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A modified normalized min-sum algorithm for LDPC decoding using order statistics

INTERNATIONAL JOURNAL OF SATELLITE COMMUNICATIONS AND NETWORKING 2017年第2期35卷 163-175页

作者： Xue, Wen Ban, Tian Wang, Jianxin Nanjing Univ Sci & Technol Sch Elect & Opt Engn Nanjing 210094 Jiangsu Peoples R China

In this paper, we propose a new modified normalized min-sum algorithm for low-density parity-check decoding. Instead of normalizing the results of the check node renew calculations by a single modification factor, we use two different modification factors to normalize the results of check node renew calculations. One modification factor for the position of the first minimum value and another modification factor for other positions. We obtain two modification factors by theoretical analysis using the theory of order statistics. Simulation results show that the new modified normalized min-sun algorithm achieves better bit error rate performance than normalized min-sun algorithm without adding implementation complexity. Copyright (C) 2016 John Wiley & Sons, Ltd.

关键词： LDPC decode sum-product algorithm min-sum algorithm normalized MSA modified NMSA order statistics

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On implementation of min-sum algorithm and its modifications for decoding low-density parity-check (LDPC) codes

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IEEE TRANSACTIONS ON COMMUNICATIONS 2005年第4期53卷 549-554页

作者： Zhao, JG Zarkeshvari, F Banihashemi, AH Carleton Univ BCWS Ottawa ON K1S 5B6 Canada Carleton Univ Dept Syst & Comp Engn Ottawa ON K1S 5B6 Canada

The effects of clipping and quantization on the performance of the min-sum algorithm for the decoding of low-density parity-check (LDPC) codes at short and intermediate block lengths are studied. It is shown that in many cases, only four quantization bits suffice to obtain close to ideal performance over a wide range of signal-to-noise ratios. Moreover, we propose modifications to the min-sum algorithm that improve the performance by a few tenths of a decibel with just a small increase in decoding complexity. A quantized version of these modified algorithms is also studied. It is shown that, when optimized, modified quantized min-sum algorithms perform very close to, and in some cases even slightly outperform, the ideal belief-propagation algorithm at observed error rates.

关键词： clipping iterative decoding algorithms low-density parity-check (LDPC) codes max-product algorithm max-sum algorithm min-sum algorithm modified min-sum algorithms quantization

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Analysis of the min-sum algorithm for Packing and Covering Problems via Linear Programming

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IEEE TRANSACTIONS ON INFORMATION THEORY 2015年第10期61卷 5295-5305页

作者： Even, Guy Halabi, Nissim Tel Aviv Univ Sch Elect Engn IL-69978 Tel Aviv Israel

Message-passing algorithms based on belief-propagation (BP) are successfully used in many applications, including decoding error correcting codes and solving constraint satisfaction and inference problems. The BP-based algorithms operate over graph representations, called factor graphs, that are used to model the input. Although in many cases, the BP-based algorithms exhibit impressive empirical results, not much has been proved when the factor graphs have cycles. This paper deals with packing and covering integer programs in which the constraint matrix is zero-one, the constraint vector is integral, and the variables are subject to box constraints. We study the performance of the min-sum algorithm when applied to the corresponding factor graph models of packing and covering linear programmings (LPs). We compare the solutions computed by the min-sum algorithm for packing and covering problems to the optimal solutions of the corresponding LP relaxations. In particular, we prove that if the LP has an optimal fractional solution, then for each fractional component, the minsum algorithm either computes multiple solutions or the solution oscillates below and above the fraction. This implies that the min-sum algorithm computes the optimal integral solution only if the LP has a unique optimal solution that is integral. The converse is not true in general. For a special case of packing and covering problems, we prove that if the LP has a unique optimal solution that is integral and on the boundary of the box constraints, then the min-sum algorithm computes the optimal solution in pseudopolynomial time. Our results unify and extend recent results for the maximum weight matching problem and for the maximum weight independent set problem.

