The Rate-Distortion Function for Product of Two Sources With Side-Information at Decoders

This paper investigates a lossy source coding problem, in which two decoders can access their respective side-information. The correlated sources are a product of two component correlated sources, and we exclusively investigate the case such that each component is degraded. We show the rate-distortion function for that case and give the following observations. When the components are degraded in matched order, the rate-distortion function of the product sources is equal to the sum of the componentwise rate-distortion functions. On the other hand, the former is strictly smaller than the latter when the component sources are degraded in mismatched order. The converse proof for the mismatched case is motivated by the enhancement technique used for broadcast channels. For binary Hamming and Gaussian examples, we evaluate the rate-distortion functions.