Optimized low-delay source-channel-relay mappings

The three-node relay channel with a Gaussian source is studied for transmission subject to a low-delay constraint. A design algorithm for joint source¿channel mappings is proposed and numerically evaluated. The designed system is compared with reference systems, based on modular source and channel coding, and the distortion-rate function for the Gaussian source using known achievable rates for the relay channel. There is a significant gain, in terms of decreased power, in using the (locally) optimized systems compared with the reference systems. The structure of the resulting source mapping and the relay mapping is visualized and discussed in order to gain understanding of fundamental properties of optimized systems. Interestingly, the design algorithm generally produces relay mappings with a structure that resembles Wyner-Ziv compression.