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The error performance of generalised spatial modulation (GSM) can be further enhanced by applying Plotkin polar codes (PPCs) to GSM. This motivates us to propose a Plotkin polar coded GSM (PPC-GSM) scheme where GSM signals are protected by the PPCs. We further extend the PPC-GSM scheme to cooperative scenarios based on a natural split in the Plotkin’s construction and propose the coded cooperative scheme with two sources called network polar coded cooperative GSM (NPCC-GSM). In the Plotkin’s construction, two shorter codes (subcodes) were derived from a longer code. The constructed polar subcodes were then utilised to achieve coded cooperation between two sources and offer a network coding. Furthermore, we investigate the network polar coded cooperative spatial modulation (NPCC-SM) scheme as a suitable benchmark to the proposed NPCC-GSM scheme. The simulation results reveal that for the same spectral efficiency the NPCC-GSM scheme performs nearly the same as the NPCC-SM scheme in terms of bit error rate performance, but with a significant reduction in the number of transmit antennas. Moreover, the NPCC-GSM scheme outperforms the PPC-GSM scheme under identical conditions. The enhanced performance is made possible due to the synergy between two sources and the joint decoding at the destination.

Network polar coded cooperative GSM scheme based on Plotkin’s construction