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On Optimization and Analysis of enumerative Sphere Shaping for Short Blocklengths

JOURNAL OF LIGHTWAVE TECHNOLOGY 2022年第22期40卷 7265-7278页

作者： Chen, Yizhao Chen, Junda Li, Weihao Zhang, Mingming Liu, Deming Tang, Ming Huazhong Univ Sci & Technol Sch Cyber Sci & Engn Wuhan 430074 Peoples R China Huazhong Univ Sci & Technol Sch Opt & Elect Informat Natl Engn Lab Next Generat Internet Access Networ Wuhan 430074 Peoples R China

enumerative sphere shaping (ESS) has drawn considerable attention in recent years, yielding a practical solution for the application of probabilistic shaping in the short-blocklength regime. However, ESS suffers from some energy-efficiency degradation for binary transmission, because it orders sequences lexicographically. In this work, we propose the optimum ESS (OESS), as an optimized version of ESS, which can always achieve the lowest average energy at any blocklength. We conduct a comprehensive study on ESS and OESS in terms of energy efficiency, distribution, rate loss and practical performance. Moreover, we propose to use the reverse trellis to obtain the sequence energy distribution of ESS and OESS. Numerical analysis shows that OESS leads to better energy efficiency, as well as more Maxwell-Boltzmann-like distributions compared with ESS, yielding considerably lower rate loss. The effectiveness of OESS is verified by the Monte-Carlo simulation in the linear additive white Gaussian noise channel, and an experimental transmission in a single sideband discrete-Fourier-transform spread discrete multi-tone system. Compared with conventional constant composition distribution matcher, both ESS and OESS performs remarkably better for the short blocklengths. Moreover, OESS achieves observable gains over ESS for ultrashort blocklengths of 20 and 40.

关键词： Forward error correction Symbols Energy efficiency Amplitude shift keying Quadrature amplitude modulation Probabilistic logic Optical fiber networks Discrete multi-tone enumerative coding probabilistic shaping sphere shaping

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A post-processing for the enumerative code implementation of Ziv-Lempel incremental parsing

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IEICE TRANSACTIONS ON COMMUNICATIONS 2007年第11期E90B卷 3263-3265页

作者： Kawabata, Tsutomu Univ Electro Commun Dept Informat & Commun Engn Chofu Tokyo 1828585 Japan

Ziv-Lempel incremental parsing [1] is a fundamental algorithm for lossless data compression. There is a simple enumerative implementation [7] which preserves a duality between the encoder and the decoder. However, due to its compactness, the implementation when combined with a complete integer code, allows only an input sequence with a length consistent with the parsing boundaries. In this letter, we propose a simple additional mechanism for post-processing a binary file of arbitrary length, provided the file punctuation is externally managed.

关键词： Ziv-Lempel algorithm enumerative coding post-processing issue

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Encoding of dklr-sequences using one weight set

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IEEE TRANSACTIONS ON INFORMATION THEORY 1996年第5期42卷 1553-1554页

作者： Patrovics, L Immink, KAS Philips Research Laboratories Eindhoven Netherlands

Traditional schemes for encoding and decoding runlength-constrained sequences using the enumeration principle require two sets of weighting coefficients, A new enumeration is presented requiring only one set of coeffi... 详细信息

关键词： enumerative coding runlength-limited sequences dk-constrained codes

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A Type-Aware coding Approach to Joint Source-Channel coding

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IEEE COMMUNICATIONS LETTERS 2021年第11期25卷 3454-3457页

作者： Yao, Xinyuanmeng 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 letter, we propose a type-aware coding approach to joint source-channel coding (JSCC) and present a concrete construction with polarization-adjusted convolutional (PAC) codes. A data sequence is first encoded by enumerative coding and then encoded by a data-dependent PAC code, resulting in a transmitted codeword. At the receiver, a type-search decoding algorithm is employed, and the implementation complexity can be reduced by searching only those typical types. Simulation results show that the presented JSCC scheme can outperform the conventional tandem coding scheme with a fixed-to-fixed-length source code and achieve a performance within the gap between the upper and lower bound on the minimum FER of finite-length JSCCs.

关键词： Codes Encoding Decoding Picture archiving and communication systems Indexes Convolutional codes Upper bound enumerative coding fixed-to-variable-length joint source-channel coding PAC codes type-aware coding

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A NEW IMPLEMENTATION OF THE ZIV-LEMPEL INCREMENTAL PARSING ALGORITHM

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IEEE TRANSACTIONS ON INFORMATION THEORY 1991年第5期37卷 1439-1440页

作者： KAWABATA, T YAMAMOTO, H Department of Communications and Systems University of Electro-Communications Tokyo Japan

Combining a note by Rissanen and an idea of enumerative coding we obtain a new implementation of the Ziv-Lempel incremental parsing algorithm for coding and decoding discrete data sequences.

关键词： ZIV-LEMPEL ALGORITHM enumerative coding

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A practical method for approaching the channel capacity of constrained channels

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IEEE TRANSACTIONS ON INFORMATION THEORY 1997年第5期43卷 1389-1399页

作者： Immink, KAS Research Laboratories Company Limited Eindhoven Netherlands

A new coding technique is proposed that translates user information into a constrained sequence using very long codewords, Huge error propagation resulting from the use of long codewords is avoided by reversing the conventional hierarchy of the error control code and the constrained code, The new technique is exemplified by focusing on (d, k)-constrained codes, A storage-effective enumerative encoding scheme is proposed for translating user data into long dh sequences and vice versa. For dk runlength-limited codes, estimates are given of the relationship between coding efficiency versus encoder and decoder complexity. We will show that for most common d, k values, a code rate of less than 0.5% below channel capacity can be obtained by using hardware mainly consisting of a ROM lookup table of size 1 kbyte. For selected values of d and k, the size of the lookup table is much smaller, The paper is concluded by an illustrative numerical example of a rate 256/466, (d = 2, k = 15) code, which provides a serviceable 10% increase in rate with respect to its traditional rate 1/2, (2,7) counterpart.