关键词： Belief propagation (BP) message-passing algorithms min-sum algorithm max-product algorithm dynamic programming linear programming (LP) combinatorial optimization packing problems covering problems factor graphs graph cover

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Simplified 2-Dimensional Scaled min-sum algorithm for LDPC Decoder

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JOURNAL OF ELECTRICAL ENGINEERING & TECHNOLOGY 2017年第3期12卷 1262-1270页

作者： Cho, Keol Lee, Wang-Heon Chung, Ki-Seok Hanyang Univ Dept Elect Engn Seoul South Korea Hanyang Univ Dept Elect & Comp Engn Seoul South Korea Hansei Univ Dept IT Gunpo Si Gyeonggi Do South Korea

Among various decoding algorithms of low-density parity-check (LDPC) codes, the min-sum (MS) algorithm and its modified algorithms are widely adopted because of their computational simplicity compared to the sum-product (SP) algorithm with slight loss of decoding performance. In the MS algorithm, the magnitude of the output message from a check node (CN) processing unit is decided by either the smallest or the next smallest input message which are denoted as min1 and min2, respectively. It has been shown that multiplying a scaling factor to the output of CN message will improve the decoding performance. Further, Zhong et al. have shown that multiplying different scaling factors (called a 2-dimensional scaling) to min1 and min2 much increases the performance of the LDPC decoder. In this paper, the simplified 2-dimensional scaled (S2DS) MS algorithm is proposed. In the proposed algorithm, we figure out a pair of the most efficient scaling factors which multiplications can be replaced with combinations of addition and shift operations. Furthermore, one scaling operation is approximated by the difference between min1 and min2. The simulation results show that S2DS achieves the error correcting performance which is close to or outperforms the SP algorithm regardless of coding rates, and its computational complexity is the lowest comparing to modified versions of MS algorithms.

关键词： Error-correction code Low-density parity-check code LDPC decoder min-sum algorithm Normalized min-sum algorithm

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A Fully Parallel LDPC Decoder Architecture Using Probabilistic min-sum algorithm for High-Throughput Applications

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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS 2014年第9期61卷 2738-2746页

作者： Cheng, Chung-Chao Yang, Jeng-Da Lee, Huang-Chang Yang, Chia-Hsiang Ueng, Yeong-Luh Natl Tsing Hua Univ Dept Elect Engn Hsinchu Taiwan Natl Chiao Tung Univ Dept Elect Engn Hsinchu Taiwan Natl Tsing Hua Univ Inst Commun Engn Hsinchu Taiwan

This paper presents a normalized probabilistic min-sum algorithm for low-density parity-check (LDPC) codes, where a probabilistic second minimum value, instead of the true second minimum value, is used to facilitate fully parallel decoder realization. The comparators in each check-node unit (CNU) are connected through an interconnect network based on a mix of tree and butterfly networks such that the routing and message passing between the variable-node units (VNUs) and CNUs can be efficiently realized. In order to further reduce the hardware complexity, the normalization operation is realized in the VNU rather than in the CNU. An early termination scheme is proposed in order to prevent unnecessary energy dissipation for both low and high signal-to-noise-ratio regions. The proposed techniques are demonstrated by implementing a (2048, 1723) LDPC decoder using a 90 nm CMOS process. Post-layout simulation results show that the decoder supports a throughput of 45.42 Gbps at 199.6 MHz, achieving the highest throughput and throughput-to-area ratio among comparable works based on a similar or better error performance.

关键词： High-throughput decoder low-density parity-check (LDPC) codes min-sum algorithm

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Improved min-sum algorithm based on density evolution for low-density parity check codes

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IET COMMUNICATIONS 2017年第10期11卷 1582-1586页

作者： Wang, Xiumin Cao, Weilin Li, Jun Shan, Liang Cao, Haiyan Li, Jinsong Qian, Fanglei China Jiliang Univ Coll Informat Engn Hangzhou 310018 Peoples R China Hangzhou Dianzi Univ Coll Commun Engn Hangzhou 310018 Peoples R China China Jiliang Univ Coll Opt & Elect Technol Hangzhou 310018 Peoples R China

In this study, the authors present an improved min-sum (MS) algorithm based on density evolution (DE) called the DE MS algorithm for low-density parity check codes. First, they use DE theory to calculate the probability density function of the check-to-variable message of the belief propagation (BP) algorithm and the MS/normalised MS (NMS) algorithm and furthermore to calculate the normalised factor . Then, is modified further by using the weighted average. Finally, in order to ensure the decoding performance and reduce the hardware complexity, the same is used for different signal-to-noise ratios. The simulation results show that a gain of about 0.2dB can be achieved in comparison with the classical NMS algorithm. In addition, this algorithm can obtain the same decoding performance compared with the Linear minimum Mean Square Error (LMMSE) MS algorithm whose decoding performance is very close to that of the BP algorithm, and it also saves around 24.57% of logic elements and 34.33% of memory bits compared with the LMMSE MS algorithm at the same time.

