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

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

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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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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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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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Self-Adaptive Termination Check of min-sum algorithm for LDPC Decoders Using the First Two minima

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KSII TRANSACTIONS ON INTERNET AND INFORMATION SYSTEMS 2017年第4期11卷 1987-2001页

作者： Cho, Keol Chung, Ki-Seok Hanyang Univ 222 Wangsimni Ro Seoul 133791 South Korea

Low-density parity-check (LDPC) codes have attracted a great attention because of their excellent error correction capability with reasonably low decoding complexity. Among decoding algorithms for LDPC codes, the min-sum (MS) algorithm and its modified versions have been widely adopted due to their high efficiency in hardware implementation. In this paper, a self-adaptive MS algorithm using the difference of the first two minima is proposed for faster decoding speed and lower power consumption. Finding the first two minima is an important operation when MS-based LDPC decoders are implemented in hardware, and the found minima are often compressed using the difference of the two values to reduce interconnection complexity and memory usage. It is found that, when these difference values are bounded, decoding is not successfully terminated. Thus, the proposed method dynamically decides whether the termination-checking step will be carried out based on the difference in the two found minima. The simulation results show that the decoding speed is improved by 7%, and the power consumption is reduced by 16.34% by skipping unnecessary steps in the unsuccessful iteration without any loss in error correction performance. In addition, the synthesis results show that the hardware overhead for the proposed method is negligible.

关键词： Low-density parity-check codes LDPC decoder min-sum algorithm adaptive min-sum decoding error correction codes

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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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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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An Improved min-sum Polar Code Decoding algorithm 3

An Improved Min-Sum Polar Code Decoding Algorithm

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3rd Asia-Pacific Conference on Communications Technology and Computer Science (ACCTCS)

作者： Fang, mingyuan Univ Manchester Manchester Lancs England

ISBN: (纸本)9798350310801

In 2009, the presentation of polar code, the first theory to approach the Shannon limit of communication channel coding schemes. Thus, academics and business have focused on Polar codes. Research and worldwide standards have been offered one after another, establishing the groundwork for its real-world *** paper proposes a min-sum decoding technique for enhanced Polar codes and revises the node update formula in the min-sum decoding algorithm by using the piecewise linear function to approximate the function In cosh (x) in the belief propagation decoding algorithm. Compared to the min-sum decoding algorithm, the enhanced approach improves decoding performance while somewhat increasing complexity. Compared to the belief propagation decoding algorithm, this approach decreases computational complexity significantly and is simpler to implement in hardware. Based on the min-sum method and the belief propagation algorithm, this approach is offered as a balance between complexity and performance. The simulation results demonstrate that the enhanced min-sum decoding algorithm performs similarly to its predecessor. The performance of the degree propagation decoding method is almost identical to that of the min-sum decoding technique, which is superior.

关键词： Polar Code Belief Propagation algorithm min-sum algorithm Piecewise Linear Function

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Conditional termination check min-sum algorithm for efficient LDPC decoders

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IEICE ELECTRONICS EXPRESS 2015年第24期12卷 20150738-20150738页

作者： Cho, Keol Chung, Ki-Seok Hanyang Univ Dept Elect & Comp Engn Seoul 133791 South Korea

Conditional termination check min-sum algorithm (MSA) using the difference of the first two minima is proposed for faster decoding speed and lower power consumption of low-density parity-check (LDPC) code decoders. Judging from the size of the difference in LDPC decoding scheduling, the proposed method dynamically decides whether the termination checking steps will be skipped or not. The simulation results show that the decoding speed is improved up to 7%, and the power consumption is reduced by up to 16.43% without any loss of error correcting performance. Also, the additional hardware cost of the proposed method is negligible compared to conventional LDPC decoders.

关键词： low-power LDPC decoder min-sum algorithm

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A Novel Search-Based Compute-in-Memory minimum Values Generation Scheme for Low-Complexity LDPC min-sum Decoding

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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II-EXPRESS BRIEFS 2024年第7期71卷 3498-3502页

作者： Guo, Zhipeng Zhang, Deming Zhang, Kaili Song, mingyang Zhang, Yue Zeng, Lang Beihang Univ Sch Integrated Circuit Sci & Energing Beijing 100191 Peoples R China Beihang Univ Hefei Innovat Res Inst Hefei Peoples R China

The generation of the minimum values (the first two minima and the index of the minimum) of numerous variable-to-check messages (V2CM) is the major bottleneck in efficient min-sum decoding of low-density parity-check (LDPC) codes. This brief proposed a novel search-based compute-in-memory (CIM) based minimum values generation (MVG) scheme with two search strategies sharing two core circuits, which avoids the hardware-costly cascading of comparators and multiplexers necessary in conventional comparison-based schemes. The two shared core circuits include (1) the multi-bit content-addressable memory (MCAM) circuit for fast and concurrent search on stored operands (V2CMs) and (2) the search result evaluation (SRE) circuit to generate search result evaluation signals for the update of the minimum values. The two search strategies include (1) the sequential traversal search (STS) strategy and (2) the self-adaptive dichotomic search (SaDS) strategy for low- and high-precision decoding scenarios. Eventually, with the 14nm FinFET design kit, simulation results show that, in terms of area-delay complexity (ADC), the proposed MVG scheme achieves an average of 83% reduction in both low- and high-precision-scenarios, over the conventional comparison-based schemes.

关键词： Low-density parity-check compute-in-memory minimum values generation min-sum algorithm

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