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 gx and gy. The encoder f maps correlated source outputs (X”, Y”) to two codewords WX and WY, which are sent to gx and gy, respectively. The decoders gx and gy can communicate with each other via rate-constrained channels as many times as they need, and gx reproduces X-” while gy reproduces Y”. The admissible rate-distortion region is determined for this TCS. Furthermore, the relations between the TCS and the Gray-Wyner system, Wyner’s common information, Yamamoto’s cascade communication system, and the successive refinement system are discussed.