Optimized Design of Distributed Quasi-Cyclic LDPC Coded Spatial Modulation

We propose a distributed quasi-cyclic low-density parity-check (QC-LDPC) coded spatial modulation (D-QC-LDPCC-SM) scheme with source, relay and destination nodes. At the source and relay, two distinct QC-LDPC codes are used. The relay chooses partial source information bits for further encoding, and a distributed code corresponding to each selection is generated at the destination. To construct the best code, the optimal information bit selection algorithm by exhaustive search in the relay is proposed. However, the exhaustive-based search algorithm has large complexity for QC-LDPC codes with long block length. Then, we develop another low-complexity information bit selection algorithm by partial search. Moreover, the iterative decoding algorithm based on the three-layer Tanner graph is proposed at the destination to carry out joint decoding for the received signal. The recently developed polar-coded cooperative SM (PCC-SM) scheme does not adopt a better encoding method at the relay, which motivates us to compare it with the proposed D-QC-LDPCC-SM scheme. Simulations exhibit that the proposed exhaustive-based and partial-based search algorithms outperform the random selection approach by 1 and 1.2 dB, respectively. Because the proposed D-QC-LDPCC-SM system uses the optimized algorithm to select the information bits for further encoding, it outperforms the PCC-SM scheme by 3.1 dB.