A Relay-Coding Matrix for Multi-User Cooperative Communications

In this paper, we consider a scenario that multiple users transmit data to a common destination node with the help of one relay station. We present one coding matrix that is invertible in the finite field and has maximum information spreading. We analyze the performance based on the input-out weight enumerate function (IOWEF) of the relay coding matrix and show a close match with the results of log-likelihood ratio decoding. The method gives a way to readily determine when relay coding is preferred. Further, since data from each user is generally coded with channel codes, using relay coding also enables turbo decoding that alternates between a multi-user relay decoder and single-user decoders at the destination. We show via simulations that the turbo decoding converges within only two or three iterations, yet indeed provides significant gains compared with a reference relay system without multi-user cooperation.