A Random Variable Substitution Lemma With Applications to Multiple Description Coding

We establish a random variable substitution lemma and use it to investigate the role of refinement layer in multiple description coding, which clarifies the relationship among several existing achievable multiple description rate-distortion regions. Specifically, it is shown that the El Gamal-Cover (EGC) region is equivalent to the EGC* region (an antecedent version of the EGC region) while the Venkataramani-Kramer-Goyal (VKG) region (when specialized to the 2-description case) is equivalent to the Zhang-Berger (ZB) region. Moreover, we prove that for multiple description coding with individual and hierarchical distortion constraints, the number of layers in the VKG scheme can be significantly reduced when only certain weighted sum rates are concerned. The role of refinement layer in scalable coding (a special case of multiple description coding) is also studied. Index Terms Contra-polymatroid, multiple description coding, rate-distortion region, scalable coding, successive refinement,