Practical polar code construction for degraded multiple-relay networks

In this paper, based on the characteristics of polar codes, a new decode-and-forward strategy called generalized partial information relaying protocol is proposed for degraded multiple-relay networks with orthogonal receiver components (MRNORCs). In such a protocol, with the help of partial information from previous nodes, each relay node tries to recover the received source message and re-encodes part of the decoded message for transmission to satisfy the decoding requirements for the following relay node or the destination node. In order to construct practical polar codes, the nested structures are developed based on this protocol and the information sets corresponding to the partial messages forwarded are also calculated. The proposed scheme is proved to be capable of achieving the theoretical capacity of the degraded MRN-ORCs while still retains the low-complexity feature of polar codes. We perform simulations to testify the practicability of the proposed scheme and compare polar codes by using successive-cancellation list decoder (SCLD) with traditional low-density parity-check (LDPC) codes. The results show that the obtained polar codes provide significant gain.