关键词： parity check codes communication complexity decoding min-sum algorithm density evolution low-density parity check codes DE theory probability density function check-to-variable message signal-to-noise ratios LMMSE MS algorithm decoding performance

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Efficient Implementation of a Threshold Modified min-sum algorithm for LDPC Decoders

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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II-EXPRESS BRIEFS 2020年第9期67卷 1599-1603页

作者： Liu, Yanfang Tang, Wei Mitchell, David G. M. New Mexico State Univ Klipsch Sch Elect & Comp Engn Las Cruces NM 88003 USA

In this brief, we present a hardware efficient implementation of a threshold modified min-sum algorithm (MSA) to improve the performance of a low density parity-check (LDPC) decoder. The proposed architecture introduces a novel lookup table based threshold attenuation technique, called threshold attenuated MSA (TAMSA). The proposed TAMSA implementation is shown to improve bit error rate (BER) performance compared to the conventional AMSA and MSA. Furthermore, a layered version of the TAMSA implementation is investigated to reduce hardware cost. Utilizing circuit optimization techniques, including a parallel computing structure, the proposed layered TAMSA field-programmable gate array (FPGA) implementation results show that the modified architecture requires no extra circuit power or circuit area compared to conventional AMSA, and only 0.07% extra leaf cells compared to conventional MSA.

关键词： Decoding Parity check codes Hardware Bit error rate Attenuation Table lookup Signal to noise ratio LDPC codes min-sum algorithm LDPC decoder attenuation FPGA

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Adaptive-Normalized/Offset min-sum algorithm

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IEEE COMMUNICATIONS LETTERS 2010年第7期14卷 667-669页

作者： Wu, Xiaofu Song, Yue Jiang, ming Zhao, Chunming PLA Univ Sci & Tech Nanjing Inst Commun Engn Nanjing 210007 Peoples R China Southeast Univ Natl Mobile Commun Res Lab Nanjing 210096 Peoples R China

An adaptive-normalized/offset min-sum (AN-/AO-MS) algorithm for decoding low-density parity-check (LDPC) codes is proposed. Unlike the normalized/offset min-sum (NMS/OMS) algorithm, the normalization/offset factor is adaptively adjusted according to the state of check nodes in each iteration. Simulation results show that the proposed AN-/AO-MS algorithm can perform better than the NMS/OMS algorithm while still preserving the low complexity of the min-sum algorithm.

关键词： Decoding min-sum algorithm low-density parity-check (LDPC) codes

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Design of Low Density Parity Check Decoder Using min-sum algorithm

Design of Low Density Parity Check Decoder Using Min-Sum Alg...

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2015 International Conference on Communications and Signal Processing (ICCSP)

作者： Bhojane, Sachin S. Mankar, Monica V. Asutkar, Gajendra M. Dakhole, Pravin K. Yeshwantrao Chavan Coll Engn Nagpur Maharashtra India Priyadarshini Indira Gandhi Coll Engn Nagpur Maharashtra India

ISBN: (纸本)9781479980819

Low density parity check (LDPC) code has received more attention due to their excellent error correcting performance capabilities. An LDPC code can be decoded using iterative method like the sum-product algorithm and the min-sum algorithm based on its Tanner graph. In this paper, fully parallel architecture has been designed for LDPC decoder using min-sum algorithm. This decoder modeled in Verilog synthesized and performed place and route for design using Xilinx 13.1.

关键词： fully parallel Low density parity check (LDPC) min-sum algorithm

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A Modified min-sum algorithm for Low-Density Parity-Check Codes

A Modified Min-Sum Algorithm for Low-Density Parity-Check Co...

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IEEE International Conference on Wireless Communications, Networking and Information Security (WCNIS)

作者： Han, Wei Huang, Jianguo Wu, Fangfei NW Polytech Univ Coll Marine Engn Xian 710072 Peoples R China

ISBN: (纸本)9781424458516

A modified min-sum algorithm for low-density parity check codes is proposed in this paper. The inaccurate check node messages of the min-sum algorithm compared to the belief propagation (BP) algorithm are compensated by modified variable node messages, which is different from the normalized min-sum algorithm. The modified factor is obtained before decoding program and only one extra multiplication is needed in one cycle. So the increased complexity is fairly low. The simulation results show that the bit error rate (BER) and average number of iteration of the modified min-sum algorithm arc very close to the BP algorithm, the modified algorithm can improve the BER performance compared to the min-sum algorithm while added complexity slightly.

关键词： LDPC codes belief propagation min-sum algorithm bit error rate(BER) modified factor

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