Distributed Polar Code Based on Plotkins Construction with MIMO Antennas in Frequency Selective Rayleigh Fading Channels

Abstract

A Plotkin based polar coded orthogonal frequency division multiplexing (OFDM) with multiple input and multiple output (MIMO) antennas scheme is proposed and its performance over frequency selective Rayleigh fading channel has been evaluated. In the considered Plotkins construction, the longer length code word is formed on the basis of two shorter length code words. Due to the presence of a parallel split in the design of the considered Plotkins construction, the proposed scheme is efficiently extended to coded cooperative scenarios. As the relay always plays crucial role in the design of cooperative communication system, therefore an intelligent criteria for the selection of information bits is employed at the relay node. To check the efficacy and to maintain the complete fairness in the performance of the proposed coded cooperative scheme, the authors have also developed the traditional nested polar coded cooperative scheme in the context of OFDM with MIMO antennas. The Monte Carlo simulated bit error rate (BER) performance revealed that the proposed coded cooperative scheme outperforms the traditional nested polar coded cooperative OFDM with MIMO antennas scheme by gain of $$0.5 \;{\sim}\; 0.6$$ dBs. This significant gain in BER performance of the proposed coded cooperative scheme is made possible due to the efficient selection criteria and the joint successive cancellation (SC) decoding tecnique employed at relay node and at the destination node, respectively. Moreover, the proposed coded cooperative scheme outperforms its corresponding coded non-cooperative counterpart scheme by roughly a gain of 1 dB under identical conditions.