Construction of protograph-based LDPC codes with chordless short cycles

Abstract

Controlling small size trapping sets and short cycles can result in LDPC codes with large minimum distance d min . We prove that short cycles with a chord are the root of several trapping sets and eliminating these cycles increases d min . We show that the lower bounds on d min of an LDPC code with chordless short cycles, girths 6 (and 8), and column weights γ (and 3), respectively, are 2γ (and 10), which is a significant improvement compared to the existing bounds γ + 1 (and 6). Necessary and sufficient conditions for exponent matrices of protograph-based LDPC codes with chordless short cycles are proposed for any type of protographs, single-edge and multiple-edge, regular and irregular.The application of our method to girth-6 QC-LDPC codes shows that the removal of those cycles improves previous results in the literature.