Optimized distributed Goppa codes based on spatial modulation

Abstract

The distributed Goppa coded spatial modulation (DGC‐SM) scheme is proposed in cooperative scenarios. In the proposed DGC‐SM scheme, the relay chooses the partial information from the source by using the idea of information selection, and then re‐encodes the selected information. At the destination, a distributed Goppa code is obtained corresponding to each selection. In order to get the best possible code, an optimal information selection algorithm is proposed at the relay. In the proposed optimal algorithm, all selections and source message sequences are considered, which results in high complexity. Thus, another optimized information selection algorithm with low complexity is proposed at the relay. To further enhance the capability to get the source information, two efficient joint decoding algorithms called smart decoding algorithm and improved smart decoding algorithm are proposed. Moreover, the bit error rate (BER) performance bound of the proposed DGC‐SM scheme is derived. Through the simulations, the effectiveness of the proposed two optimized information selection algorithms is confirmed. Also, it is observed that the simulation and analytical results closely match at high signal‐to‐noise ratio (SNR).