A strong direct product theorem for two-way public coin communication complexity

We show a direct product result for two-way public coin communication complexity of all relations in terms of a new complexity measure that we define. Our new measure is a generalization to non-product distributions of the two-way product subdistribution bound of [J, Klauck and Nayak 08], thereby our result implying their direct product result in terms of the two-way product subdistribution bound. We show that our new complexity measure gives tight lower bound for the set-disjointness problem, as a result we reproduce strong direct product result for this problem, which was previously shown by [Klauck 00].