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IEEE Conference on Industrial Electronics and Applications (ICIEA)

Performance analysis of QC-LDPC construction based on distance graph

Lixin Li, Zhu Meng, Fan Yang, Yang Zhang

Published Jun 1, 2013• 1 citation
Publisher

Abstract

According to the fact that the random construction method of LDPC(Low Density Parity Check) codes are lack of structure and are difficult to be implemented in hardware, two construction methods of QC-LDPC(Quasi-Cyclic LDPC) codes-sequential and random search method based on distance graph are proposed. The two algorithms can produce flexible QCLDPC codes by setting the parameters such as code length, rates and girth according to requirement. The simulation shows that: the random search method performs better than the sequential search method and the QC-LDPC codes constructed by random search method have equivalent BER performance with PEG construction method. Compared with the existing random construction method, the two methods proposed are faster, and can obtain quasi-cyclic codes which are easy to be implemented in hardware.

DOI
10.1109/iciea.2013.6566542

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According to the fact that the random construction method of LDPC(Low Density Parity Check) codes are lack of structure and are difficult to be implemented in hardware, two construction methods of QC-LDPC(Quasi-Cyclic LDPC) codes-sequential and random search method based on distance graph are proposed. The two algorithms can produce flexible QCLDPC codes by setting the parameters such as code length, rates and girth according to requirement. The simulation shows that: the random search method performs better than the sequential search method and the QC-LDPC codes constructed by random search method have equivalent BER performance with PEG construction method. Compared with the existing random construction method, the two methods proposed are faster, and can obtain quasi-cyclic codes which are easy to be implemented in hardware.
Due to quasi-cyclic structure of parity-check matrices, Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) codes reduce hardware requirements, and thus they have a higher practical value than random LDPC codes. This paper proposes an improved construction method of QC-LDPC based on PEG Algorithm, and the girth of the QC-LDPC codes has an increase of 2. Firstly, a base matrix is generated by the PEG algorithm, and then the base matrix is expanded using the unit circle permutation matrix, at the same time, the short loop of the base matrix is eliminated. This approach has the advantages of the PEG algorithm and the QC-LDPC codes, and simulation results show that bit error rate (BER) performance of the QC-LDPC codes presented in this paper is the same as or exceeds the one of randomly constructed LDPC codes.
A constant challenge in Quasi-Cyclic Low-Density Parity-Check (QC-LDP-C) codes lies on flexible code lengths and rates, conditioned by good error performance. This paper presents an optimal construction method of QC-LDPC codes on the basis of graphical model and search algorithm. Utilizing the proposed scheme, we can construct adaptable QC-LDPC codes whose girths are no less than 12, and column weights are 3. Comparing with any other QC-LDPC code construction approach, this method is much more flexible in block length and block rate. Furthermore, when construction parameters are selected, regular QC-LDPC codes can be constructed easily. Simulation results indicate that LDPC codes proposed in the method perform similarly to the classic Progressive Edge-Growth (PEG) based LDPC codes but outweigh in convenience of implementation and applications. © 2013 ICIC International.
Progressive Edge-Growth(PEG) algorithm is a method for constructing Low Density Parity-Check(LDPC) codes based on Tanner graph.Studies show that LDPC codes constructed with the algorithm can achieve excellent error-correcting performance.Based on the algorithm,the Quasi-Cyclic(QC) LDPC codes are proposed in this paper and simulations show that the QC-LDPC codes have almost the same excellent performance as the random codes constructed with the PEG algorithm.In addition,these codes have the property of quasi-cyclic structure,and the encoding and decoding can be implemented with simple shift registers.Besides,the code rates of the LDPC codes constructed with the proposed algorithm are more flexible to be adjusted.
Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) codes have practical significance in the field of engineering, thus their construction algorithm is a hot issue in the field of LDPC codes. Based on existing construction methods, particularly the method based on Progressive Edge-Growth (PEG) algorithm, a new construction method of shift matrix is proposed. It can effectively avoid the copy of cycle structures, especially short cycles in base matrix after extension. Besides, it also relieves the time cost caused by random search, and greatly improves the length of cycles when compared with algorithms based on methods such as quadratic congruence and arithmetic sequence. Those algorithms can only eliminate short cycles with length 4, while our method can provide QC-LDPC codes without length 6 at least. Cycle analysis and simulation results show that the newly constructed QC-LDPC codes have good cycle structure and error correction performance.
Based on cycle search algorithm and Progressive Edge Growth(PEG) algorithm,this paper proposes a method to construct quasi-cyclic Low-density Parity Check(LDPC) codes with big girth and linear-encoding complexity.A parity-check matrix with a form of approximate lower triangle structure is designed to achieve iterative encoding with linear-encoding complexity.PEG algorithm is used to construct the base matrix and the cycle search algorithm is used to optimize the cycle distribution.And a fast encoding method is proposed.Experimental results show that the LDPC codes constructed with the proposed method can avoid error floor and achieve better BER performance than Tanner-QC-LDPC codes and equivalent BER performance to the ones of random codes.
A novel construction method of Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) code is proposed in this paper, which is based on protograph and Balanced Block Design (BIBD) in combinational mathematics.The method is to fill the base matrix of protograph with the base set elements of BIBD in accordance with certain mathematical rules.And the base matrix of protograph proposed in the paper has special double diagonal structure, which overcomes the low weight code words in general structure and achieves rapid encoding at the same time.The QC-LDPC code in this paper possesses lower encoding complexity and less memory occupation; therefore it is easy for hardware implementation.In addition, it effectively avoids girth 4. Simulation results show that when the Bit Error Rate (BER) is 10 -7 , QC-LDPC codes based on Protograph and BIBD (PBIBD-LDPC) proposed in this paper has 0.5dB Net Coding Gain (NCG) compared with the protograph QC-LDPC codes that based on Vander monde matrix and PEG algorithm structure, and has 0.15dB NCG compared with the excellent code QC-LDPC that based on the lifting structure.