Multiterminal rate-distortion theory revisited

The problem of determining the region of achievable rates and distortions for multiterminal lossy source coding remains unsolved. We revisit the case in which two discrete-alphabet sources are to be separately encoded and communicated to a common decoder. Inner and outer bounds to the admissible rate region for this problem, which were obtained over thirty years ago by Berger and Tung and by Omura and Housewright and of late have come to be widely referred to as BT_inner and BT_outer. BT_inner has yet to be improved upon and has been conjectured to be tight in some works. Although it is widely believed that the inner and outer bound do not coincide in most problems in which the two sources are not statistically independent, even this has been established only in limited families of special cases. We provide some fresh insights into the nature of optimum encoders and especially of optimum decoders for multitermainal lossy source coding. Also, we describe computations in progress for the special case of correlated symmetric binary sources and Hamming distortion measures aimed at generating a counterexample to the tightness of BT_inner.