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Symbol-level iterative information set decoding of RS codes

ALEXANDRIA ENGINEERING JOURNAL 2023年 73卷 1-10页

作者： Genga, Yuval Oyerinde, Olutayo Versfeld, Jaco Univ Witwatersrand Sch Elect & Informat Engn Johannesburg South Africa Stellenbosch Univ Dept Elect & Elect Engn Matieland South Africa

This paper presents the implementation of a low-complex iterative symbol-level decoding scheme for Reed-Solomon codes. Most soft-decision iterative decoders for Reed-Solomon codes work on a bit level due to the efficient passing of soft information due to the sparsity of the binary parity check matrix. These decoders yield a good error correction performance, but this comes at the cost of an increased computational complexity resulting from working at a bit-level. This study aims to lower the computational complexity of iterative decoding of Reed-Solomon codes by intro-ducing a high-performance soft-decision iterative Reed-Solomon decoder that works on a symbol -level, in contrast to the bit-level implementation used in most iterative Reed-Solomon decoders. The proposed algorithm utilises soft information to decode while applying information set decoding techniques to an extended parity check matrix. The use of the extended parity check matrix provides additional parity check equations which assist the algorithm in determining the correct information set of symbols used in the decoding process. For a given on;k thorn Reed-Solomon code, the algorithm converges to a valid codeword by correctly decoding a specified information set of k symbols from the received vector. Simulations run show the proposed algorithm performs favourably when com-pared to other symbol-level iterative decoders while working at a relatively lower complexity.(c) 2023 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY-NC-ND license (http://***/ licenses/by-nc-nd/4.0/).

关键词： Reed Solomon codes Soft-input soft-output decoding Iterative decoding message passing decoding Information set decoding decoding complexity

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Analysis and Design of Binary message passing Decoders

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IEEE TRANSACTIONS ON COMMUNICATIONS 2012年第3期60卷 601-607页

作者： Lechner, Gottfried Pedersen, Troels Kramer, Gerhard Univ S Australia Inst Telecommun Res Adelaide SA 5001 Australia Aalborg Univ Dept Elect Syst Sect Nav & Commun NavCom Aalborg Denmark Univ So Calif Los Angeles CA USA Alcatel Lucent Bell Labs Murray Hill NJ USA

Binary message passing decoders for low-density parity-check codes are studied by using extrinsic information transfer charts. The channel delivers hard or soft decisions and the variable node decoder performs all computations in the log-likelihood ratio ( L-value) domain. A hard decision results in the Gallager B algorithm and examples show that increasing the channel output alphabet to two bits gains more than 1.0 dB in signal to noise ratio when using optimized codes. Finally, it is shown that errors on cycles consisting only of degree two and three variable nodes cannot be corrected and a necessary and sufficient condition for the existence of a cycle-free subgraph is derived.

关键词： Extrinsic information transfer charts Gallager B algorithm low-density parity-check codes message passing decoding

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Analysis of Absorbing Sets and Fully Absorbing Sets of Array-Based LDPC Codes

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IEEE TRANSACTIONS ON INFORMATION THEORY 2010年第1期56卷 181-201页

作者： Dolecek, Lara Zhang, Zhengya Anantharam, Venkat Wainwright, Martin J. Nikolic, Borivoje MIT Dept Elect Engn & Comp Sci Cambridge MA 02139 USA Univ Calif Berkeley Dept Elect Engn & Comp Sci Berkeley CA 94720 USA

The class of low-density parity-check (LDPC) codes is attractive, since such codes can be decoded using practical message-passing algorithms, and their performance is known to approach the Shannon limits for suitably large block lengths. For the intermediate block lengths relevant in applications, however, many LDPC codes exhibit a so-called "error floor," corresponding to a significant flattening in the curve that relates signal-to-noise ratio (SNR) to the bit-error rate (BER) level. Previous work has linked this behavior to combinatorial substructures within the Tanner graph associated with an LDPC code, known as (fully) absorbing sets. These fully absorbing sets correspond to a particular type of near-codewords or trapping sets that are stable under bit-flipping operations, and exert the dominant effect on the low BER behavior of structured LDPC codes. This paper provides a detailed theoretical analysis of these (fully) absorbing sets for the class of C-p,C-gamma array-based LDPC codes, including the characterization of all minimal (fully) absorbing sets for the array-based LDPC codes for gamma = 2, 3, 4, and moreover, it provides the development of techniques to enumerate them exactly. Theoretical results of this type provide a foundation for predicting and extrapolating the error floor behavior of LDPC codes.

