On the Design of Serially Concatenated LDGM Codes for BIAWGN Channels.

In this paper, we first prove a necessary condition for the successful decoding of serially concatenated low-density generator-matrix (SCLDGM) codes under sum-product (SP) decoding in binary input additive white Gaussian noise (BIAWGN) channels. We show that the inner decoder of such codes must at least produce a certain bit error rate (BER) called critical BER in order for the outer decoder to achieve successful decoding. We verify this condition by providing asymptotic curves for the SCLDGM codes using discretized density evolution (DDE) method. We finally propose a DDE-based optimization approach that utilizes the concept of the critical BER to construct optimized SCLDGM codes that approach the Shannon limit. We also present asymptotic and simulation results of our optimized codes that verify the effectiveness of the proposed optimization approach.