Cycle Analysis in Expanded QC LDPC Codes

Abstract

A quasi-cyclic (QC) low-density parity-check (LDPC) code can be viewed as the protograph code with circulant permutation matrices. In this paper, we use permutation matrices to form protograph LDPC codes. In protograph LDPC codes, we present cycle relationships of the mother matrix and the protograph LDPC code. It is derived that the girth of a protograph LDPC code is no smaller than its mother matrix .And cycles in the protograph LDPC codes are uniquely induced by the cycles in its mother matrix.