Network Coding Design for Multi-Source Multi-Relay Cooperative Wireless Networks

In this paper, we study the design of network codes for multi-source, multi-relay networks over frequency non-selective slow fading channels. Specifically, we consider a system with M sources each having independent information to be transmitted to a common destination with the help of N relays (called an M - N - 1 system). A finite field (non-binary) based method is suggested to design binary network codes. For construction of the codes, we investigate full system diversity achieving criteria and constraints imposed by it in terms of linear independence of columns (or sets of columns) of generator matrix for codes over finite fields (including binary). First, we design such full diversity achieving codes over polynomial fields of the form GF(2(K)) and then using a novel uplifting technique (matrix representation of finite fields), convert these back into frame based binary codes to reduce encoding complexity at relays (as only binary operations are used). Simulation results confirm the diversity claims of the proposed codes under perfect as well as realistic source-to-relay (S-R) channel links. We also apply belief propagation (BP) decoding on these codes. The codes are compared with that from existing algorithm and similar performance is observed with smaller frame size for the case considered.