Source coding theory for a triangular communication system

A rate-distortion problem is considered for a triangular communication system (TCS), which has one encoder f and two decoders g _X and g_Y. The encoder f maps correlated source outputs (X^K,Y^K) to two codewords W_X and W_Y, which are sent to g_X and g_Y, respectively. The decoders g_X and g_Y can communicate with each other via rate-constrained channels as many times as they need, and g_X reproduces Xˆ^K while g _Y reproduces Yˆ^K. The admissible rate-distortion region is determined for this TCS. Furthermore, the relations between the TCS and the Gray-Wyner (1974) system, Wyner's (1974) common information, Yamamoto's cascade communication system (1981), and the successive refinement system are discussed