Channel simulation via interactive communications

Abstract

In this paper, we study the problem of channel simulation via interactive communication, known as the coordination capacity, in a two-terminal network. We assume that two terminals observe i.i.d. copies of two random variables and would like to generate i.i.d. copies of two other random variables jointly distributed with the observed random variables. The terminals are provided with two-way communication links, and shared common randomness, all at limited rates. