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/sub X/ and g/sub Y/. The encoder f maps correlated source outputs (X/sup K/,Y/sup K/) to two codewords W/sub X/ and W/sub Y/, which are sent to g/sub X/ and g/sub Y/, respectively. The decoders g/sub X/ and g/sub Y/ can communicate with each other via rate-constrained channels as many times as they need, and g/sub X/ reproduces X/spl circ//sup K/ while g/sub Y/ reproduces Y/spl circ//sup 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.