  This paper investigates a lossy source coding problem in which two decoders
can access their side-information respectively. 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 component-wise rate distortion functions. On the
otherhand, 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.
