Multiterminal source coding achievable rates and reliability

Some open problems concerning classical multiterminal configuration in which two correlated sources {X} and {Y} are encoded separately and decoded by common decoder with respect to a fidelity criterion for messages of both sources are resolved. The results of Berger and Yeung (1989) are expanded in two directions. First, we determine the "rate-distortion" region R(/spl Delta/) of achievable rates R/sub x/, R/sub y/ for a given /spl Delta/=(/spl Delta//sub x/,/spl Delta//sub y/) with /spl Delta//sub x/ the permissible distortion level for reproduction of X and /spl Delta//sub y/- for Y. Thus we give a full solution of the problem noted by Kaspi and Berger (1982) (they constructed the inner bound for R(/spl Delta/)), and solved by Berger and Yeung for the case of "one distortion". Second, we introduce the notion of "rate-reliability, distortion" region for the multiterminal source encoding problem; more precisely, the region of admissible rates of codes ensuring exponential decrease with a given exponent E>0 of the probability of exceeding the distortion levels /spl Delta//sub x/ or /spl Delta//sub y/. The inner and outer bounds for this region R(E,/spl Delta/) are constructed. The analytical representation obtained for R(/spl Delta/) proved to be somewhat simpler than that considered by Kaspi and Berger and by Berger and Yeung. Ours uses only variables pertaining to the problem statement with no auxiliary ones.