Common Function Reconstruction with Information Swapping Terminals

Consider a communication setup consisting of two terminals, each with access to one of two correlated sources. The terminals can swap information and both terminals want to reconstruct a deterministic function of the two sources under the requirements that reconstructions at the two terminals must satisfy average distortion constraints and the two reconstructions must be identical with high probability. In this paper, we develop an achievability and a converse to the problem assuming discrete memoryless sources. Furthermore, we demonstrate that our bounds are separately tight for a few special cases of the problem.