Decoding on Graphs: LDPC-Coded MISO Systems and Belief Propagation

This paper proposes a new approach for decoding LDPC codes over MISO channels. Since in an n_T times 1 MISO system with a modulation of alphabet size 2^M, n_T transmitted symbols are combined and produce one received symbol at the receiver, we propose considering the LDPC-coded MISO system as an LDPC code over 2^MnT-ary alphabet. Consequently, we propose a modified Tanner graph to introduce belief propagation for decoding MISO-LDPC systems. As a result, the MISO symbol detection and binary LDPC decoding steps are merged into a single message passing decoding. We also propose an efficient method that significantly reduces the complexity of belief propagation decoding in MISO-LDPC systems. Furthermore, we show that our proposed decoder outperforms the conventional decoder for short length LDPC codes in unknown channel scenarios.