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Decoding of NB-ldpc codes Over Subfields

IEEE TRANSACTIONS ON COMMUNICATIONS 2021年第2期69卷 716-727页

作者： Wijekoon, Viduranga Bandara Viterbo, Emanuele Hong, Yi Monash Univ ECSE Dept Clayton Vic 3800 Australia

non-binary low-density parity-check (NB-ldpc) codes can offer promising performance advantages but suffer from high decoding complexity. To tackle this challenge, in this paper, we consider NB-ldpc codes over finite fields as codes over subfields as a means of reducing decoding complexity. In particular, our approach is based on a novel method of expanding a non-binary Tanner graph over a finite field into a graph over a subfield. This approach offers several decoding strategies for a single NB-ldpc code, with varying levels of performance-complexity trade-offs. Simulation results demonstrate that in a majority of cases, performance loss is minimal when compared with the complexity gains.

关键词： Decoding Additives Complexity theory Kernel Parity check codes Simulation Memory management non-binary ldpc codes graph expansion iterative decoding

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A Novel Graph Expansion and a Decoding Algorithm for NB-ldpc codes

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IEEE TRANSACTIONS ON COMMUNICATIONS 2020年第3期68卷 1358-1369页

作者： Wijekoon, V. B. Viterbo, Emanuele Hong, Yi Micheloni, Rino Marelli, Alessia Monash Univ Dept Elect & Comp Syst Engn Clayton Vic 3800 Australia Microsemi Microchip Corp Flash Signal Proc Labs I-20871 Vimercate Italy

non-binary low-density parity-check (NB-ldpc) codes are known to offer several advantages over their binary counterparts, but the higher complexity, and the resource-hungry nature of decoding algorithms have so far restricted their practical usage. In this paper, we propose a new decoding algorithm for NB-ldpc codes over finite fields of characteristic 2, based on a novel binary expansion of the Q-ary Tanner graph. While it offers substantial complexity gains, simulation results demonstrate that the performance loss of the new algorithm, in comparison to the best known decoder, is quite small. Furthermore, due to being based on a binary graph, it is particularly attractive for hardware implementations. We also suggest a simplified version of the algorithm, which offers even higher gains in complexity.

关键词： non-binary ldpc codes graph expansion iterative decoding

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nonbinary Protograph-Based ldpc codes Based on Additive Group of Finite Field

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IEEE COMMUNICATIONS LETTERS 2016年第4期20卷 636-639页

作者： Wang, Ruyan Li, Yong Zhao, Hui Chongqing Univ Posts & Telecommun Key Lab Opt Commun & Networks Chongqing 400065 Peoples R China

This letter proposes a flexible construction method of nonbinary protograph-based low-density parity-check codes based on finite field additive group operation from node perspective. First, nonzero element labels of nodes are optimized by minimum distance of corresponding binary image of rows of the parity-check matrix. Then, quasi-girth calculating method is proposed to jointly optimize node permutation label so as to improve global code's minimum distance upper bound. Simulation results illustrate the excellent performance of the proposed codes with adequately selected node's value label and permuting label.

关键词： non-binary ldpc codes protograph finite field minimum distance girth

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An Improved Reliability-Based Decoding Algorithm for NB-ldpc codes

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IEEE COMMUNICATIONS LETTERS 2021年第4期25卷 1153-1157页

作者： Song, Suwen Tian, Jing Lin, Jun Wang, Zhongfeng Nanjing Univ Sch Elect Sci & Engn Nanjing 210023 Peoples R China

When non-binary low-density parity-check (NB-ldpc) codes with low column weights are adopted, the iterative reliability-based majority-logic decoding (IRB-MLGD) algorithms suffer from severe performance degradation compared to message passing algorithms. In this brief, based on the improved iterative soft reliability-based (IISRB)-MLGD algorithm, we propose a perturbation-injected (P)-IISRB algorithm, where a regular perturbation is introduced to alleviate the periodic point problem that is the main reason for IISRB decoding failure. Compared with the conventional IISRB, the new algorithm significantly improves the decoding performance, lowering the error-floor by at least two orders of magnitude for the example code. Besides, instead of traditionally pre-computing and storing all the q-ary channel reliability measures, a real-time computing method is presented, which reduces the memory cost from O(q) to O(log(2) q).

