Decoding of Short LT Codes over BIAWGN Channels with Gauss-Jordan Elimination-Assisted Belief Propagation Method

Belief propagation (BP) algorithm has been widely used for decoding LT codes. It is well known that the premature termination of the BP decoding due to the lack of degree one symbols in the ripple impairs the decoding performance of the code. This problem has been well studied and tackled for binary erasure channel (BEC). However, for binary input additive white Gaussian noise (BIAWGN) channels, the issue still remains unaddressed. In this paper, we propose Gauss-Jordan elimination (GJE)-assisted BP algorithm to address this problem and study its decoding performance for short LT codes over BIAWGN channels. The use of GJE can effectively help the BP decoder continue the decoding process whenever it gets stuck due to the premature termination. Simulation results show that, under the same channel conditions and transmission overheads, the bit error rate (BER) performance obtained using the GJE-assisted BP method significantly outperforms the one obtained using the traditional BP algorithm.