Polarization of Multi-Relay Channels: A Suitable Method for DF and CF Relaying with Orthogonal Receiver

Polar codes, that have been recently introduced by Arikan, are one of the first codes that achieved the capacity for vast numerous channels and they also have low complexity in symmetric memoryless channels. Polar codes are constructed based on a phenomenon called channel polarization. This paper discusses relay channel polarization in order to achieve the capacity and show that if inputs of two different relay channels follow the Arikan polarization structure, then they will be categorized as good and bad relay channels. Also, it has been shown that the eencoding and decoding complexity for these codes is , and their error probability is like the Arikan's work. In order to validate our construction of polar codes for relay channels, some numerical examples for this idea have been presented. Also, the efficiency of this construction for decode-and-forward and compress-and-forward relaying strategies have been analyzed by using simulation results for finite block length in relay channels with orthogonal receiver.