Practical compute-and-forward approaches for the multiple access relay channel

We consider a multiple access relay channel (MARC) network consisting of two sources, one relay, and one common destination applying compute-and-forward (CF) strategy. We show that the direct application of CF to the MARC network results in poor error performance bounded by (p + 1)−1, the probability of rank deficiency of the coefficient matrix over Fp. To solve this problem, we propose two practical approaches. First, given an optimal coefficient vector at the relay, the destination is restricted to select a coefficient vector ensuring a full rank coefficient matrix. Second, given an optimal coefficient vector at the destination obtained via a small amount of feedback, the relay is restricted to choose a coefficient vector guaranteeing a full rank coefficient matrix. We simulate these CF implementation strategies using self-similar nested Ε8 lattice codes and confirm that both of the proposed schemes outperform the direct implementation in terms of achievable transmission rate and frame-error-rate performance. Furthermore, we confirm that with a small amount of feedback, the second strategy is better than the first one. In addition, we present in detail a modified Fincke-Pohst algorithm for computing the coefficient candidates and show its efficiency compared to an exhaustive search.