Multiterminal Source Coding with an Entropy-Based Distortion Measure
  In this paper, we consider a class of multiterminal source coding problems, each subject to distortion constraints computed using a specific, entropy-based, distortion measure. We provide the achievable rate distortion region for two cases and, in so doing, we demonstrate a relationship between the lossy multiterminal source coding problems with our specific distortion measure and (1) the canonical Slepian-Wolf lossless distributed source coding network, and (2) the Ahlswede-K\"{o}rner-Wyner source coding with side information problem in which only one of the sources is recovered losslessly. 
Thomas Courtade and Richard Wesel
cs.IT math.IT