Performance Analysis and Code Design for Cooperative Relay Channels

We treat the LDPC code design for relay channels in this paper. The capacity of relay channels has been analyzed in current literature. How to approach such capacity with the aid of good codes is, however, a challenging problem. An efficient structure is proposed to decouple the factor graph (FG) of a B-block transmission into successive partial FGs, and then, the code design can be performed over the partial FG. Based on this efficient structure, we develop the approaches to find the optimum code ensemble. In particular, we formulate the relay and the destination operations as virtual multiple-antenna channels. Moreover, we develop the approaches based on the binary symmetric channel modelling for the relay and Gaussian approximation to fast estimate the extrinsic mutual information of the destination detector output. Then we can analyze the performance of the relay system using the EXIT technique. Differential evolution is employed to search for the optimum code ensemble. Extensive simulations are further carried out to show the results of the proposed optimum code design.