Distortion Minimization in Gaussian Source Coding with Fading Side Information

We consider a layered approach to source coding that minimizes expected distortion when side information is available through a fading channel. Specifically, we assume a Gaussian source encoder whereby the decoder receives a compressed version of the symbol at a given rate, as well as an uncompressed version over a separate side-information channel with slow fading and noise. The decoder knows the realization of the slow fading but the encoder knows only its distribution. We consider a layered encoding strategy with a base layer describing the source assuming worst-case fading on the side-information channel, and subsequent layers describing the source under better fading conditions. Optimization of the layering scheme utilizes the Heegard–Berger rate-distortion function that describes the rate required to meet a different distortion constraint for each fading state. The expected distortion minimization is formulated as a convex optimization problem in which the problem size is shown to be linear in the number fading states. At an asymptotically large encoding rate, we showed that the distortion exponent is independent of the side-information fading distribution. Under a wide class of fading distributions such as Rayleigh, Rician, Nakagami, and log-normal, it is observed that the optimal rate allocation concentrates approximately at a single layer. Moreover, we showed that a continuous rate allocation is not necessary for optimal expected distortion. Hence for a practical source coding scheme, the encoder only needs to target a single sideinformation channel condition. Index Terms Source coding, distortion, Heegard–Berger, side information, fading channel, convex optimization.