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Capacity-Approaching Protograph Codes

IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS 2009年第6期27卷 876-888页

作者： Divsalar, Dariush Dolinar, Sam Jones, Christopher R. Andrews, Kenneth CALTECH Jet Prop Lab Pasadena CA 91109 USA

This paper discusses construction of protograph-based low-density parity-check (LDPC) codes. Emphasis is placed on protograph ensembles whose typical minimum distance grows linearly with block size. Asymptotic performance analysis for both weight enumeration and iterative decoding threshold determination is provided and applied to a series of code constructions. Construction techniques that yield both low thresholds and linear minimum distance growth are introduced by way of example throughout. The paper also examines implementation strategies for high throughput decoding derived from first principles of belief propagation on bipartite graphs.

关键词： Protograph codes LDPC codes weight enumeration iterative decoding threshold rate-compatible codes decoder Implementation

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Construction of Protograph LDPC Codes Based on the Convolution Neural Network

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China Communications 2023年第5期20卷 84-92页

作者： Zhiyuan Xiao Liguang Li Jin Xu Jin Sha School of Electronic Science and Engineering Nanjing UniversityNanjing 210023China Institute of Wireless Research ZTE CorporationShenzhen 518055China

This paper presents an intelligent protograph construction *** LDPC codes have shown excellent error correction performance and play an important role in wireless *** search or manual construction are often used to obtain a good protograph,but the efficiency is not high enough and many experience and skills are *** this paper,a fast searching algorithm is proposed using the convolution neural network to predict the iterative decoding thresholds of protograph LDPC codes effectively.A special input data transformation rule is applied to provide stronger generalization *** proposed algorithm converges faster than other *** iterative decoding threshold of the constructed protograph surpasses greedy algorithm and random search by about 0.53 dB and 0.93 dB respectively under 100 times of density *** results show that quasi-cyclic LDPC(QC-LDPC)codes constructed from the proposed algorithm have competitive performance compared to other papers.

关键词： LDPC codes protograph codes iterative decoding threshold neural network

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A Method for Constructing Parity-Check Matrices of Quasi-Cyclic LDPC Codes Over GF(q)

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JOURNAL OF COMMUNICATIONS TECHNOLOGY AND ELECTRONICS 2018年第12期63卷 1524-1529页

作者： Kruglik, S. A. Potapova, V. S. Frolov, A. A. Skolkovo Inst Sci & Technol Moscow 121205 Russia Russian Acad Sci Kharkevich Inst Informat Transmiss Problems Moscow 127051 Russia

An algorithm for constructing parity-check matrices of non-binary quasi-cyclic low-density parity-check (NB QC-LDPC) codes is proposed. The algorithm finds short cycles in the base matrix and tries to eliminate them by selecting the circulants and the elements of GF(q). The algorithm tries to eliminate the cycles with the smallest number edges going outside the cycle. The efficiency of the algorithm is demonstrated by means of simulations. In order to explain the simulation results we also derive upper bounds on the minimum distance of NB QC-LDPC codes.

关键词： LDPC code parity-check matrix iterative decoding threshold Tanner graph cycle Galois field

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The Design of Rate-Compatible Protograph LDPC Codes

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IEEE TRANSACTIONS ON COMMUNICATIONS 2012年第10期60卷 2841-2850页

作者： Thuy Van Nguyen Divsalar, Dariush Univ Texas Dallas Dept Elect Engn Richardson TX 75083 USA CALTECH Jet Prop Lab Pasadena CA 91109 USA

This paper presents a simple yet effective method for designing nested families of LDPC codes. Rate compatible codes are essential for many communication applications, e. g. hybrid automatic repeat request (HARQ) systems, and their design is nontrivial due to the difficulty of simultaneously guaranteeing the quality of several related codes. Puncturing can be used to generate rate-compatible LDPC codes, but it produces a gap to capacity that, in practice, often significantly exceeds the gap of the mother code. We propose an alternative method based on successively extending a high-rate protograph. The resulting codes not only inherit the advantages of protograph codes, namely low encoding complexity and efficient decoding algorithms, but also cover a wide range of rates and have very good performance with iterative decoding thresholds that are within 0.2 dB of their capacity limits.

关键词： LPDC codes protograph codes rate-compatible iterative decoding threshold EXIT chart

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On Design of Protograph LDPC Codes for Large-Scale MIMO Systems

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IEEE ACCESS 2020年 8卷 46017-46029页

作者： Vu, Hieu D. Nguyen, Thuy V. Nguyen, Diep N. Nguyen, Hieu T. Posts & Telecommun Inst Technol Fac Informat Technol Hanoi 10000 Vietnam Univ Technol Sydney Sch Elect & Data Engn Ultimo NSW 2007 Australia Univ South Eastern Norway Dept Sci & Ind Syst Fac Technol Nat Sci & Maritime Sci N-3603 Kongsberg Norway

