Protograph-based LDPC codes with chordless short cycles and large minimum distance

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.