Systematic lossy source transmission over Gaussian time-varying channels

Systematic lossy transmission of a Gaussian source over a time-varying Gaussian channel is considered. A noisy version of the source is transmitted in an uncoded fashion to the destination through a time-varying Gaussian “base channel”, constituting the systematic part of the transmission. A second time-varying Gaussian channel, called the “enhancement channel”, orthogonal to the first one, is available for coded transmission of the source sequence. A block fading model for both channels is considered, and the average end-to-end distortion is studied assuming perfect channel state information only at the receiver. It is shown that if the enhancement channel is static and the base channel gain has a discrete or continuous-quasiconcave distribution, then the separation theorem applies. However, when both channels are block fading, separation theorem does not hold anymore. A lower bound is obtained by providing the enhancement channel state to the encoder, and it is shown that uncoded transmission is exactly optimal for certain base channel fading distributions, while the enhancement channel fading has arbitrary distribution. A joint decoding scheme is also presented and is shown to outperform uncoded transmission and separate source and channel coding for other base channel distributions.