Two-way source coding with a fidelity criterion

Let
(X_{i}, Y_{i}), i= 1,2 \cdots
, be a sequence of independent, identically distributed bivariate random variables and consider the following communication situation. The
X
component of the process is observed at some location, say
A
, while the
Y
component is observed at a different location, say
B
. The
X(Y)
component of the process has to be reproduced at location
B(A)
. It is desired to find the amount of information that should be exchanged between the two locations, so that the distortions incurred will not exceed some predetermined tolerance. A "single-letter characterization" of a certain region
{\cal****}^{K} \subset {\cal R}^{4}
of rates and distortions is given. This region contains (all, and only) the achievable rates and distortions for the special case where block coding is used and the information is conveyed through a one-way link that can switch direction only
K
times per block.