On cooperation in multi-terminal computation and rate distortion

A receiver wants to compute a function of two correlated sources separately observed by two transmitters. One of the transmitters is allowed to cooperate with the other transmitter by sending it some data before both transmitters convey information to the receiver. Assuming noiseless communication, what is the minimum number of bits that needs to be communicated by each transmitter to the receiver for a given number of cooperation bits? In this paper, first a general inner bound to the above three dimensional rate region is provided and shown to be tight in a number of interesting settings: the function is partially invertible, full cooperation, one-round point-to-point communication, two-round point-to-point communication, and cascade. Second, the related Kaspi-Berger rate distortion problem is investigated where the receiver now wants to recover the sources within some distortion. By using ideas developed for establishing the above inner bound, a new rate distortion inner bound is proposed. This bound always includes the time sharing of Kaspi-Berger´s inner bounds and inclusion is strict in certain cases.