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Wireless and Optical Communications Conference

Construction of Quasi-Cyclic LDPC codes with large girth based on circulant permutation matirx

Peng Yang, Xiaoxiao Bao, Hui Zhao

Published May 1, 2013• 4 citations
Publisher

Abstract

In this paper, we propose an algorithm for removing short-cycles in Quasi-Cyclic (QC) Low-density parity-check (LDPC) codes. First using an algorithm with lower computational complexity, all the cycles in the parity check matrix H are found. Then following a ruler, we adjust the shift value of circulant permutation matrix (CPM) to remove the short-cycles. This algorithm could ensure that the code after cycle removal process preserves the quasi-cyclic structure. Simulation results show that: comparing with the codes (504,252) and (1008, 504), we achieve 0.1dB improvement both.

DOI
10.1109/wocc.2013.6676434

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IEEE Communications Letters•Sep 25, 2017•9 citations
In this paper, we propose an algorithm for removing short-cycles in Quasi-Cyclic (QC) Low-density parity-check (LDPC) codes. First using an algorithm with lower computational complexity, all the cycles in the parity check matrix H are found. Then following a ruler, we adjust the shift value of circulant permutation matrix (CPM) to remove the short-cycles. This algorithm could ensure that the code after cycle removal process preserves the quasi-cyclic structure. Simulation results show that: comparing with the codes (504,252) and (1008, 504), we achieve 0.1dB improvement both.
In this paper, we propose a novel method with low complexity for constructing quasi-cyclic LDPC codes. The algorithm chooses every circulant permutation matrix sequentially, and makes sure that the current circulant permutation matrix forms no cycles of length 4 and 6 with the existent matrices, finally a family of (3,L)(3,L)(3,L) QC-LDPC codes with girth at least 8 is obtained. The main complexity of the algorithm is checking cycles of length 6, the number of which is no more than L2L^2L2. Simulation results show that, when block length is 1008 and using the iterative belief propagation decoding, the LDPC code constructed by the proposed algorithm out performs the random code about 0.1dB at the bit-error-rate of $ 10^{ - 5}$.
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.
By classifying cycle types within the parity-check matrix of a quasi-cyclic(QC) low-density parity-check(LDPC) code,a method without repetition or omission is proposed to detect all the cycles with lengths smaller than twelve.Based on this cycle detection method,a new approach is presented to construct large girth QC-LDPC codes by using some heuristic strategies.The approach includes three steps.Firstly,under the infinite cyclic permutation matrix(CPM) size condition,two integer sequences satisfying the girth constraint are found using a heuristic strategy.Secondly,according to the designed code rate,several integer pairs are extracted from the two sequences so as to form a shift matrix.Finally,by employing the recently proposed theoretical lower bound by Zhang et.al,a range of consecutive CPM sizes in which the girth never decrease is accurately computed from the shift matrix.Compared with Liu-Han's method,the new approach possesses two advantages in the sense that:(1) Not only girth-10+ QC-LDPC codes but also girth-12 ones can be constructed to have consecutive CPM sizes;(2) girth-10+ and girth-12 QC-LDPC codes can be generated with very high code rates,due to the new cycle detection method which significantly accelerates the sequence search procedure.
In this paper, we present an improvement of the PEG algorithm for constructing quasi-cyclic low-density parity-check (QC-LDPC) codes with large girth. We introduce the concept of PEG-undetectable cycles on the computation tree in the PEG algorithm for QC-LDPC codes and give a predictive method to avoid these undetected cycles. The aim is to select only the candidates that ensure the maximization of local girth for a code of girth g ≥ 10 and thus avoid a posteriori verification after the creation of a new edge i.e. keep the predictive philosophy of the PEG algorithm. The proposed method is applicable to both regular and irregular codes and also protograph type-I codes. Simulation results are presented to demonstrate the efficiency of our method in terms of minimum circulant permutation matrix pminand error performance.
In this letter, we study the construction of quasi-cyclic (QC) low-density parity-check (LDPC) codes by array dispersion and masking. We first propose a class of arrays of circulant permutation matrices (CPMs) of arbitrary size obtained by dispersion. Based on this class of arrays of CPMs, a class of QC-LDPC codes is constructed. For these resulting codes, we analyze their cycle structure and derive the numbers, which indicate how many cycles pass through each CPM in their parity-check matrices. Following the indication numbers with the order from largest to smallest, we replace the corresponding CPMs with zero matrices (ZMs) of the same size one by one until a targeted masking termination condition is satisfied. Then, the resultant arrays of CPMs and ZMs give a large class of QC-LDPC codes. Numerical results show that the codes constructed perform well over the additive white Gaussian noise (AWGN) channel when decoded with the sum-product algorithm.
In this letter, we consider the construction of quasi-cyclic (QC) low-density parity-check (LDPC) codes by jointly optimizing the girth g and the number of g-cycles. We first propose a sub-array detection method to accelerate the detection of cycles, and by detecting the non-repeated automatic enumerative cycles in the frame of sub-arrays, cycle detection time can be greatly reduced. Furthermore, a local optimal searching algorithm combined with pre-masking is presented, by orderly searching the local optimal p j,l for each circulant permutation matrix (CPM), a class of QC-LDPC codes with possibly enlarged g, less number of g-cycles, and arbitrary attainable degree distribution could be constructed. Simulation results show that the codes constructed by the proposed method perform well in error floor region.