Optimum Decoding of Full Decode and Forward Scheme over Cooperative Relay Channels

Optimum decoding of the cooperative full decode and forward (DF) scheme is derived. It is shown that optimum decoding requires marginalization of a so called partially observed likelihood function over all relay decoder outcomes. Bhattacharyya bound on relay decoding error is used to fully factorize the partially observed likelihood function. The full factorization will allow efficient marginalization over the joint source-relay code space. A tight analytical error bound is derived that its computation further requires efficient tools to compute weight structure of the joint source-relay code. For a simple (7,4) Hamming code under fast fading condition the derived optimum decoder significantly outperforms the conventional decoder. The optimum decoder is more robust to weak source-relay link conditions.