On the Duality of Layered Transmission for Fading and Packet Erasure Channels

We consider layered transmission of a successively refinable source over a quasi-static fading channel, where the goal is to minimize the expected end-to-end distortion of the received signal. The existing literature on this problem has been limited to either Gaussian sources or design metrics that are valid only for asymptotically high signal to noise ratios (SNR). In this paper, we explicitly solve the rate allocation problem for an arbitrary source and a finite SNR. We establish a duality relationship between this problem and that of packet transmission over erasure channels. The optimal rate allocation problem is then solved using the dual solution for the erasure channel. Numerical results for a MIMO Rayleigh fading channel and a practical image coder are presented.