On the girth of Tanner (3,7) quasi-cyclic LDPC codes

Document Type: Research Paper

Authors

1 Shahrekord University

2 Malek Ashtar University

Abstract

‎‎S‎. ‎Kim et al‎. ‎have been analyzed the girth of some algebraically‎ ‎structured quasi-cyclic (QC) low-density parity-check (LDPC)‎ ‎codes‎, ‎i.e‎. ‎Tanner $(3,5)$ of length $5p$‎, ‎where $p$ is a prime of‎ ‎the form $15m+1$‎. ‎In this paper‎, ‎by extension this method to‎ ‎Tanner $(3,7)$ codes of length $7p$‎, ‎where $p$ is a prime of the‎ ‎form $21m‎+ ‎1$‎, ‎the girth values of Tanner $(3,7)$ codes will be‎ ‎derived‎. ‎As an advantage‎, ‎the rate of Tanner $(3,7)$ codes is‎ ‎about $0.17$ more than the rate of Tanner $(3,5)$ codes‎.

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