Rematch-and-Forward: Joint Source-Channel Coding for Parallel Relaying With Spectral Mismatch

The Gaussian parallel relay network, introduced by Schein and Gallager, consists of a concatenation of a Gaussian additive broadcast channel from a single encoder to a layer of relays followed by a Gaussian multiple-access channel from the relays to the final destination (decoder), where all noises are independent. This setup exhibits an inherent conflict between digital and analog relaying; while analog relaying (known as “amplify-and-forward”, A&F) suffers from noise accumulation, digital relaying (known as “decode-and-forward”) looses the potential “coherence gain” in combining the relay noises at the decoder. For a large number of relays, analog relaying has better performance, however it is limited to white channels of equal bandwidth. In this work, we present a generalization of the analog approach for bandwidth mismatch and colored channels, a strategy coined “Rematch and Forward” (R&F). It is shown that this strategy exploits the full bandwidth of the individual channels, without sacrificing the coherence gain offered by A&F. Specifically, for given individual-link capacities, R&F remains within a constant gap from the network capacity for any number of relays and any bandwidth ratio between the sections. Our approach is based upon applying suitable joint source/channel coding techniques, thus we demonstrate how advances in that field can benefit “pure” digital problems.