Analysis of nonbinary ldpc codes using gaussian approximation

In this paper, we generalize the defini- tion of the binary-input symmetric-output channel in (l) to a q-ary input channel and prove that, under the Gaussian assumption, the density evolution of the q- ary sum-product decoding for such a channel is fully characterized by (q - 1) quantities. We describe the approximate density evolution for regular low-density parity-check (LDPC) codes and show that the (q - 1)- dimensional integration involved in the approach can be simplified using a dimension reduction algorithm for the case of q = 2p.