关键词： Absorbing set bit-flipping error floor low-density parity-check (LDPC) codes message passing decoding near-codeword trapping set

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Joint Uplink-Downlink Cooperative Interference Management With Flexible Cell Associations

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IEEE TRANSACTIONS ON COMMUNICATIONS 2020年第9期68卷 5420-5434页

作者： Singhal, Manik Seyfi, Tolunay Gamal, Aly El Purdue Univ Elect & Comp Engn ECE Dept W Lafayette IN 47907 USA

We study information theoretic models of interference networks that consist of K Base Station (BS) - Mobile Terminal (MT) pairs. BS i is connected to the MTs with indices in the set {i, i + 1,..., i + L}. We fix the value of L and study the per user Degrees of Freedom (puDoF) in large networks. We assume that each MT can be associated with Nc BSs, and these associations are determined by a cloud-based controller that has a global view of the network. AnMT has to be associated with a BS, for the BS to transmit its message in the downlink, or have its decoded message in the uplink. We propose puDoF inner bounds for arbitrary values of L for the uplink, and prove their optimality when only zero-forcing schemes are allowed. We then introduce new achievable average uplink-downlink puDoF values, and show their optimality for the range when N-c <= L/2 and when we restrict our attention to zero-forcing schemes. Additionally, for the remaining range, we characterize the optimal downlink scheme when the uplink-optimal associations are used. Finally, we show that the proposed scheme is information theoretically optimal for Wyner's linear interference network.

关键词： message passing decoding uplink-downlink duality Cloud Radio Access Networks (C-RAN) locally connected networks information theoretic converse

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Analysis of Verification-Based decoding on the q-ary Symmetric Channel for Large q

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IEEE TRANSACTIONS ON INFORMATION THEORY 2011年第10期57卷 6754-6770页

作者： Zhang, Fan Pfister, Henry D. Texas A&M Univ Dept Elect & Comp Engn College Stn TX 77843 USA

Anew verification-based message-passing decoder for low-density parity-check (LDPC) codes is introduced and analyzed for the q-ary symmetric channel (q-SC). Rather than passing messages consisting of symbol probabilities, this decoder passes lists of possible symbols and marks some lists as verified. The density evolution (DE) equations for this decoder are derived and used to compute decoding thresholds. If the maximum list size is unbounded, then one finds that any capacity-achieving LDPC code for the binary erasure channel can be used to achieve capacity on the q-SC for large q. The decoding thresholds are also computed via DE for the case where each list is truncated to satisfy a maximum list-size constraint. Simulation results are also presented to confirm the DE results. During the simulations, we observed differences between two verification-based decoding algorithms, introduced by Luby and Mitzenmacher, that were implicitly assumed to be identical. In this paper, the node-based algorithms are evaluated via analysis and simulation. The probability of false verification (FV) is also considered and techniques are discussed to mitigate the FV. Optimization of the degree distribution is also used to improve the threshold for a fixed maximum list size. Finally, the proposed algorithm is compared with a variety of other algorithms using both density evolution thresholds and simulation results.

