Two-terminal distributed source coding with alternating messages for function computation

A two-terminal interactive distributed source coding problem with alternating messages is studied. The focus is on function computation at both locations with a probability which tends to one as the blocklength tends to infinity. A single-letter characterization of the rate region is provided. It is observed that interaction is useless (in terms of the minimum sum-rate) if the goal is pure source reproduction at one or both locations but the gains can be arbitrarily large for (general) function computation. For doubly symmetric binary sources and any function, interaction is useless with even infinite messages, when computation is desired at only one location, but is useful, when desired at both locations. For independent Bernoulli sources and the Boolean AND function computation at both locations, an interesting achievable infinite-message sum-rate is derived. This sum-rate is expressed, in analytic closed-form, in terms of a two-dimensional definite integral with an infinitesimal rate for each message.