关键词： Reliability Iterative decoding Perturbation methods Decoding Real-time systems Memory management Computational complexity Error-correction codes non-binary ldpc codes reliability-based decoding majority-logic decoding perturbation

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Optimized Trellis-Based Min-Max Decoder for NB-ldpc codes

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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II-EXPRESS BRIEFS 2020年第1期67卷 57-61页

作者： Tian, Jing Song, Suwen Lin, Jun Wang, Zhongfeng Nanjing Univ Sch Elect Sci & Engn Nanjing 210023 Jiangsu Peoples R China

non-binary low-density parity-check (NB-ldpc) codes outperform their binary counterparts in many cases. However, an NB-ldpc decoder usually requires excessive hardware resources and memory consumption. The trellis-based min-max decoding algorithm (TMMA), a well-known algorithm proposed in recent years, achieves good tradeoff between decoding performance and hardware complexity. Note that the check node processing unit (CNU) occupies the most hardware consumption. Based on the TMMA, many simplifications for the CNU have been developed with slight performance loss. The current TMMA with L truncations (L-TMMA) is promising for higher hardware efficiency than others. In this brief, based on the L-TMMA, we propose a new CNU design by incorporating algorithmic transformation and architectural optimization to further reduce the hardware complexity and thereby the critical path without any performance degradation. Synthesis results show that the proposed design achieves the lowest hardware consumption and the highest clock frequency with a small latency compared to the state-of-the-arts. Specifically, it saves more than 1/3 hardware resources compared with its original one.

关键词： Decoding Hardware Complexity theory Computer architecture Iterative decoding Circuits and systems Error correction codes non-binary ldpc codes iterative decoding min-max decoding algorithm low-complexity decoding VLSI

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Practical Coding Schemes based on ldpc codes for Distributed Parametric Regression

Practical Coding Schemes based on LDPC Codes for Distributed...

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2024 Information Theory Workshop

作者： Wei, Jiahui Dupraz, Elsa Mary, Philippe IMT Atlantique CNRS UMR 6285 Lab STICC Brest France Univ Rennes UMR CNRS INSA IETR Rennes France

ISBN: (纸本)9798350348941;9798350348934

In the framework of goal-oriented communications, this paper investigates parametric regression over coded data. For this problem, information-theoretic bounds are provided in terms of rate versus regression generalization error, by considering quantize and binning achievability schemes. Alternatively, this paper focuses on practical implementations by proposing a coding scheme that combines a scalar quantizer with a non-binary ldpc code for the binning part. Given that the ldpc decoder requires prior knowledge of the regression parameters, the paper introduces a novel method to estimate these parameters directly over the ldpc-coded syndrome, without the need for prior decoding. This technique allows to both address the regression task and initialize the ldpc decoder for further data reconstruction. Monte-Carlo simulations show the efficiency of the proposed approach in terms of regression generalization error.

关键词： Distributed source coding goal-oriented communications parametric regression non-binary ldpc codes

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Low Complexity Encoding of ldpc codes for High-Rate and High-Speed Communication

Low Complexity Encoding of LDPC Codes for High-Rate and High...

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1st International Conference on Distributed Frameworks and Applications

作者： Kim, Jeong Ki Balakannan, S. P. Lee, Moon Ho Kim, Chang Joo Chungbuk Natl Univ Div Elect & Informat Engn 664-14 Duckjin Dong 1Ga Jeonju 561756 South Korea ETRI Taejon 305701 South Korea

ISBN: (纸本)9781424423125

One of the weak points for ldpc encoding is the computational complexity in Communication System. An efficient encoding was presented by Richardson who approached making codeword by using parity check matrices with low density. In this paper, we focus on computational complexity of Richardson's ldpc matrix which is composed by matrix A, B, C, D, E and T. We propose two schemes for low complexity encoding. First one accomplishes T-1 = E = I and restricts D consisting of dual diagonal matrices and second one achieves T-1 = phi(-1) = I. Therefore the constraint reduces complexity from O(n +g(2)) to O(n) and efficiently omits some process of encoding. Also, we perform numerical experiments on our matrices. Proposed schemes can be useful for high-rate and high-speed communication systems due to reduced complexity and retrenched processes of encoding.

