Decode‐and‐forward polar coding scheme for receive diversity: a relay partially perfect retransmission for half‐duplex wireless relay channels

Abstract

Recently, it is shown that the channel polarisation phenomenon of Arikan's polar codes with their original multilevel construction happens in several levels with perfect, partially perfect and useless bit channels. On the basis of this construction, this study aims to illustrate design principles and decoding steps of cooperative decode-and-forward polar coding schemes for half-duplex relay channel. In these schemes, the authors consider the use of relay retransmission of partially perfect bit channels in time-division process. The source node transmits its polar-coded information to both the relay and the destination nodes during the first time slot. For the second transmission period, the relay first decodes the source signal then after reconstruction of the polarisation matrix, the extracted partially perfect bit channels are recoded using another polar code and finally transmitted to the destination node. At destination, the signals received from both source and relay nodes are processed by using multi-stage successive cancellation decoding for retrieving the original information bits. They demonstrate via numerical results that by carefully constructed polarisation matrix at relay node, their cooperative polar coding schemes can achieve better performances than other previous schemes.