On Distributed Successive Refinement with Lossless Recovery

The problem of successive refinement in distributed source coding and in joint source-channel coding is considered. The emphasis is placed on the case where the sources have to be recovered losslessly in the second stage. In distributed source coding, it is shown that all sources are successively refinable in sum rate, with respect to any (joint) distortion measure in the first stage. In joint source-channel coding, the sources are assumed independent and only a (per letter) function is to be recovered losslessly in the first stage. For a class of multiple access channels, it is shown that all sources are successively refinable with respect to a class of linear functions. Finally, when the sources have equal entropy, a simple sufficient condition of successive refinability is provided for partially invertible functions.