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作者： Jian, Yung-Yih Texas A&M University

学位级别：Ph.D.

This dissertation studies methods to achieve reliable communication over unreliable channels. Iterative decoding algorithms for low-density parity-check (LDPC) codes and generalized LDPC (GLDPC) codes are analyzed. A new class of error-correcting codes to enhance the reliability of the communication for high-speed systems, such as optical communication systems, is proposed. The class of spatially-coupled GLDPC codes is studied, and a new iterative hard- decision decoding (HDD) algorithm for GLDPC codes is introduced. The main result is that the minimal redundancy allowed by Shannon’s Channel Coding Theorem can be achieved by using the new iterative HDD algorithm with spatially-coupled GLDPC codes. A variety of low-density parity-check (LDPC) ensembles have now been observed to approach capacity with iterative decoding. However, all of them use soft (i.e., non-binary) messages and a posteriori probability (APP) decoding of their component codes. To the best of our knowledge, this is the first system that can approach the channel capacity using iterative HDD. The optimality of a codeword returned by the weighted min-sum (WMS) algorithm, an iterative decoding algorithm which is widely used in practice, is studied as well. The attenuated max-product (AttMP) decoding and weighted min-sum (WMS) decoding for LDPC codes are analyzed. Applying the max-product (and belief-propagation) algorithms to loopy graphs are now quite popular for best assignment problems. This is largely due to their low computational complexity and impressive performance in practice. Still, there is no general understanding of the conditions required for convergence and/or the optimality of converged solutions. This work presents an analysis of both AttMP decoding and WMS decoding for LDPC codes which guarantees convergence to a fixed point when a weight factor, β, is sufficiently small. It also shows that, if the fixed point satisfies some consistency conditions, then it must be both a linear-program

关键词： LDPC codes GLDPC codes density evolution product codes spatial coupling iterative hard-decision decoding belief propagation max-product algorithm min-sum algorithm linear programming decoding Thesis

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min-sum algorithm with Maximum Average Mutual Information Quantization

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INTERNATIONAL JOURNAL OF FUTURE GENERATION COMMUNICATION AND NETWORKING 2013年第4期6卷 73-81页

作者： Chen, Zhengkang Zhang, Huisheng Li, Lixin Qi, Nan Northwestern Polytech Univ Sch Elect & Informat Xian 710129 Shaanxi Peoples R China

The specific methods of the maximum average mutual information quantization are analyzed and deduced. With this method to quantify the initial message, the variable messages and check messages are converted into integers. Then the min-sum decoding algorithm based on integer arithmetic is implemented. Simulation results demonstrate that the decoding performance of min-sum algorithm based on integer with 7-bit maximum average mutual information quantization is almost the same as that of min-sum algorithm based on integer with 8-bit uniform quantization. Meanwhile, all the variables in the algorithm are fixed-length integers, so it is convenient for hardware implementation. Although the decoding performance is slightly worse than that of the sum-product decoding algorithm, the decoding time is greatly reduced. So it is very convenient for future generation communication.

关键词： Low Density Parity Check Codes (LDPC) maximum average mutual information quantization uniform quantization min-sum algorithm integer operation

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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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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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Novel modified min-sum decoding algorithm for low-density parity-check codes

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The Journal of China Universities of Posts and Telecommunications 2010年第4期17卷 1-5,46页

作者： LIU Hai-yang , QU Wen-ze, LIU Bin, LI Jiang-peng, LUO Shi-dong, CHEN Jie Institute of Microelectronics, Chinese Academy of Sciences, Beijing 100029, China [a] Institute of Microelectronics Chinese Academy of Sciences Beijing 100029 China

The problem of improving the performance of min-sum decoding of low-density parity-check （LDPC） codes is considered in this paper. Based on min-sum algorithm, a novel modified min-sum decoding algorithm for LDPC codes is proposed. The proposed algorithm modifies the variable node message in the iteration process by averaging the new message and previous message if their signs are different. Compared with the standard min-sum algorithm, the modification is achieved with only a small increase in complexity, but significantly improves decoding performance for both regular and irregular LDPC codes. Simulation results show that the performance of our modified decoding algorithm is very close to that of the standard sum-product algorithm for moderate length LDPC codes.

