Bounds on the Size of Parity-Check Matrices for Quasi-Cyclic Low-Density Parity-Check Codes | IEEE Journals & Magazine | IEEE Xplore

Bounds on the Size of Parity-Check Matrices for Quasi-Cyclic Low-Density Parity-Check Codes


Abstract:

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 fo...Show More

Abstract:

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.
Published in: IEEE Transactions on Information Theory ( Volume: 59, Issue: 11, November 2013)
Page(s): 7288 - 7298
Date of Publication: 28 August 2013

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