Feedback Coding Schemes for Gaussian Parallel Relay Networks

Previously, it has been shown that the destination-to-source feedback helps to significantly increase the achievable rate of the Gaussian relay network (GRN) with single source-destination, and the proposed feedback scheme is based on the well-known Schalkwijk-Kailath (SK) scheme and the amplify-and-forward (AF) relay strategy. In this paper, we would like to know whether additional feedback links help to further enhance the transmission rate, and if there does not exist destination-source feedback, how to design feedback scheme for the single source-destination GRN with destination-relay and relay-source feedback links? To answer the aforementioned questions, first, we study the Gaussian parallel relay network (GPRN) with feedback links from destination to both source and relay nodes. A new hybrid scheme, which combines the SK scheme with AF and compute-and-forward relay strategies, is proposed. We show that this new scheme may further enhance the achievable rate for the same model with only destination-source feedback. Next, we study the GPRN with destination-relay and relay-source feedback links. A time sharing scheme which combines the SK-type schemes for the broadcast channel and the multiple-access channel is proposed. Numerical results show that even without destination-source feedback, other feedback links can still provide rate gain for some cases.