Lossy-Forward Relaying for Lossy Communications: Rate-Distortion and Outage Probability Analyses

This paper presents an in-depth performance analysis of lossy communications in a single-relay system, where the recovered information is not necessarily lossless in both the relay and the destination. In this system, the relay continues transmitting the sequence with source-relay link errors to the destination even if errors are detected after decoding, i.e., so-called Lossy-Forward (LF) strategy. The problem can be decomposed into two parts as follows: a point-to-point coding problem in the source-relay (S-R) link, and a lossy source coding problem with a LF relay in the source-destination (S-D) and relay-destination (R-D) links. To begin with, we derive the admissible rate region of the lossy source coding problem with a LF relay for a specified distortion requirement. Then, we focus on the analysis of outage probability over block Rayleigh fading channels. Finally, a practical encoding/decoding scheme is proposed for the evaluation of system performance by computer simulations. Due to the suboptimal channel coding and incomplete utilization of joint typicality, the theoretical performance cannot be achieved in the simulation; however, the tendency of curves in simulations matches that in theoretical calculation