Parity check network coding for wireless cooperative communications

We develop a cooperative decode-and-forward strategy of distributed Source-Relay network coding for a three-node relay model, in which Relay and Source both send their own messages to Destination. First, we present a cooperative communication protocol to achieve decode-and-forward capacity by leveraging transmit rates between Source and Relay and designing distributed Source-Relay network coding accordingly. Afterwards, multi-dimension Low-density parity-check (LDPC) code is constructed as a layered structure, where Source LDPC, Relay LDPC, and network LDPC code are organically integrated to realize a distributed design. Our design randomly embeds network-coded message into the layered structure as effective extra checks offering side information for both Source and Relay. Based on derivation of the algebraic relationship between constituent codes, a good multi-dimension LDPC code profile is generated. Meanwhile, network coding complexity maintains linear to the block length. The coding scheme is demonstrated to approach decode-and-forward capacity and still provides effective spatial diversity.