Bounds on the size of parity-check matrices for quasi-cyclic low-density parity-check codes
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- Bounds on the size of parity-check matrices for quasi-cyclic low-density parity-check codes
- Kim, Kyung-Joong; Chung, Jin-Ho; Yang, Kyeongcheol
- Cycle; Cycle property; girth; Greedy algorithms; Low-density parity-check (LDPC) codes; Quasi cyclic low density parity check codes; Quasicyclic codes; Quasicyclic low-density parity-check (QC-LDPC) code
- Issue Date
- IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
- IEEE TRANSACTIONS ON INFORMATION THEORY, v.59, no.11, pp.7288 - 7298
- In this paper, we investigate the cycle properties of quasi-cyclic low-density parity-check (QC-LDPC) codes. Using the sequence representation of a parity-check matrix for a QC-LDPC code, we analyze a necessary and sufficient condition for a cycle of a given length to exist. We then derive bounds which are necessary conditions for a QC-LDPC code to have a given girth in terms of its parameters. We also give a bound which is a sufficient condition for a QC-LDPC code of a given girth to be constructed by a greedy algorithm. The bounds derived here are applicable to any regular or irregular QC-LDPC codes as well as they improve the existing bounds in many classes of regular LDPC codes.
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