding source coding

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An enumerative method for runlength-limited codes: Permutation codes

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IEEE TRANSACTIONS ON INFORMATION THEORY 1999年第6期45卷 2199-2204页

作者： Datta, S McLaughlin, SW Georgia Inst Technol Sch Elect & Comp Engn Atlanta GA 30332 USA

Permutation codes, introduced by Slepian, were shown to perform well on an additive white Gaussian noise (AWGN) channel. Unfortunately, these codes required large lookup tables, making them quite complex to implement even though the maximum-likelihood decoder is very simple. In this correspondence, we present an enumeration scheme which encodes and decodes permutation codes with low complexity. We concentrate on the use of permutation codes for constructing high-rate codes that satisfy runlength-limited constraints. Wolf showed that permutation codes can be used for runlength constraints and that they have rate that asymptotically achieves the capacity of a noiseless, runlength-limited constrained channel. Wolf, however, gave no efficient encoders/decoder. Our code construction is enumerative, but unlike other enumerative codes, has storage requirements that are a function of the runlength parameters d and k instead of the block length n. In addition, these codes have error detection and correction capabilities. Finally, we use this approach to construct (0, G/I) codes whereby all, odd-numbered occurrences of double-adjacent errors are detected. As an example, a 99.2% efficient, rate 496/528, (0, 6/3) code is presented.

关键词： enumerative coding magnetic recording permutation codes runlength-limited codes

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A UNIVERSAL VARIABLE-TO-FIXED LENGTH SOURCE CODE BASED ON LAWRENCE ALGORITHM

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IEEE TRANSACTIONS ON INFORMATION THEORY 1992年第2期38卷 247-253页

作者： TJALKENS, TJ WILLEMS, FMJ Faculty of Electrical Engineering Eindhovan University of Technology Eindhoven Netherlands

The Lawrence algorithm is a universal binary variable-to-fixed length source coding algorithm. Here, a modified version of this algorithm is introduced and its asymptotic performance is investigated. For M (the segment set cardinality) large enough, it is shown that the rate R(theta) as a function of the source parameter-theta satisfies R(theta) almost-equal-to h(theta . (1 + log log M/2 log M), for 0 < theta < 1. Here h( . ) is the binary entropy function. In addition to this, it is proven that no codes exist that have a better asymptotic performance, thereby establishing the asymptotic optimality of our modified Lawrence code. The asymptotic bounds show that universal variable-to-fixed length codes can have a significantly lower redundancy than universal fixed-to-variable length codes with the same number of codewords.

关键词： UNIVERSAL SOURCE coding enumerative coding VARIABLE-TO-FIXED LENGTH CODES ASYMPTOTIC REDUNDANCY

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Binary cyclic-gap constant weight codes with low-complexity encoding and decoding

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DESIGNS CODES AND CRYPTOGRAPHY 2024年第12期92卷 4247-4277页

作者： Sasidharan, Birenjith Viterbo, Emanuele Dau, Son Hoang Monash Univ ECSE Dept Clayton Vic Australia RMIT Univ Melbourne Vic Australia

In this paper, we focus on the design of binary constant weight codes that admit low-complexity encoding and decoding algorithms, and that have size M=2k\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$M=2<^>k$$\end{document} so that codewords can conveniently be labeled with binary vectors of length k. For every integer & ell;>= 3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ell \ge 3$$\end{document}, we construct a (n=2 & ell;,M=2k & ell;,d=2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(n=2<^>\ell , M=2<^>{k_{\ell }}, d=2)$$\end{document} constant weight code C[& ell;]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{{\mathcal {C}}}}[\ell ]$$\end{document} of weight & ell;\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ell $$\end{document} by encoding information in the gaps between successive 1's of a vector, and call them as cyclic-gap constant weight codes. The code is associated with a finite integer sequence of length & ell;\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \us

关键词： Constant weight codes Cyclic-gap code Low complexity Nonlinear codes Binary codes enumerative coding

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Maximum runlength-limited codes with error control capabilities

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IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS 2001年第4期19卷 602-611页

作者： van Wijngaarden, AJ Immink, KAS Univ Essen Inst Expt Math Digital Commun Dept D-45326 Essen Germany

New methods are presented to protect maximum runlength-limited sequences against random and burst errors and to avoid error propagation. The methods employ parallel conversion techniques and enumerative coding algorithms that transform binary user information into constrained codewords. The new schemes have a low complexity and are very efficient. The approach can be used for modulation coding in recording systems and for synchronization and line coding in communication systems. The schemes enable the usage of high-rate constrained codes, as error control can be provided with similar capabilities as for unconstrained sequences.

关键词： burst correction codes enumerative coding forward error correction modulation coding Reed-Solomon codes runlength codes synchronization

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