Two-Stage Successive Wyner–Ziv Lossy Forward Relaying for Lossy Communications: Rate-Distortion and Outage Probability Analyses

This article presents in-depth rate-distortion and outage probability analyses for two-stage successive Wyner-Ziv (WZ) wireless communication networks. The system model assumes Lossy Forward (LF) cooperative communication where lossless reconstruction is not necessarily required at the relay. This paper aims to quantitatively derive the relationship in distortions between the Source-to-Destination and the Source-to-Relay links. Hence, the design parameters are the distortion levels at the relay and destination. The admissible rate-distortion regions are first analyzed for the two stages separately, where the relay is referred to as Helper. The rate constraints with the links involved in the end-to-end (E2E) communications are then derived. Distortion Transfer Function (DTF) is introduced as a mathematical tool for analyzing the distortions of networks having multiple stages. It is shown that the higher the correlation between the Source and Helper observations, as well as the larger the E2E tolerable distortion, the larger the admissible rate region. The outage probability of the two-stage successive WZ system is evaluated, assuming that the second stage suffers from block Rayleigh fading while the first stage performs over a static wireless channel. The E2E outage probability is also analyzed with the distortion requirements at Helper and Destination as parameters in independent and correlated fading variations. It is demonstrated that the decay of the outage probability curve exhibits a second-order diversity in a low-to-medium value range of average signal-to-noise ratios (SNRs) when the helper distortion is relatively low. It is shown, however, that as long as the reconstruction at Helper is lossy, the outage probability curve asymptotically converges to the decay corresponding to the first-order diversity at high average SNRs.