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 assistance of one relay station. We present one type of coding matrices that are invertible in the finite field and have maximum information spreading. We analyze the performance based on the input-output weight enumerate function (IOWEF) of the relay coding matrix and show a close match with the results of the 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 a number of single-user decoders at the destination. We show via simulations that the turbo decoding converges within only two or three iterations, yet provides significant gains compared with a reference relay system without the multi-user cooperation.