A Message-Passing Algorithm for Counting Short Cycles in Nonbinary LDPC Codes
Sunghye Cho, Kyungwhoon Cheun, Kyeongcheol Yang · 2018
Trapping sets with short cycles are known to give a detrimental effect on the error floor performance of a low-density parity-check (LDPC) code. Unlike in binary LDPC codes., short cycles in a nonbinary low-density parity-check (NB-LDPC) code may be even more harmful to its performance if they do not satisfy the so-called full rank condition (FRC). This is because they may induce low-weight codewords or absorbing sets in that case. Thus, it is crucial to count the number of short cycles not satisfying the FRC as well as the number of short cycles for analyzing the performance of an NB-LDPC code. In this paper, we first develop a novel message-passing algorithm and identify how it is related to the FRC. We then propose a low-complexity algorithm for counting the number of short cycles not satisfying the FRC in an NB-LDPC code, as well as the number of short cycles.