Compress-and-forward on a multiaccess relay channel with computation at the receiver

We study a system in which two sources communicate with a destination with the help of a half-duplex relay. We consider a decoding strategy, based on the compute-and-forward strategy, in which the destination decodes two integer-valued linear combinations that relate the transmitted codewords. In this strategy, the relay compresses its observation using Wyner-Ziv compression and then forwards it to the destination. The destination appropriately combines what it gets from the direct transmission and the relay. Then, using this combination, it computes two integer-valued linear combinations. We discuss the encoding/decoding strategy, and evaluate the achievable sum-rate. Next, we consider the problem of allocating the powers and selecting the integer-valued coefficients of the recovered linear combinations in order to maximize the sum-rate. For the model under consideration, the optimization problem is NP hard. We propose an iterative algorithm to solve this problem using coordinate descent method. The results are illustrated through some numerical examples.