The Achievable Distortion of DF Relaying with Average Power Constraint at the Relay

This letter concerns the achievable distortion of a Gaussian source over a two-hop network with the aid of a relay, where the relay is subject to an average power constraint and employs the decode and forward strategy. It is assumed that the Gaussian source is hierarchically encoded through the use of a scalable source coding approach and is sent to the relay using a multi-layer channel code. Then, the relay encodes the retrieved information through the use of a single-layer code and transmit the encoded information to the destination. Accordingly, the optimal power allocation strategy is derived, showing the proposed method outperforms existing works addressed in the literature when the relay is subject to an average power constraint and the objective is to minimize the mean square distortion at the destination.