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This paper investigates a lossy source coding problem in which two decoderscan access their side-information respectively. The correlated sources are aproduct of two component correlated sources, and we exclusively investigate thecase such that each component is degraded. We show the rate-distortion functionfor that case, and give the following observations. When the components aredegraded in matched order, the rate distortion function of the product sourcesis equal to the sum of the component-wise rate distortion functions. On theotherhand, the former is strictly smaller than the latter when the componentsources are degraded in mismatched order. The converse proof for the mismatchedcase is motivated by the enhancement technique used for broadcast channels. Forbinary Hamming and Gaussian examples, we evaluate the rate-distortionfunctions.

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