Protograph-based LDPC codes with chordless short cycles and large minimum distance
Farzane Amirzade, Mohammad‐Reza Sadeghi, Daniel Panario · 2022
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, girth 6 and column weights$\gamma$is$2\gamma$. This is a significant improvement compared to the existing bounds$\gamma+1$• Several exponent matrices of protograph-based LDPC codes with chordless short cycles are proposed for any type of pro-tographs, single-edge and multi-edge. These numerical results as well as simulations show that the removal of short cycles with a chord improves previous results in the literature.