关键词： Efficient encoding non-binary ldpc codes GF(q) Circulant permutation matrices Computational complexity

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Gallager B Decoder on Noisy Hardware

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IEEE TRANSACTIONS ON COMMUNICATIONS 2013年第5期61卷 1660-1673页

作者： Yazdi, S. M. Sadegh Tabatabaei Cho, Hyungmin Dolecek, Lara Qualcomm Inc Ctr Res & Dev San Diego CA 92121 USA Univ Calif Los Angeles Dept Elect Engn Los Angeles CA 90095 USA Stanford Univ Dept Elect Engn & Comp Sci Stanford CA 94305 USA

Conventional communications theory assumes that the data transmission is noisy but the processing at the receiver is entirely error-free. Such assumptions may have to be revisited for advanced (silicon) technologies in which hardware failures are a major concern at the system-level. Hence, it is important to characterize the performance of a communication system with both noisy processing components and noisy data transmission. Coding systems based on low-density parity check (ldpc) codes are widely used for a variety of applications. In this paper, we focus on probabilistic analysis of the ldpc Gallager B decoder built out of faulty components. Using the density evolution technique, we find approximations for the optimal threshold of the decoder and the symbol error rate (SER) of the decoded sequence as functions of both the channel error rate and error rates of the decoder components, for both binary and non-binary regular ldpc codes. Furthermore, we study the convergence of the output SER and the decoding threshold of the decoder for different ranges of error rates. We verify our results using MATLAB simulations and hardware emulation of noisy decoders. Results presented in this paper can serve as systematic design guidelines in resource allocation for noisy decoders. Informed resource allocation is of particular relevance to emerging data storage and processing applications that need to maintain high levels of reliability despite hardware errors in advanced technologies.

关键词： Error analysis Gallager B algorithm faulty hardware ldpc codes non-binary ldpc codes

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Source Coding with Side Information at the Decoder and Uncertain Knowledge of the Correlation

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IEEE TRANSACTIONS ON COMMUNICATIONS 2014年第1期62卷 269-279页

作者： Dupraz, Elsa Roumy, Aline Kieffer, Michel Univ Paris 11 L2S CNRS SUPELEC F-91192 Gif Sur Yvette France INRIA F-35042 Rennes France Inst Univ France F-75013 Paris France

This paper considers the problem of lossless source coding with side information at the decoder, when the correlation model between the source and the side information is uncertain. Four parametrized models representing the correlation between the source and the side information are introduced. The uncertainty on the correlation appears through the lack of knowledge on the value of the parameters. For each model, we propose a practical coding scheme based on non-binary Low Density Parity Check codes and able to deal with the parameter uncertainty. At the encoder, the choice of the coding rate results from an information theoretical analysis. Then we propose decoding algorithms that jointly estimate the source vector and the parameters. As the proposed decoder is based on the Expectation-Maximization algorithm, which is very sensitive to initialization, we also propose a method to produce first a coarse estimate of the parameters.

关键词： Source coding with side information non-binary ldpc codes Expectation-Maximization algorithm

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Achieving Near Capacity of non-binary ldpc Coded Large MIMO Systems with a Novel Ultra Low-Complexity Soft-Output Detector

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IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS 2013年第10期12卷 5185-5199页

作者： Suthisopapan, Puripong Kasai, Kenta Meesomboon, Anupap Imtawil, Virasit Khon Kaen Univ Fac Engn Dept Elect Engn Khon Kaen Thailand Tokyo Inst Technol Grad Sch Sci & Engn Dept Commun & Integrated Syst Tokyo 1528550 Japan

Recently, it has been proved that both MMSE and MF detectors are near optimal detection for large scale MIMO systems, e.g., MIMO systems with hundreds of antennas. In order to attain near capacity region with reasonable complexity, lowcomplexity detector with soft-output generation is necessary for coded large MIMO systems. We show in this paper that the nonbinary ldpc codes and well-known soft-output MMSE detector can be utilized to significantly reduce the gap to capacity. We also propose a novel soft-output MF-based detector for the non-binary ldpc coded large MIMO systems. With this proposed detector, capacity approaching performance, i.e., the gap to capacity of 1.6 dB, can be achieved with ultra low-complexity detection, e.g., just 0.28% of MMSE detection. Moreover, use of the proposed scheme in large MIMO systems is found to be robust to the presence of imperfect channel estimation and spatial fading correlation which are both the realistic scenarios for large MIMO systems.

关键词： Large MIMO systems hundreds of antennas non-binary ldpc codes MMSE detection MF detection softoutput detection.

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