Cooperative partial message relaying based on distributed polar codes for the two-relay network

A cooperative partial message relaying (CPMR) scheme based on distributed polar codes (DPC) is proposed to achieve the maximal decode-and-forward (DF) rate of the stochastically degraded symmetric binary-input two-relay network with orthogonal receiver components (TRN-ORCs). In the proposed scheme, the code design problem of the degraded TRN-ORCs is transformed into a problem of polar codes with CPMR protocol. According to the nested structure of polar codes, the messages transmitted by the source and the first relay are recovered successfully at the two relays, respectively, and then the two relays yield correct partial messages for transmission to solve the uncertainty of the source message at the destination. With the help of the CPMR protocol, the destination should be able to reconstruct the source message correctly. In addition to the practical consideration of the construction of the CPMR protocol based on DPC, we also derived that the block error probability of the proposed scheme can be upper bounded by O(2^-Nβ) for any constant β (0 < β < 1/2), and sufficiently large block length N.