Distortion exponent of parallel fading channels

We consider the end-to-end distortion achieved by transmitting a continuous amplitude source over M parallel, independent quasi-static fading channels. We analyze the high SNR expected distortion behavior characterized by the distortion exponent. We first give an upper bound for the distortion exponent in terms of the bandwidth ratio between the channel and the source assuming the availability of the channel state information at the transmitter. Then we propose joint source-channel coding schemes based on layered source coding and multiple rate channel coding. We show that the upper bound is tight for large and small bandwidth ratios. For the rest, we provide the best known distortion exponents in the literature. By suitably scaling the bandwidth ratio, our results would also apply to block fading channels.