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

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 ar...

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Bibliographic Details
Published in:IEEE transactions on information theory 2012-03, Vol.58 (3), p.1825-1836
Main Authors: HUANG, Jen-Fa, HUANG, Chun-Ming, YANG, Chao-Chin
Format: Article
Language:English
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
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Summary: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.
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2011.2173246