M-user cooperative wireless communications based on nonbinary network codes

We propose a new method of applying network coding for cooperative wireless networks. The network consists of multiple (M ges 2) users having independent information to be transmitted to a common base station (BS). These users form partners and relay information for each other. The transmission blocks are subject to block-fading with independent fading coefficients for each block. Designed non-binary network codes over finite fields are used on top of channel codes. Assuming perfect error detection, erroneous blocks out from channel decoders are discarded (erasure). Thus, relaying nodes may not have information messages of some partners (erasure in inter-user channels), and the BS may not decode some blocks correctly either. The network topology from the point of view of network coding is dynamic. To improve performance, we propose dynamic-network codes (deterministic codes for dynamic networks) for the cooperative networks. The codes are designed such that the BS can rebuild user information from a minimum possible set of coding blocks. In this sense, dynamic-network codes achieve the min-cut for cooperative networks with a dynamic topology. For block fading channels, the proposed scheme obtains high asymptotic performance. For two-user networks, we calculate the resulting outage probabilities. We also present simulations with specific channel codes. Numerical results show substantial improvement over previous schemes. Then, we generalize the results to multiple-user (M > 2) networks. We investigate the existence of deterministic dynamic-network codes for multiple-user networks, and show that the diversity order of the proposed scheme can achieve 2M - 1.