Protograph low-density parity-check (LDPC) codes and large-scale multi-input multi-output (LS-MIMO) systems have achieved great interest with various practical applications. However, how to effectively evaluate and design protograph LDPC codes for LS-MIMO systems remains a challenging yet critical problem, especially for low-latency applications. To solve that design challenge, the protograph extrinsic information transfer chart (PEXIT) algorithm for LS-MIMO systems, so-called LS-MIMO-PEXIT algorithm, is first derived based on the mutual information functions of messages that are passed on the joint MIMO detection and LDPC decoding graph. The proposed LS-MIMO-PEXIT algorithm plays a vital role in the optimization process of designing new protograph LDPC codes, tailored for LS-MIMO communications systems. Experiment results demonstrate that the analytical results based on the LS-MIMO-PEXIT algorithm are in good agreement with the simulation results under various input constraints, including the coding rate, the number of decoding iterations, and the LS-MIMO configuration. On top of that, the new protograph LDPC codes designed using our LS-MIMO-PEXIT algorithm achieve a coding gain from 0.2 dB at a low coding rate to 0.4 dB at a high coding rate in comparison with the state-of-the-art protograph codes in the literature. Additionally, we incorporate the practical design experience and the theoretical analysis of mutual functions into a two-step procedure to search for protograph LDPC codes that do not have error-floor behavior at frame error rate (FER) or bit error rate (BER) as low as respectively. Together with the coding gain, the error-floor-free feature of the proposed protograph LDPC codes is vitally important for future wireless networks where the ultra-reliability is one of the critical requirements.

关键词： Large-scale multiple-input multiple-output (LS-MIMO) protograph low-density parity-check (LDPC) codes channel coding protograph extrinsic information transfer chart iterative decoding threshold low latency

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Accumulate Repeat Accumulate Check Accumulate Codes

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IEEE TRANSACTIONS ON COMMUNICATIONS 2017年第11期65卷 4585-4599页

作者： Jeon, Ki Jun Kim, Kwang Soon Yonsei Univ Dept Elect & Elect Engn 50 Yonsei Ro Seoul 120749 South Korea

In this paper, a novel accumulate-repeat-accumulate-check-accumulate (ARACA) code is proposed as a subclass of protograph-based low-density parity-check (LDPC) codes. The key feature of the proposed ARACA code is represented by the outer connection doping in the protograph. This feature can provide the linear minimum distance growth (LMDG) property at a good iterative decoding threshold while maintaining an efficient encoder structure. The effect of the outer connection doping on the typical minimum distance, the iterative decoding threshold, and the LMDG property is discussed and analyzed by comparing case examples and using the asymptotic protograph ensemble weight enumerator. Some good ARACA code protographs are provided for a wide range of code rates. In addition, an efficient and universal encoding procedure and the corresponding encoder structure are provided for them. The performance of the proposed ARACA code is evaluated and compared with well-known good LDPC codes. The simulation results confirm the superiority of the proposed ARACA codes in terms of encoding complexity and frame error rate performance, especially at low-rates in an ultra-reliable regime.

关键词： ARACA codes protograph LDPC codes efficient encoder LMDG iterative decoding threshold

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On the Global and Local decoding of q-Ary SC-LDPC Codes With Moderate Coupling Length

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IEEE COMMUNICATIONS LETTERS 2021年第9期25卷 2815-2819页

作者： Zhu, Mingyang Jiang, Ming Zhao, Chunming Southeast Univ Natl Mobile Commun Res Lab Nanjing 210096 Peoples R China Purple Mt Labs Nanjing 211111 Peoples R China

This letter discusses a special type of q-ary spatially coupled low-density parity-check (SC-LDPC) codes with the potential for local decoding (LD). We demonstrate that q-ary SC-LDPCL (suffix "L" stands for locality) code ensembles have better decoding thresholds than the corresponding binary ensembles. We also develop local window decoding (LWD) to improve local decoding performance. The q-ary codes are constructed from low-order finite fields that guarantees relatively low complexity. The provided examples show that q-ary SC-LDPCL codes outperform the corresponding binary codes in both global and local decoding.

关键词： q-ary spatially coupled LDPC codes iterative decoding threshold global and local decoding

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Quasi-Cyclic Protograph-Based Raptor-Like LDPC Codes for Short Block-Lengths

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IEEE TRANSACTIONS ON INFORMATION THEORY 2019年第6期65卷 3758-3777页

作者： Ranganathan, Sudarsan V. S. Divsalar, Dariush Wesel, Richard D. Univ Calif Los Angeles Dept Elect & Comp Engn Los Angeles CA 90095 USA CALTECH Jet Prop Lab 4800 Oak Grove Dr Pasadena CA 91109 USA

Protograph-based Raptor-like low-density parity-check codes (PBRL codes) are a family of easily encodable rate-compatible low-density parity-check (LDPC) codes. PBRL codes have an excellent performance across all design rates. Quasi-cyclic (QC) PBRL code families permit high-speed decoder implementations. PBRL codes designed thus far, for both long and short block-lengths, have been based on optimizing the iterative decoding threshold of the protograph of the PBRL family at various design rates. This paper introduces a design method to obtain better QC PBRL code families at short block-lengths (of a few hundred bits) for low frame error rate (FER) requirements. We first select a protomatrix for the highest design rate. To add a new row to lower the rate, we keep all the previously obtained rows of the PBRL protomatrix fixed and select the new row that maximizes an upper bound on the minimum distance of any QC-LDPC code that can be obtained from the protomatrix. The new QC PBRL code families outperform the original PBRL codes at short block-lengths by providing a significantly better low-FER performance. The standard approach to computing the aforementioned upper bounds requires complexity that grows exponentially with the size of the protomatrix. However, we show that the structure of the PBRL protomatrix lets us obtain the upper bounds with complexity that grows only linearly with the size of the PBRL protomatrix. Using the complexity reduction results, we also establish an equivalence between the exhaustive search to design a new row for the PBRL protomatrix according to the new design method and an integer linear program.

关键词： Channel codes iterative decoding threshold LDPC codes minimum distance permanents PBRL codes Raptor codes rate-compatible codes

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