On the transmission of a memoryless Gaussian source over a memoryless fading channel

We consider the transmission of a discrete memoryless Gaussian source over a discrete memoryless fading channel with additive white Gaussian noise (AWGN) where the decoder has perfect channel state information (CSI). Our goal is to characterize the optimal tradeoff between the average transmission power constraint, P and the average estimation distortion, D. It is well known that for point-to-point transmission of a single Gaussian source over an AWGN channel, if the channel bandwidth is equal to the source bandwidth, linear (scalar) joint source-channel coding, i.e., uncoded transmission, achieves the optimal power-distortion tradeoff (Shannonpsilas limit). But this result does not hold in the presence of fading. In this work, we show that a relatively simple joint source-channel coding scheme, proposed by Lapidoth et al., which is based on the transmission of scaled versions of vector-quantized source sequences, can approach the optimal power-distortion tradeoff. This coding scheme is still optimal when the CSI is available at both the encoder and the decoder.