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Journal of Signal Processing

Low-complexity Cycle Elimination Algorithms for QC LDPC Codes

HU Shu-kai

Published Jan 1, 2013• 0 citations
OpenAlex

Abstract

Quasi-cyclic LDPC code is a kind of half-structured low density parity check code.Its block-based property leads to highly structured integrated circuits implementation,without significant performance loss.An algorithm searching shift values for the nonzero entries in base matrix of a Quasi-cyclic LDPC code is proposed along with its improved version.By expanding the Tanner graph of the corresponding expansion matrix,cycles with given length can be detected.Unlike some former algorithms,arithmetic operations are avoided,which leads to a considerable complexity reduction.Given the same base matrix with code rate 0.5 as is used in the IEEE 802.16e standard,LDPC codes constructed by the proposed algorithms have better cycle distributions and achieve slightly improved error-correction performance than the IEEE 802.16e LDPC code as well.

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Quasi-cyclic LDPC code is a kind of half-structured low density parity check code.Its block-based property leads to highly structured integrated circuits implementation,without significant performance loss.An algorithm searching shift values for the nonzero entries in base matrix of a Quasi-cyclic LDPC code is proposed along with its improved version.By expanding the Tanner graph of the corresponding expansion matrix,cycles with given length can be detected.Unlike some former algorithms,arithmetic operations are avoided,which leads to a considerable complexity reduction.Given the same base matrix with code rate 0.5 as is used in the IEEE 802.16e standard,LDPC codes constructed by the proposed algorithms have better cycle distributions and achieve slightly improved error-correction performance than the IEEE 802.16e LDPC code as well.
A novel construction algorithm for quasi-cyclic low-density parity-check codes is proposed,with which we can obtain the improved girth of the corresponding Tanner graph by generalizing Yang et al.'s constraint for any cycle detected in the base matrix to detect and break the cycles in the parity check matrix.Compared with the existing cycle elimination(CE) algorithm,a better error performance can be achieved and cycle-8 free.Simulation results show that the proposed algorithm for constructing the irregular LDPC code of rate 1/2 achieves the performance of codeword error rate of 2×10-6at Eb/N0=1.5dB with 80 iterations by the belief-propagation decoding algorithm.
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.
In this paper, an algorithm for removing cycles in quasi-cyclic(QC) LDPC codes is presented. This algorithm can ensure that the code after cycle removal process preserves the quasi-cyclic structure and significantly improves the flexibility in parameter selection (such as the length of the code) of algebraic constructions of QC-LDPC codes. Besides, it has far lower computational complexity than the existing cycle removal algorithm. Experimental results show that this algorithm is very effective in improving the performance of the QC-LDPC codes and can construct code which has better performance than the corresponding binary LDPC code based on IEEE 802.16e standard.
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.
Quasi Cyclic Low Density Parity Check(QC-LDPC) code is an important branch of LDPC code research.It is a kind of constructed LDPC code with check matrix H constructed by quasi cyclic method.IEEE 802.16e proposes a parity check matrix with quasi cyclic character which makes the encoding and hardware easy to be implemented.This article will mainly introduce the encoding process and analyze the decoding performance of various decoding algorithms.Simulations show that Min-Sum(MS) algorithm compares to the Log-BP performance has approximately 0.5dB loss for high-speed rate coding.And the performance of Normalized Min-Sum(NMS) and Row Weight Matched Min-Sum(Rwm-MS) with relatively low complexity is nearly the same as that of Log-BP algorithm.
Techniques for searching for good quasi-cyclic (QC) LDPC block codes of short and moderate lengths which are suitable for practical purposes are studied. To facilitate implementations only codes whose parity-check matrices having bidiagonal structure of their submatrices and consequently having low encoding complexity are considered. The problem of finding QC LDPC codes with the near-optimum frame or bit error rate performance is split into two independent steps: searching for the near-optimum column degree distribution of the parity-check matrix together with the best base matrix for this degree distribution and searching for the near-optimum labeling of the chosen base matrix. Sets of parameters and criteria for both steps are introduced and discussed. They allow further reduction of the search complexity without significant loss of the search optimality. New QC LDPC block codes of various code rates are obtained and their BER and FER performances are compared with those of the LDPC block codes as well as the turbo codes defined in the IEEE 802.16 WiMAX standard.