Heegard-Berger and Cascade Source Coding Problems with Common Reconstruction Constraints

摘要

For the HB problem with the CR constraint, the rate-distortion function isderived under the assumption that the side information sequences are(stochastically) degraded. The rate-distortion function is also calculatedexplicitly for three examples, namely Gaussian source and side information withquadratic distortion metric, and binary source and side information witherasure and Hamming distortion metrics. The rate-distortion function is thencharacterized for the HB problem with cooperating decoders and (physically)degraded side information. For the cascade problem with the CR constraint, therate-distortion region is obtained under the assumption that side informationat the final node is physically degraded with respect to that at theintermediate node. For the latter two cases, it is worth emphasizing that thecorresponding problem without the CR constraint is still open. Outer and innerbounds on the rate-distortion region are also obtained for the cascade problemunder the assumption that the side information at the intermediate node isphysically degraded with respect to that at the final node. For the threeexamples mentioned above, the bounds are shown to coincide. Finally, for the HBproblem, the rate-distortion function is obtained under the more generalrequirement of constrained reconstruction, whereby the decoder's estimate mustbe recovered at the encoder only within some distortion.