The joint source-channel coding problem of sending a Gaussian source with minimum average end-to-end distortion over a time-varying fading channel with time-varying correlated side information at the decoder is studied. A block fading model for both the channel and the side information qualities is considered. Perfect state information of the channel and the side information states is assumed at the receiver, while the transmitter has only a statistical knowledge. The performance is measured in terms of the distortion exponent, which quantifies the exponential decay rate of the expected distortion at high SNR. The effects on the distortion exponent of the bandwidth ratio, the side information quality and the side information diversity are analysed. Two upper bounds on the distortion exponent are derived by providing different channel state information to the encoder, and lower bounds are presented based on separate source and channel coding, joint decoding, uncoded transmission and hybrid digital-analog transmission schemes. In particular, the optimal distortion exponent is characterized in certain regimes by showing that hybrid analog-digital transmission or joint decoding schemes meet the optimal performance.