Capacity bounds for the alternative relaying diamond channel with conferencing links

In this paper, the diamond relay channel is considered, which consists of one source-destination pair and two relay nodes connected with rate-limited out-of-band conferencing links. In particular, we focus on the half-duplex alternative relaying strategy, in which the two relays operate alternatively over time. With different amounts of delay, two conferencing strategies are proposed, each of which can be implemented by either a general two-side conferencing scheme (for which both of the two conferencing links are used) or a special-case one-side conferencing scheme (for which only one of the two conferencing links is used). Based on the most general two-side conferencing scheme, we derive the achievable rates by using the decode-and-forward (DF) relaying scheme. By further exploiting the properties of the optimal solutions, the simpler one-side conferencing is shown to be equally good as the two-side conferencing in term of the achievable rates under arbitrary channel conditions. Based on this, the DF rate in closed-form is obtained, and the principle to use which one of the two conferencing links for one-side conferencing is also established. Moreover, the DF scheme is shown to be upper-bound-achieving under certain conditions with even one-side conferencing. Finally, numerical results are provided to validate our analysis.