Enumerators for protograph-based ensembles of nonbinary LDPC codes
D. Divsalar, Lara Dolecek · 2011
This paper considers the ensemble enumerators of protograph-based nonbinary (PB NB) LDPC codes. Equipped with combinatorial definitions extended to the nonbinary domain, ensemble enumerators of codeword weight, trapping set size and stopping set size are calculated. The exact enumerators are presented in the finite-length regime, and the corresponding growth rates are calculated in the asymptotic regime. Our results can provide useful analytical tools for a range of communication and storage applications employing nonbinary LDPC codes.