关键词： False verification list decoding low density parity check codes message passing decoding q-ary symmetric channel verification decoding

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On the bit-error rate of product accumulate codes in optical fiber communications

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JOURNAL OF LIGHTWAVE TECHNOLOGY 2004年第2期22卷 640-646页

作者： Li, J Cai, Y Narayanan, KR Lucero, A Pilipetskii, A Georghiades, CN Lehigh Univ Dept Elect & Comp Engn Bethlehem PA 18015 USA Texas A&M Univ Dept Elect Engn College Stn TX 77843 USA Tyco Telecommun Eatontown NJ 07724 USA

Product accumulate (PA) codes were proposed as a class of high-rate low-complexity, capacity-approaching codes on additive white Gaussian noise (AWGN) channels. In this paper, we investigate the performance of the PA codes on intensity modulated optical fiber channels where the amplified spontaneous emission (ASE) noise dominates all other noise sources. We consider binary ON-OFF keying (OOK) modulation and iterative soft-decision message-passing decoding for the PA codes. Three channel models for the ASE noise dominated channel are investigated: asymmetric chi-square, asymmetric Gaussian, and symmetric Gaussian channels (i.e., AWGN). At low signal-to-noise ratios (SNRs), due to the lack of tight bounds, code performance is evaluated using simulations of typical PA coding schemes. For high SNRs that are beyond simulation capabilities, we derive the pairwise error probability of the three channels and explore an average upper bound on the bit-error rate over the ensemble of PA codes. We show that AWGN channels, although fundamentally different from chi-square channels, can serve as a reference to approximate the performance of high-rate PA codes.

关键词： amplified spontaneous emission (ASE) noise forward-error correction (FEC) iterative decoding message passing decoding optical fiber communication serially concatenated codes union bounds

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Compressed FEC Codes With Spatial-Coupling

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IEEE COMMUNICATIONS LETTERS 2017年第5期21卷 987-990页

作者： Liang, Chulong Ma, Junjie Ping, Li City Univ Hong Kong Dept Elect Engn Hong Kong Hong Kong Peoples R China Columbia Univ Dept Stat New York NY 10027 USA

An error floor problem is observed for a spatially coupled sparse-regression (SCSR) code with limited sparsity in low-to-medium rates. This letter presents a scheme that also involves spatial-coupling and compressed-sensing (SCCS) similar to SCSR. We replace position modulation in SCSR by a general concatenated forward error control code. We introduce a chaining principle that improves the error floor behavior of the underlying code. We show that SCCS based on chained Hadamard codes can offer significantly improved performance.

关键词： Approximate message passing (AMP) compressed sensing concatenated codes Hadamard codes message passing decoding sparse-regression (SR) codes spatial coupling (SC) turbo codes

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Channel Coding Toward 6G: Technical Overview and Outlook

IEEE OPEN JOURNAL OF THE COMMUNICATIONS SOCIETY

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IEEE OPEN JOURNAL OF THE COMMUNICATIONS SOCIETY 2024年 5卷 2585-2685页

作者： Rowshan, Mohammad Qiu, Min Xie, Yixuan Gu, Xinyi Yuan, Jinhong Univ New South Wales Sch Elect Engn & Telecommun Sydney NSW 2052 Australia

Channel coding plays a pivotal role in ensuring reliable communication over wireless channels. With the growing need for ultra-reliable communication in emerging wireless use cases, the significance of channel coding has amplified. Furthermore, minimizing decoding latency is crucial for critical-mission applications, while optimizing energy efficiency is paramount for mobile and the Internet of Things (IoT) communications. As the fifth generation (5G) of mobile communications is currently in operation and 5G-advanced is on the horizon, the objective of this paper is to assess prominent channel coding schemes in the context of recent advancements and the anticipated requirements for the sixth generation (6G). In this paper, after considering the potential impact of channel coding on key performance indicators (KPIs) of wireless networks, we review the evolution of mobile communication standards and the organizations involved in the standardization, from the first generation (1G) to the current 5G, highlighting the technologies integral to achieving targeted KPIs such as reliability, data rate, latency, energy efficiency, spectral efficiency, connection density, and traffic capacity. Following this, we delve into the anticipated requirements for potential use cases in 6G. The subsequent sections of the paper focus on a comprehensive review of three primary coding schemes utilized in past generations and their recent advancements: low-density parity-check (LDPC) codes, turbo codes (including convolutional codes), and polar codes (alongside Reed-Muller codes). Additionally, we examine alternative coding schemes like Fountain codes (also known as rate-less codes), sparse regression codes, among others. Our evaluation includes a comparative analysis of error correction performance and the performance of hardware implementation for these coding schemes, providing insights into their potential and suitability for the upcoming 6G era. Lastly, we will briefly explore consider

