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Transmission of a Gaussian source over a time-varying Gaussian channel isstudied in the presence of time-varying correlated side information at thereceiver. A block fading model is considered for both the channel and the sideinformation, whose states are assumed to be known only at the receiver. Theoptimality of separate source and channel coding in terms of average end-to-enddistortion is shown when the channel is static while the side information statefollows a discrete or a continuous and quasiconcave distribution. When both thechannel and side information states are time-varying, separate source andchannel coding is suboptimal in general. A partially informed encoder lowerbound is studied by providing the channel state information to the encoder.Several achievable transmission schemes are proposed based on uncodedtransmission, separate source and channel coding, joint decoding as well ashybrid digital-analog transmission. Uncoded transmission is shown to be optimalfor a class of continuous and quasiconcave side information statedistributions, while the channel gain may have an arbitrary distribution. Tothe best of our knowledge, this is the first example in which the uncodedtransmission achieves the optimal performance thanks to the time-varying natureof the states, while it is suboptimal in the static version of the sameproblem. Then, the optimal \emph{distortion exponent}, that quantifies theexponential decay rate of the expected distortion in the high SNR regime, ischaracterized for Nakagami distributed channel and side information states, andit is shown to be achieved by hybrid digital-analog and joint decoding schemesin certain cases, illustrating the suboptimality of pure digital or analogtransmission in general.

Joint Source-Channel Coding with Time-Varying Channel and Side-Information