Achievable rate regions of multi‐way relay channel with direct links

Abstract

Rate regions of a multi‐way relay channel with direct links (MWRC‐DLs), where K users exchange their messages via a relay terminal and all users can overhear each other directly, are studied in this study. Under the assumption that a restricted encoder is employed at each user, the cut‐set outer bound on the capacity region is derived first. Then, achievable rate regions of the MWRC‐DLs with decode‐and‐forward (DF) and compress‐and‐forward (CF) strategies are characterised. Meanwhile, the explicit expressions of the outer bound and the achievable rate regions for the Gaussian MWRC‐DLs are also derived. It is shown that the rate regions of the DF and CF strategies for the two‐way relay channel and the multiple‐access relay channel can be obtained from those of the MWRC‐DLs. To give more insights on the two strategies of the MWRC‐DLs system, the common rates of a symmetric Gaussian network are analysed. It is shown that the CF strategy achieves common rates within 1/2( K − 1) bits of the capacity when the relay's power is at least ( K − 1) times as large as the user power. Numerical examples are also provided to verify the theoretical analysis.