关键词： Codes 5G mobile communication 3GPP 6G mobile communication Reliability Iterative decoding 3G mobile communication Channel coding error control coding error correction codes wireless mobile communications 5th generation 5G 6th generation 6G encoding decoding channel polarization polar codes PAD codes monomial codes CRC low-density parity-check codes LDPC codes convolutional codes turbo codes spatially coupled codes fountain codes spinal codes raptor codes Luby transform codes LT codes lattice codes nonbinary codes sparse regression codes SPARC machine learning neural codes neural decoding successive cancellation decoding beleif propagation decoing message passing decoding BCJR decoding iterative decoding Viterbi decoding Fano decoding automorphism ensemble decoding min-sum algorithm bit-flipping PPV bound normal approximation coded modulation bit-interleaving puncturing shortening repetition ratecompatible codes application layer channel coding physical layer waveform non-terrestrial networks free space optical links modulation block error rate BLER frame error rate FER reliability latency complexity enhanced mobile broadband eMBB machine-type communications MTC ultra-reliable low-latency URLLC key performance indicator KPI hardware architecture waveform design

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Ensemble Analysis of Pseudocodewords of Protograph-Based Non-Binary LDPC Codes

Ensemble Analysis of Pseudocodewords of Protograph-Based Non...

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IEEE Information Theory Workshop (ITW)

作者： Divsalar, Dariush Dolecek, Lara CALTECH Jet Prop Lab 4800 Oak Grove Dr Pasadena CA 91109 USA Univ Calif Los Angeles Dept Elect Engn Los Angeles CA 90095 USA

ISBN: (纸本)9781457704376

This paper presents a method for evaluating pseudocodeword weight enumerators of nonbinary LDPC codes built out of protographs. The ensemble enumerators are evaluated for both the finite-length and infinite-length regimes. Results of this type can be particularly useful for designing structured nonbinary LDPC codes with good properties under message passing or linear programming decoding.

关键词： Conferences Iterative decoding Linear code Niobium Vectors binary codes decoding ensemble enumerator finite-length regime infinite-length regime linear codes linear programming linear programming decoding message passing decoding parity check codes protog

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Repeat accumulate coded modulation with partial iterative demapping

Repeat accumulate coded modulation with partial iterative de...

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International Symposium on Communications and Information Technologies (ISCIT2005)

作者： Chen, XQ Yu, P Yang, HW Yang, DC Beijing Univ Posts & Telecommun Sch Telecommun Engn Beijing 100088 Peoples R China

ISBN: (纸本)0780395387

Repeat Accumulate (RA) codes are the known simplest one among the family of the capacity-approaching codes. It is much simpler than Turbo codes and Low Density Parity Check (LDPC) codes, and hence is a competitive choice for the applications of B3G/3G or 4G systems. The main drawback of RA codes, the low code rate, can be overcome by concatenating RA codes with Wary modulations. In this paper, we have investigated the performance of RA coded modulation with iterative demapping (RACM-ID) and a sub-optimal algorithm referred to as RA coded modulation with partial iterative demapping (RACM-PID) is proposed. The algorithm is equivalent to reduce the degree of the modulation nodes which is the most calculation cost in the Tanner graph, and thus we have reduced a large part of the calculation complexity of iterative demapping (ID) while keeping the most of the performance gain due to ID. Simulation results are presented for 8PSK and 16QAM examples.

关键词： Repeat Accumulate (RA) codes M-ary modulations partial iterative demapping (PID) message passing decoding

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