On optimal weighted-sum rates for the modulo sum problem

In a seminal work Körner and Marton showed that for computing the module-two sum of doubly symmetric binary sources, linear codes achieved the optimal rates and outperformed random coding and binning based arguments. Körner also showed the optimality of Slepian-Wolf based random coding for the same problem for a different class of pairwise distributions. We show that the optimal sum-rate is given by linear codes for a larger class of binary distributions, thus extending the optimality results for this problem.