Design of QC-LDPC Codes at Finite Lengths

Girth plays an important role in the design of low-density parity-check (LDPC) codes. Motivated by the works on the girth of some classes of Tanner quasi-cyclic (QC) LDPC codes, e.g., Tanner (3, 5), (3, 7), (3, 11), and (5, 7) codes, we, in this paper, study the girth of Tanner $(J,L)$ QC-LDPC codes where $J$ and $L$ can be any two positive integers. According to the sufficient and necessary conditions for the existence of cycles of lengths 4, 6, 8, and 10, we propose an algorithm to determine the girth of Tanner $(J,L)$ QC-LDPC codes with finite code lengths. Through the analysis of the obtained girth values, we generalize the laws of the girth distributions of Tanner $(J,L)$ QC-LDPC codes. Furthermore, based on the exponent matrices of Tanner $(J,L)$ QC-LDPC codes with known girths, we employ the column selection method and/or the masking technique to construct binary/nonbinary LDPC codes. The numerical results show that the constructed LDPC codes have good performance under iterative decoding over the additive white Gaussian noise channel.Girth plays an important role in the design of low-density parity-check (LDPC) codes. Motivated by the works on the girth of some classes of Tanner quasi-cyclic (QC) LDPC codes, e.g., Tanner (3, 5), (3, 7), (3, 11), and (5, 7) codes, we, in this paper, study the girth of Tanner$(J,L)$QC-LDPC codes where$J$and$L$can be any two positive integers. According to the sufficient and necessary conditions for the existence of cycles of lengths 4, 6, 8, and 10, we propose an algorithm to determine the girth of Tanner$(J,L)$QC-LDPC codes with finite code lengths. Through the analysis of the obtained girth values, we generalize the laws of the girth distributions of Tanner$(J,L)$QC-LDPC codes. Furthermore, based on the exponent matrices of Tanner$(J,L)$QC-LDPC codes with known girths, we employ the column selection method and/or the masking technique to construct binary/nonbinary LDPC codes. The numerical results show that the constructed LDPC codes have good performance under iterative decoding over the additive white Gaussian noise channel.

IEEE AccessDec 10, 201821 citations

Constructions of QC LDPC codes based on integer sequences

Lijun Zhang, Bing Li, L. L. Cheng

Science China Information SciencesMay 12, 20144 citations

Quasi-Cyclic LDPC Codes with Large Girth and Few Short Cycles

Yuanhua Liu

In this paper, we present an improved method for obtaining quasi-cyclic low-density parity-check (QC-LDPC) codes of larger length by combining some component QC-LDPC codes of smaller length.Large girth can be obtained by carefully designing one large girth component code of smaller length.The other component codes are properly designed to obtain a lot of QC-LDPC codes with much few short cycles.Simulations show that compared with CRT based QC-LDPC codes and PEG based QC-LDPC codes, the proposed QC-LDPC codes have much less short cycles and better performance.In this paper, we present an improved method for obtaining quasi-cyclic low-density parity-check (QC-LDPC) codes of larger length by combining some component QC-LDPC codes of smaller length.Large girth can be obtained by carefully designing one large girth component code of smaller length.The other component codes are properly designed to obtain a lot of QC-LDPC codes with much few short cycles.Simulations show that compared with CRT based QC-LDPC codes and PEG based QC-LDPC codes, the proposed QC-LDPC codes have much less short cycles and better performance.

International Conference on Manufacturing Science and Engineering (ICMSE)Jan 1, 20180 citations

Design of good QC-LDPC codes without small girth in the p-plane

Ling-jun, Kong, Yang Yang +1 more

Journal of Systems Engineering and ElectronicsJan 1, 20110 citations

(3, L) quasi-cyclic LDPC codes: Simplified exhaustive search and designs

Cheng Sun, Hengzhou Xu, Dan Feng +1 more

There exist lots of (3, L)-regular quasi-cyclic (QC) LDPC codes constructed from finite fields, protographs, array codes, and computer search under some design rules. For a given code length and rate, how to select the best one from these codes is considerable. In this paper, we study (3, L)-regular QC LDPC codes from the perspective of graph isomorphism, and non-isomorphic (3, L)-regular QC LDPC codes are determined. By analyzing the cycle structures of the resulting non-isomorphic codes, an efficient algorithm for counting cycles is presented. Also proposed is a simplified exhaustive search of non-isomorphic (3, L)-regular QC LDPC codes free of cycles of length less than g0, where g0is the estimated optimal girth value for a given code length. Based on these two algorithms, we can easily construct a (3, L)-regular QC LDPC code with optimized cycle distribution for a given L and code length. Numerical results show that the constructed codes have better performance under the iterative decoding algorithms.There exist lots of (3, L)-regular quasi-cyclic (QC) LDPC codes constructed from finite fields, protographs, array codes, and computer search under some design rules. For a given code length and rate, how to select the best one from these codes is considerable. In this paper, we study (3, L)-regular QC LDPC codes from the perspective of graph isomorphism, and non-isomorphic (3, L)-regular QC LDPC codes are determined. By analyzing the cycle structures of the resulting non-isomorphic codes, an efficient algorithm for counting cycles is presented. Also proposed is a simplified exhaustive search of non-isomorphic (3, L)-regular QC LDPC codes free of cycles of length less than g0, where g0is the estimated optimal girth value for a given code length. Based on these two algorithms, we can easily construct a (3, L)-regular QC LDPC code with optimized cycle distribution for a given L and code length. Numerical results show that the constructed codes have better performance under the iterative decoding algorithms.

International Symposium on Turbo Codes and Iterative Information ProcessingSep 1, 201610 citations

DESIGN OF QUASI-CYCLIC LDPC CODES BASED ON EUCLIDEAN GEOMETRIES

Liu, Yuanhua, Niu +5 more

Journal of Electronics (China)Jan 1, 20101 citation

Tanner

(J,L)

Quasi-Cyclic LDPC Codes: Girth Analysis and Derived Codes

(J,L)

QC-LDPC codes where

J

and

L

can be any two positive integers. According to the sufficient and necessary conditions for the existence of cycles of lengths 4, 6, 8, and 10, we propose an algorithm to determine the girth of Tanner

(J,L)

QC-LDPC codes with finite code lengths. Through the analysis of the obtained girth values, we generalize the laws of the girth distributions of Tanner

(J,L)

QC-LDPC codes. Furthermore, based on the exponent matrices of Tanner

(J,L)

QC-LDPC codes with known girths, we employ the column selection method and/or the masking technique to construct binary/nonbinary LDPC codes. The numerical results show that the constructed LDPC codes have good performance under iterative decoding over the additive white Gaussian noise channel.