Two-way source coding with a fidelity criterion
IEEE Transactions on Information Theory
Communication complexity
Some complexity questions related to distributive computing(Preliminary Report)
STOC '79 Proceedings of the eleventh annual ACM symposium on Theory of computing
IEEE Transactions on Information Theory
From information to exact communication
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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A two-terminal interactive function computation problem with alternating messages is studied within the framework of distributed block source coding theory. For any arbitrary fixed number of messages, a single-letter characterization of the minimum sum-rate function was provided in previous work using traditional information-theoretic techniques. This, however, does not directly lead to a satisfactory characterization of the infinite-message limit, which is a new, unexplored dimension for asymptotic-analysis in distributed block source coding involving potentially infinitesimal-rate messages. This paper introduces a new convex-geometric approach to provide a blocklength-free single-letter characterization of the infinite-message minimum sum-rate function as a functional of the joint source pmf. This characterization is not obtained by taking a limit as the number of messages goes to infinity. Instead, it is in terms of the least element of a family of partially-ordered marginal-perturbations-concave functionals associated with the functions to be computed. For computing the Boolean AND function of two independent Bernoulli sources at one and both terminals, the respective infinite-message minimum sum-rates are characterized in closed analytic form. These sum-rates are achievable using infinitely many infinitesimal-rate messages. The convex-geometric functional viewpoint also suggests an iterative algorithm for evaluating any finite-message minimum sum-rate function.