Construction of One-Coincidence Sequence Quasi-Cyclic LDPC Codes of Large Girth

• Published in: IEEE transactions on information theory Vol. 58; no. 3; pp. 1825 - 1836
• Main Authors: Huang, Jen-Fa, Huang, Chun-Ming, Yang, Chao-Chin
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.03.2012; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Applied sciences; Arrays; Channels; Coding, codes; Construction; Cycle-governing equations (CGEs); Educational institutions; Equations; Error correction & detection; Exact sciences and technology; Gain; girth; Indexes; Information theory; Information, signal and communications theory; low-density parity-check (LDPC) code; Mathematical analysis; Mathematical model; Matrices; Matrix methods; Normal distribution; one-coincidence sequence (OCS); Parity check codes; Permutations; quasi-cyclic (QC); Signal and communications theory; Signal to noise ratio; Simulation; Telecommunications and information theory; Cyclic code; Cycle-governing equations (CGEs); Tanner graph; low-density parity-check (LDPC) code; Algorithm; quasi-cyclic (QC); AWGN channels; Simulation; girth; one-coincidence sequence (OCS); Error correcting code; Parity check codes; Parity check; Signal to noise ratio
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2011.2173246

One approach for designing the one-coincidence sequence (OCS) low-density parity-check (LDPC) codes of large girth is investigated. These OCS-LDPC codes are quasi-cyclic, and their parity-check matrices are composed of circulant permutation matrices. Generally, the cycle structures in these codes are determined by the shift values of circulant permutation matrices, and the existence of cycles in the corresponding Tanner graph is governed by certain cycle-governing equations (CGEs). Therefore, finding the proper shift values is the key point to increase the girth of these codes. In this paper, we provide an effective method to systematically find out the CGEs for these codes of girth 6, 8, and 10, respectively. Then, one less computation-intensive algorithm is used to generate the proper shift values for constructing the OCS-LDPC codes of large girth. Simulation results show that significant gains in signal-to-noise ratio over an additive white-Gaussian noise channel can be achieved by increasing the girth of the OCS-LDPC codes.