Estimating with randomized encoding the joint empirical distribution in a correlated source

In order to put the present model and our results into the right perspectives we describe first key steps in multiuser source coding theory. We are given a discrete memoryless double source (DMDS) with alphabets X , Y, and generic variables X , Y , i.e., a sequence of independent replicas (Xt, Yt), t = 1, 2, . . . of the pair of random variables (X, Y ) taking values in the finite sets X and Y, respectively.