A Symbolic Dynamical System Approach to Lossy Source Coding with Feedforward

It is known that modeling an information source via a symbolic dynamical system evolving over the unit interval, leads to a natural lossless compression scheme attaining the entropy rate of the source, under general conditions. We extend this notion to the lossy compression regime assuming a feedforward link is available, by modeling a source via a two-dimensional symbolic dynamical system where one component corresponds to the compressed signal, and the other essentially corresponds to the feedforward signal. For memoryless sources and an arbitrary bounded distortion measure, we show this approach leads to a family of simple deterministic compression schemes that attain the rate-distortion function of the source. The construction is dual to a recent optimal scheme for channel coding with feedback.