Partial Decoding for Synchronous and Asynchronous Gaussian Multiple Relay Channels

Relaying diversity is a key technology to increase capacity in wireless networks. In this paper, the capacity of a single source-destination wireless channel, aided by a set of N potential relays, is studied. For such a link (analyzed under full- duplex and half-duplex constraint), we derive a capacity upper bound based upon the max-flow-min-cut theorem stated by Cover in [1]. Furthermore, a lower bound is proposed considering the achievable with partial decoding at the relay nodes. To maximize the later, optimum relay selection is carried out. Both bounds are then applied to Gaussian channels with channel knowledge at both transmitter and receiver sides, and two synchronization modes are addressed: the synchronous mode, where relays perform coherent beamforming, and the asynchronous mode. Results show that, surprisingly, partial decoding is more spectrally efficient for the half-duplex scheme, becoming the capacity achieving technique for low number of relays.