On Körner-Marton's sum modulo two problem

Abstract

In this paper we study the sum modulo two problem proposed by Korner and Marton. In this source coding problem, two transmitters who observe binary sources X and Y, send messages of limited rate to a receiver whose goal is to compute the sum modulo of X and Y. This problem has been solved for the two special cases of independent and symmetric sources. In both of these cases, the rate pair (H(X|Y), H(Y|X)) is achievable. The best known outer bound for this problem is a conventional cut-set bound, and the best known inner bound is derived by Ahlswede and Han using a combination of Slepian-Wolf and Korner-Marton's coding schemes. In this paper, we propose a new outer bound which is strictly better than the cut-set bound. In particular, we show that the rate pair (H(X|Y), H(Y|X)) is not achievable for any binary sources other than independent and symmetric sources. Then, we study the minimum achievable sum-rate using Ahlswede-Han's region and propose a conjecture that this amount is not less than minimum of Slepian-Wolf and Korner-Marton's achievable sum-rates. We provide some evidences for this conjecture.