On a source-coding problem with two channels and three receivers

This paper treats the problem of communicating a memoryless unit-variance Gaussian source to three receivers. Two channels are available, each with a separate receiver. A third receiver has the outputs of both channels available. We obtain an expression for the simultaneously achievable distortions (mean-squared error). This problem applies to the following situation: Assume that high-quality reproduction of a source is desired at a single receiver which is connected to the source over a pair of links operating in parallel. Further assume that the links are unreliable in that either may fail, and that the source encoder is unaware of the failures. One can then ask how "robust" a system designed for this situation can be. That is, what are the limits on the fidelity achievable when both links are functioning if graceful degradation is required during the failure of either link? An inverse relation between performance in the two modes is obtained in the sense that, as performance in the presence of both links approaches its theoretical optimum, average distortion during failures becomes large. Conversely, if near-ideal performance during link failures is desired, then the distortion achieved when both links operate is far from its optimum value.