Distortion Minimization in Gaussian Source Coding with Fading Side Information

We consider a layered approach to source coding that minimiz es expected distortion when side information is available through a fading channel. Specifically, we assu me a Gaussian source encoder whereby the decoder receives a compressed version of the symbol at a given rate, a s well as an uncompressed version over a separate side-information channel with slow fading and noise. The de coder knows the realization of the slow fading but the encoder knows only its distribution. We consider a layer ed encoding strategy with a base layer describing the source assuming worst-case fading on the side-information cha nel, and subsequent layers describing the source under better fading conditions. Optimization of the layeri ng scheme utilizes the Heegard–Berger rate-distortion function that describes the rate required to meet a differen t distortion constraint for each fading state. The expected distortion minimization is formulated as a convex optimiza tion problem in which the problem size is shown to be linear in the number fading states. At an asymptotically l arge encoding rate, we showed that the distortion exponent is independent of the side-information fading dis tribution. Under a wide class of fading distributions such as Rayleigh, Rician, Nakagami, and log-normal, it is ob erved that the optimal rate allocation concentrates approximately at a single layer. Moreover, we showed that a c ontinuous rate allocation is not necessary for optimal expected distortion. Hence for a practical source coding sc heme, the encoder only needs to target a single sideinformation channel condition. Index Terms Source coding, distortion, Heegard–Berger, side informat ion, fading channel, convex optimization.