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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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A New Low-Resolution min-sum Decoder Based on Dynamic Clipping for LDPC Codes

A New Low-Resolution Min-Sum Decoder Based on Dynamic Clippi...

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IEEE/CIC International Conference on Communications in China (ICCC)

作者： He, Huanyu Chu, Lei Qiu, Robert Caiming Shanghai Jiao Tong Univ Dept Elect Engn Shanghai Peoples R China

ISBN: (纸本)9781728107325

Compared with the sum-product algorithm (SPA) with high decoding complexity for low-density parity-check (LDPC) codes, its approximated version, the min-sum algorithm (MSA), reduces the computational complexity at the cost of slight performance degradation. In order to compensate the oversized check-node messages in the MSA, the effect of clipping on variable-node messages is investigated under two-bit resolution. Our results show that the performance of clipped MSA degrades at the high bit error rate (BER) and increases at the low BER as clipping threshold enlarges. Based on these results, we propose a modified quantized MS decoding algorithm where the adaptive clipping threshold is applied on the variable-node messages according to the number of unsatisfied checks per-iteration. The adaptive rule is designed for easy hardware implementations. Numerical results show that the proposed algorithm has considerable improvement in performance compared with the MSA under two-bit precision. And it can achieve the performance near the SPA for some short-length LDPC codes.

关键词： Low-density parity-check codes min-sum algorithm clipping quantization error floor

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Convergence and correctness of belief propagation for the Chinese postman problem

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JOURNAL OF GLOBAL OPTIMIZATION 2019年第3期75卷 813-831页

作者： Dai, Guowei Li, Fengwei Sun, Yuefang Xu, Dachuan Zhang, Xiaoyan Nanjing Normal Univ Inst Math Nanjing 210023 Jiangsu Peoples R China Nanjing Normal Univ Sch Math Sci Nanjing 210023 Jiangsu Peoples R China Cent China Normal Univ Fac Math & Stat Wuhan 430079 Hubei Peoples R China Shaoxing Univ Dept Math Shaoxing 312000 Peoples R China Beijing Univ Technol Dept Informat & Operat Res Coll Appl Sci Beijing 100124 Peoples R China

Belief Propagation (BP), a distributed, message-passing algorithm, has been widely used in different disciplines including information theory, artificial intelligence, statistics and optimization problems in graphical models such as Bayesian networks and Markov random fields. Despite BP algorithm has a great success in many application fields and many progress about BP algorithm has been made, the rigorous analysis about the correctness and convergence of BP algorithm are known in only a few cases for arbitrary graph. In this paper, we will investigate the correctness and convergence of BP algorithm for determining the optimal solutions of the Chinese postman problem in both undirected and directed graphs. As a main result, we prove that BP algorithm converges to the optimal solution of the undirected Chinese postman problem within O(n) iterations where n represents the number of vertices, provided that the optimal solution is unique. For the directed case, we consider the directed Chinese postman problem with capacity and show that BP algorithm also converges to its optimal solution after O(n) iterations, as long as its corresponding linear programming relaxation has the unique optimal solution.

关键词： Belief propagation (BP) Message-passing algorithm min-sum algorithm Convergence Undirected Chinese postman problem Directed Chinese postman problem

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A Two-Bit Precision Decoding algorithm for LDPC Codes Over the Binary Symmetric Channel

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IEEE WIRELESS COMMUNICATIONS LETTERS 2019年第1期8卷 109-112页

作者： Cho, Sunghye Yang, Kyeongcheol Pohang Univ Sci & Technol POSTECH Dept Elect Engn Pohang 37673 South Korea Samsung Elect Co Ltd DRAM Design Team Memory Business Suwon 16677 South Korea

The min-sum algorithm as an approximation of the sum-product algorithm (SPA) for decoding of LDPC codes has much lower computational complexity, but slightly worse performance than the SPA. However, severe performance degradation might occur when it is realized in hardware due to the finite precision effect, especially in two-bit precision. In order to overcome this problem, we propose a two-hit precision decoding algorithm. The proposed algorithm employs one of several decoders adaptively, based on the syndrome weight of the estimated decoder output every iteration. Numerical results show that it has similar performance to the SPA over the binary symmetric channel.

关键词： Binary symmetric channel low-density parity-check code min-sum algorithm error floor syndrome weight

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Design and FPGA Implementation of a Quasi-Cyclic LDPC Decoder 6th

Design and FPGA Implementation of a Quasi-Cyclic LDPC Decode...

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6th International Conference on Communications, Signal Processing, and Systems (ICCSPS)

作者： Zhao, Honglin Zhang, Haiyue Harbin Inst Technol Xidazhijie 92 Harbin 150006 Heilongjiang Peoples R China

ISBN: (纸本)9789811065712;9789811065705

The excellent error correction performance of Low-Density Parity Check code has made it widely used in many modern communication systems, including space communication system. This paper describes a design and FPGA implementation of a quasi-cyclic LDPC decoder based on min-sum algorithm. The partially parallel design solves the contradiction between the consumption of hardware resource and decoding efficiency. The decoder achieves up to a BER of 10(-3) at 4 dB, and a throughput of 300 Mbps per iteration for a code length of 8176.

