Non-Binary LDPC Codes with Large Alphabet Size

We study LDPC codes for the channel with input $x\in {\mathbb{F}}_q^m$ and output $y=x+z\in {\mathbb{F}}_q^m$. The aim of this paper is to evaluate decoding performance of $q^m$-ary non-binary LDPC codes for large $m$. We give density evolution and decoding performance evaluation for regular non-binary LDPC codes and spatially-coupled (SC) codes. We show the regular codes do not achieve the capacity of the channel while SC codes do.