Feed-Forward Rate Distortion Function and Markov Sources

The problem of channel coding with feedback has been extensively studied over the last 50 years. Using an ideal feedback link, the encoder knows all previously received channel outputs. Recently the duality between channel coding and rate distortion has been established in [15] and [3], leading to the problem of source coding with feed-forward. In this project we first study the general formula for the feed-forward rate distortion function given by Venkataramanan et al. [8]. They studied the source coding problem when a feed-forward link is available for general sources and general distortion measures. They derived the feed-forward rate distortion function for an arbitrary source in terms of the directed information which was originally introduced by Massey [5]. It is shown that the general formula given for source coding with feed-forward is closely related to the general formula for channel coding with feedback given by Tatikonda [4]. We then study another formula for the feed-forward rate distortion function recently proposed by Naiss et al. which is tractable and computable [17]. They also calculated the exact rate distortion function for first order asymmetric Markov sources. An original contribution of this project is an alternative achievability proof for the feed-forward rate distortion function of first order asymmetric Markov sources. I