关键词： LDPC min-sum algorithm Partially parallel decoder FPGA

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High Performance LDPC Decoder design using FPGA 9

High Performance LDPC Decoder design using FPGA

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9th International Conference on Emerging Trends in Engineering and Technology - Signal and Information Processing (ICETET-SIP)

作者： Pawankar, Shraddha Mohota, Nilesh JD Coll Engn & Management Nagpur Maharashtra India JD Coll Engn & Management Dept Elect Nagpur Maharashtra India

ISBN: (纸本)9781728135069

LDPC codes are an important aspect of 5G communication systems. This paper presents high performance design of Low-density parity-check decoder on reconfigurable FPGA. LDPC codes are one of the most efficient error correcting codes for implementation on FPGA. The main aim is to implement a low complexity architecture of the LDPC decoder on the FPGA (Field Programmable Gate Array). The two main components of LDPC are VNU and CNU. Our efficient decoding structure will reduce the complexity with the help of check node unit (CNU) and the variable node unit (VNU) using min-sum algorithm for getting fewer slice resources. Here, we have used multiplexed storage structure for storing nod message to get the result in minimum FPGA resources. LDPC is quite an integral part in deep space communications and its potential utilization in the area which is highly explored. In space data systems it is quite important to have a LDPC decoder which has both low complexity and high performance architecture. Therefore the low-complexity method becomes an efficient method to achieve the requirements put in future by many wired and wireless communication system.

关键词： LDPC decoder Low-complexity implementation min-sum algorithm

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High performance short-block binary regular LDPC codes

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ALEXANDRIA ENGINEERING JOURNAL 2018年第4期57卷 2633-2639页

作者： Mostari, Latifa Taleb-Ahmed, Abdelmalik Hassiba Benbouali Univ Chlef Fac Technol Dept Elect Chlef Algeria Univ Valenciennes & Hainaut Combresis LAMIH UMR CNRS 8201 Valenciennes France

LDPC code shows a good performance with long-block codes. However, certain channels are constrained to use short-block codes due to latency. Therefore, concatenated LDPC codes with iterative decoding is a good choice to get a good performance. Concatenated binary LDPC codes were introduced as a class of concatenated codes in which the LDPC codes are irregular codes having different parameters. Although irregular LDPC codes are more efficient than regular codes, irregular LDPC codes have an error floor and a higher encoding complexity than regular code. In this paper, in order to get a good performance/complexity trade-off with a short-block code, we investigate a parallel concatenation of two identical regular binary LDPC codes, using an inter-leaver. Simulation results show that the proposed code outperforms a single LDPC code. The proposed code needs less time decoding delay than a single LDPC code with the same iteration number. Also, the proposed code needs a less number of iterations to achieve the same performance of a single LDPC code that leads to less decoding complexity and decoding delay. A simplified algorithm, the min-sum algorithm, that is used to decode the component codes shows a small performance loss with respect to the sum-product algorithm. (C) 2018 Faculty of Engineering, Alexandria University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://***/licenses/by-nc-nd/4.0/).

关键词： LDPC code Parallel concatenation Iterative decoding sum-product algorithm min-sum algorithm

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A Novel Truncation Rule for the EMS Decoding of Non-binary LDPC Codes 12

A Novel Truncation Rule for the EMS Decoding of Non-binary L...

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12th International Conference on Signal Processing and Communications (SPCOM)

作者： Deka, Kuntal Rajesh, A. Bora, P. K. Indian Inst Technol Goa Farmagudi India Indian Inst Technol Guwahati Gauhati India

ISBN: (纸本)9781538638217

This paper presents a novel truncation rule for the extended min-sum (EMS) decoding of non-binary low-density parity-check (NB-LDPC) codes. The conventional NB-LDPC decoders involve vector-messages of length equal to the field size q. The complexity of these decoders increases significantly as q increases. In the EMS algorithm, the vector-messages are truncated by discarding the less-likely symbols. In this paper, we propose a truncation rule so that the lengths of the vector-messages are reduced to the so-far best limit without compromising on the error correction capability. We devise a proximity matrix which helps to identify the essential components of a vector-message for truncation. The proposed truncation rule has been applied to several NB-LDPC codes of different field sizes. Simulation results for these codes show that the proposed rule can achieve the maximum truncation with negligible performance loss.

关键词： Non-binary LDPC codes min-sum algorithm EMS algorithm truncation rule

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Special session: Low Power LDPC Deocder using Adaptive Forced Convergence algorithm 60

Special session: Low Power LDPC Deocder using Adaptive Force...

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60th IEEE International Midwest Symposium on Circuits and Systems (MWSCAS)

作者： Bae, JeongHyeon Choi, ByungJun Sunwoo, MyungHoon Ajou Univ Dept Elect & Comp Engn Suwon South Korea Opticis Seongnam South Korea

ISBN: (纸本)9781509063895

LDPC codes have been applied in recent communication standards, such as WiFi, WiGig, and 10G Based-T Ethernet as a forward error correction code. However, LDPC codes require a large number of computational complexity for high performances. To solve this problem, various studies have been continuously performed for reducing computational complexity. In this paper, we propose an adaptive forced convergence algorithm to deactivate the variable nodes and check nodes for reducing the computational complexity using only one adaptive threshold value.

关键词： LDPC codes LDPC decoder min-sum algorithm adaptive forced convergence forced convergence

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