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Scientia Sinica Informationis

A class of quasi-cyclic LDPC codes from B_2(mod m)sequences

Zhang Guo

Published Jan 1, 2012• 0 citations
OpenAlex

Abstract

A new class of binary low-density parity-check(LDPC)codes is proposed based on B2(mod m) sequences.The parity-check matrix of such a code has a column weight of three and a row weight of an arbitrary integer,and a quasi-cyclic structure.The parity-check matrix also has a girth at least 8,and corresponds to a code with minimal distance at least 12.When m is prime,an 8-cycles reduction method is presented to completely avoid the two types of 8-cycles within the total four types existed in the Tanner graph.Simulation results show that,for a prime integer m,the new LDPC code outperforms the random(quasi-)regular counterpart generated by the PEG algorithm.Finally,a heuristic algorithm based on a strategy called neighboring extension search is presented to search for the B2(mod m)sequences whose lengths approach or meet the upper bound.

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International Conference on Wireless Communications and Signal Processing (WCSP)•Oct 1, 2016•1 citation
A new class of binary low-density parity-check(LDPC)codes is proposed based on B2(mod m) sequences.The parity-check matrix of such a code has a column weight of three and a row weight of an arbitrary integer,and a quasi-cyclic structure.The parity-check matrix also has a girth at least 8,and corresponds to a code with minimal distance at least 12.When m is prime,an 8-cycles reduction method is presented to completely avoid the two types of 8-cycles within the total four types existed in the Tanner graph.Simulation results show that,for a prime integer m,the new LDPC code outperforms the random(quasi-)regular counterpart generated by the PEG algorithm.Finally,a heuristic algorithm based on a strategy called neighboring extension search is presented to search for the B2(mod m)sequences whose lengths approach or meet the upper bound.
A new class of binary low-density parity-check (LDPC) codes is proposed based on B2(mod m) sequences. The parity-check matrix of such a code has a column weight of three and a row weight of an arbitrary integer, and a quasi-cyclic structure. The parity-check matrix also has a girth at least 8, and corresponds to a code with minimal distance at least 12. When m is prime, an 8-cycles reduction method is presented to completely avoid the two types of 8-cycles within the total four types existed in the Tanner graph. Simulation results show that, for a prime integer m, the new LDPC code outperforms the random (quasi-) regular counterpart generated by the PEG algorithm. Finally, a heuristic algorithm based on a strategy called neighboring extension search is presented to search for the B2(mod m) sequences whose lengths approach or meet the upper bound.
This paper,based on algebra and graph,proposes a method for constructing structured low-density parity-check(LDPC) codes.In this method,the authors design a connected graph with three kinds of special path to ensure that the Tanner graph of the parity check matrix mapped from the connected graph is without short cycles.The construction method results in two classes of(3,k)-regular quasi-cyclic LDPC codes with girth 8 and 12 respectively.Furthermore,by extending this construction method,two classes of LDPC codes with column weight 2,whose girths are respectively 16 and 24,can be obtained.The simulation studies show that these codes can achieve better performance than randomly constructed regular LDPC codes over AWGN channels with iterative decoding.At the BER of 10-5,the new proposed(3,6)-regular(4356,2205) QC-LDPC code performs 1.48dB from the Shannon limit.Moreover,it outperforms the random regular LDPC code of comparable parameters by 0.1dB.For the new proposed structured LDPC codes with column weight 2,they can achieve about 2dB coding gains with respect to the random regular LDPC codes with similar block lengths and code rates.
Multitype quasi-cyclic (QC) low-density parity-check (LDPC) codes are a class of protograph LDPC codes lifted cyclically from protographs with multiple edges, represented by two weight and slope matrices. For a given weight-matrix, an approach is proposed to find the maximum-achievable girthgmax⁡g_{\max }gmax​of the corresponding multitype QC-LDPC codes by some inevitable chains having less complexity than the existing methods. This advantage leads to some new patterns of the weight matrices such that the corresponding codes have some improvements in terms of the maximum-achievable girths or the minimum-distance upper-bounds. In continue, for a given weight-matrix with maximum-achievable girthgmax⁡g_{\max }gmax​, some slope-matrices are constructed by a depth-first search algorithm for which the corresponding multitype QC-LDPC codes with even girthggg,g≤gmax⁡g\le g_{\max }g≤gmax​, have smaller lengths, higher rates, or larger minimum-distances than the state-of-the-art achievements. Simulation results show that the constructed codes have some error-rate advantages than PEG, random-like, CCSDS, and 802.11n/ac IEEE standard LDPC codes.
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.
Short cycles in the Tanner graph of a given LDPC code has negative effect on the performance of iterative decoding. To improve the performance, we presented an approach for constructing Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) codes whose associated Tanner graph has large girth and a small amount of short cycles. Each column block of the parity check matrix was designed by adding circulant permutation sub-matrices one after another, provided the current parity check matrix has minimal number of short cycles. The condition for the proposed QC-LDPC codes to have girth at least 6 was also analyzed. Regular and irregular QC-LDPC codes with various lengths and rates can be constructed. Simulations show that the proposed QC-LDPC codes have less short cycles and better performance than existing progressive edge growth based QC-LDPC codes.
In this paper, we propose a new approach to construct quasi-cyclic low-density parity-check (QC-LDPC) codes using Hamming codewords of weight three, namely the HM-QC-LDPC codes. Thanks to the distance property of Hamming codes, length four cycles are avoided from the Tanner graph of the constructed codes, resulting in codes of girth six. This approach can be further extended to construct QC-LDPC codes of girth eight. Our numerical results show that the proposal has a better cycle profile than the progressive-edge-growth (PEG) constructed codes, and consequently prevails in performance. Moreover, the constructed QC-LDPC code prevails the LDPC code of the IEEE802.22 standard by 0.2 dB at the bit error rate (BER) of 10-8when the codeword length is within hundreds of bits, making it a promising candidate for scenarios where strict decoding latency is imposed.