The multiple-relay channel with estimate-and-forward relaying

In this paper we consider the multiple-relay channel. For this scenario there are two well known results: the decode-and-forward (DAF) result of [Xie and Kumar, 2005] and the estimate-and forward (EAF) result of [Kramer et al., 2005]. However, the FAF result does not lend itself to numerical evaluation due to the large number of parameters to be determined and the non-convex nature of the optimization problem for finding the maximum rate. Therefore, for a given channel we cannot tell what is the EAF rate while keeping the expressions in their general form. We propose a specific assignment for the FAF auxiliary variables that satisfy the feasibility constraints and allow us to obtain an explicit EAF-based rate expression. This expression can be easily computed, and compared against the DAF-based rate. We give an example of a channel where this FAF rate is superior to both the DA F and the point-to-point rates.