This paper focuses on the performance of aWyner-Ziv coding scheme for which the correlation between the source and the side information is modeled by a hidden Markov model with Gaussian emission. Such a signal model takes the memory of the correlation into account and is hence able to describe the bursty nature of the correlation between sources in applications such as sensor networks, video coding etc. This paper provides bounds on the rate-distortion performance of a Wyner-Ziv coding scheme for such model. It proposes a practical coding scheme able to exploit the memory in the correlation. Finally, the contribution to each part of the coding and decoding scheme is analysed.