Achievable Region for Multiterminal Source Coding with Lossless Decoding in All Sources Except One

In this paper, we consider a class of multiterminal source coding problems, where all sources, except one, are reconstructed perfectly. Our framework generalizes the hitherto open single helper problems due to Csiszar and Korner, by adding complete side information at the decoder, and lossy reconstruction of the remaining source. In this setup we obtain a single-letter characterization (bearing resemblance with the Slepian-Wolf formula) of the achievable rate-distortion region. Thus we establish that perfect reconstruction in all but one source constitutes a sufficient structural condition for existence of single-letter description in the general multiterminal setup. We also show that known coding theorems are special cases.