关键词： LDPC codes sum-product algorithm min-sum algorithm modified 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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2010 IEEE International Conference Conferenhce on Wireless Communications,Networking and Information Security(2010 IEEE 无线通信、网络技术与信息安全国际会议 WCNIS)

作者： Wei Han Jianguo Huang Fangfei Wu College of Marine Engineering Northwestern Polytechnical University Xi’an China

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 *** simulation results show that the bit error rate (BER) and average number of iteration of the modified min-sum algorithm are 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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Adaptive-Normalized min-sum algorithm

Adaptive-Normalized Min-Sum Algorithm

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The 2010 2nd International Conference on Future Computer and Communication(第二届未来计算机与通信国际会议 ICFCC 2010)

作者： Xiaofu Wu Yue Song Long Cui Chunming Zhao ming Jiang Institute of Communications Engineering PLA Univ.of Sci.&Tech. Nanjing 210007 CHINA National Mobil Institute of Communications Engineering PLA Univ.of Sci.&Tech. Nanjing 210007 CHINA National Mobile Commun.Research Lab. Southeast University Nanjing 210096 CHINA

ISBN: (纸本)9781424458219;9781424458240

An adaptive-normalized min-sum (AN-MS) algorithm for decoding low-density parity-check (LDPC) codes is proposed. Unlike the normalized min-sum (NMS) algorithm, the normalization factor is adaptively adjusted according to the state of check nodes in each iteration. Simulation results show that the proposed AN-MS algorithm can perform better than the NMS 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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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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Convergence of Weighted min-sum Decoding Via Dynamic Programming on Trees

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IEEE TRANSACTIONS ON INFORMATION THEORY 2014年第2期60卷 943-963页

作者： Jian, Yung-Yih Pfister, Henry D. Texas A&M Univ Dept Elect & Comp Engn College Stn TX 77843 USA

Applying the max-product (and sum-product) algorithms to loopy graphs is now quite popular for best assignment problems. This is largely due to their low computational complexity and impressive performance in practice. Still, there is no general understanding of the conditions required for convergence or optimality of converged solutions or both. This paper presents an analysis of both attenuated max-product decoding and weighted min-sum decoding for low-density parity-check (LDPC) codes, which guarantees convergence to a fixed point when a weight factor, beta, is sufficiently small. It also shows that, if the fixed point satisfies some consistency conditions, then it must be both a linear-programming (LP) and maximum-likelihood (ML) decoding solution. For (d(v), d(c))-regular LDPC codes, the weight factor must satisfy beta(d(v) - 1) < 1 to guarantee convergence to a fixed point, whereas the results proposed by Frey and Koetter require instead that beta(d(v) - 1)(d(c) - 1) < 1. In addition, the range of the weight factor for a provable ML decoding solution is extended to 0 < beta(d(v) - 1) <= 1. In addition, counterexamples that show a fixed point might not be the ML decoding solution if beta(d(v) - 1) > 1 are given. Finally, connections are explored with recent work on the threshold of LP decoding.

关键词： Belief propagation max-product algorithm min-sum algorithm LDPC codes LP decoding

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Area-efficient min-sum decoder design for high-rate quasi-cyclic low-density parity-check codes in magnetic recording

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IEEE TRANSACTIONS ON MAGNETICS 2007年第12期43卷 4117-4122页

作者： Zhong, Hao Xu, Wei Xie, Ningde Zhang, Tong Rensselaer Polytech Inst Troy NY 12180 USA LSI Corp San Jose CA 95134 USA

We report a silicon area efficient method for designing a quasi-cyclic (QC) low-density parity-check (LDPC) code decoder. Our design method is geared to magnetic recording that demands high code rate and very high decoding throughput under stringent silicon cost constraints. The key to designing the decoder is to transform the conventional formulation of the min-sum decoding algorithm in such a way that we can readily develop a hardware architecture with several desirable features: 1) silicon area saving potential inherent in the min-sum algorithm for high-rate codes can be fully exploited;2) the decoder circuit critical path may be greatly reduced;and 3) check node processing and variable node processing can operate concurrently. For the purpose of demonstration, we designed application-specific integrated circuit decoders for four rate-8/9 regular-(4, 36) QC-LDPC codes that contain 512-byte, 1024-byte, 2048-byte, and 4096-byte user data per codeword, respectively. Synthesis results show that our design method can meet the beyond-2 Gb/s throughput requirement in future magnetic recording at minimal silicon area cost.

关键词： decoder low-density parity-check (LDPC) min-sum algorithm very large scale integration (VLSI)

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