Source coding with feedforward using the posterior matching scheme

This paper considers the problem of source coding with feedforward, where an encoder compresses an i.i.d. source into a message, and the decoder takes this message, along with causal noiseless side information, to construct an estimate of the source. The posterior matching scheme is an optimal feedback communication scheme for memoryless channels that results in the channel outputs being i.i.d. The duality between channel coding with feedback and source coding with feedforward motivates the idea of dualizing posterior matching for this setting. We demonstrate, using a Lyapunov exponent approach, that such a scheme attains the rate-distortion function.