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This paper considers the problem of source coding with feed-forward, 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 memory-less channels that result in the channel outputs being i.i.d. The duality between channel coding with feedback and source coding with feed-forward motivates the idea of dualizing posterior matching for this setting. They demonstrate, using a Lyapunov exponent approach, that such a scheme attains the rate-distortion function.
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