关键词： constrained code enumerative coding recording code runlength-limited

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Two-dimensional weight-constrained codes through enumeration bounds

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IEEE TRANSACTIONS ON INFORMATION THEORY 2000年第4期46卷 1292-1301页

作者： Ordentlich, E Roth, RM Icompress Inc Santa Clara CA 95051 USA Technion Israel Inst Technol Dept Comp Sci IL-32000 Haifa Israel

For a rational alpha is an element of (0, 1), let A(n x m, alpha) be the set of binary n x m arrays in which each row has Hamming weight alpha m and each column has Hamming weight alpha n, where alpha m and alpha n are integers. (The special case of two-dimensional balanced arrays corresponds to alpha = 1/2 and even values for n and m,) The redundancy of A(n x m, alpha) is defined by rho(n x m, alpha) = nmH(alpha) - log(2) \A(n x m, alpha)\ where H(x) = -x log(2) x - (1 - x) log(2)(1 - x), Bounds on rho(n x m, alpha) are obtained in terms of the redundancies of the sets A(l, alpha) of all binary e-vectors with Hamming weight alpha l, l is an element of {n, m}, Specifically, it is shown that rho(n x m, alpha) less than or equal to nP(m, alpha) + m rho(n, alpha) where rho(l, alpha) = lH(alpha) - log(2) \A(l, alpha)\ and that this bound is tight up to an additive term O(n + log m), A polynomial-time coding algorithm is presented that maps unconstrained input sequences into A(n x m, alpha) at a rate H(alpha) - (rho(m, alpha)/m).

关键词： balanced codes DC-free codes enumerative coding two-dimensional coding weight-constrained codes

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On Row-by-Row coding for 2-D Constraints

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IEEE TRANSACTIONS ON INFORMATION THEORY 2009年第8期55卷 3565-3576页

作者： Tal, Ido Etzion, Tuvi Roth, Ron M. Univ Calif San Diego Ctr Magnet Recording Res La Jolla CA 92093 USA Technion Israel Inst Technol Dept Comp Sci IL-32000 Haifa Israel

A constant-rate encoder-decoder pair is presented for a fairly large family of two-dimensional (2-D) constraints. Encoding and decoding is done in a row-by-row manner, and is sliding-block decodable. Essentially, the 2-D constraint is turned into a set of independent and relatively simple one-dimensional (1-D) constraints;this is done by dividing the array into fixed-width vertical strips. Each row in the strip is seen as a symbol, and a graph presentation of the respective I-D constraint is constructed. The maxentropic stationary Markov chain on this graph is next considered: a perturbed version of the corresponding probability distribution on the edges of the graph is used in order to build an encoder which operates in parallel on the strips. This perturbation is found by means of a network flow, with upper and lower bounds on the flow through the edges. A key part of the encoder is an enumerative coder for constant-weight binary words. A fast realization of this coder is shown, using floating-point arithmetic.

关键词： enumerative coding flow networks Kronecker product parallel encoding row-by-row coding runlength-limited (RLL) constraints two-dimensional (2-D) constraints

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Message encoding and retrieval for spread and cyclic orbit codes

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DESIGNS CODES AND CRYPTOGRAPHY 2018年第2期86卷 365-386页

作者： Horlemann-Trautmann, Anna-Lena Univ St Gallen Fac Math & Stat St Gallen Switzerland

Spread codes and cyclic orbit codes are special families of constant dimension subspace codes. These codes have been well-studied for their error correction capability, transmission rate and decoding methods, but the question of how to encode and retrieve messages has not been investigated. In this work we show how a message set of consecutive integers can be encoded and retrieved for these two code families.

关键词： Network coding Subspace codes enumerative coding Orbit codes Finite spreads Discrete logarithm

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Efficient coding schemes for the hard-square model

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IEEE TRANSACTIONS ON INFORMATION THEORY 2001年第3期47卷 1166-1176页

作者： Roth, RM Siegel, PH Wolf, JK Technion Israel Inst Technol Dept Comp Sci IL-32000 Haifa Israel Univ Calif San Diego Dept Elect & Comp Engn La Jolla CA 92093 USA Univ Calif San Diego Ctr Magnet Recording Res La Jolla CA 92093 USA

The hard-square model, also known as the two-dimensional (2-D) (1, infinity)-RLL constraint, consists of all binary arrays in which the 1 's are isolated both horizontally and vertically. Based on a certain probability measure defined on those arrays, an efficient variable-to-fixed encode;scheme is presented that maps unconstrained binary words into arrays that satisfy the hard-square model, For sufficiently targe arrays, the average rate of the encoder approaches a value which is only 0.1% below the capacity of the constraint. A second, fixed-rate encoder is presented whose rate for large arrays is within 1.2% of the capacity value.

关键词： constrained codes enumerative coding hard-square model maxentropic probability measure permutation codes two-dimensional (2-D) run-length-limited (RLL) constraints variable-to-fixed encoders

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