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(Δ) of achievable rates R_x, R_y for a given Δ=(Δ_x,Δ_y) with Δ_x the permissible distortion level for reproduction of X and Δ_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(Δ)), 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 Δ_x or Δ_y. The inner and outer bounds for this region R(E,Δ) are constructed. The analytical representation obtained for R(Δ) 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