Tradeoffs in Random Network Coded Multiple-Access Relay Networks

We consider random linear network coding in noisy multiple-access relay channel where multiple sources communicate with a single destination with the help of multiple relays. The channels are subject to path loss, fading, and noise, and the sources and relays are randomly located inside a unit square centered around the destination. We derive the union bound on the average probability of decoding error with the maximum likelihood decoding at the destination and determine the fundamental tradeoff among node density, rate, reliability, and signal-to-noise ratio (SNR). The tradeoff provides a complete view on the reliability-rate tradeoff at any given SNR and node density, and shows how the energy and node density can be traded in achieving a given reliability-rate pair. The insight provided by the analysis is useful for understanding the performance of network coding in noisy multiple-access relay channel.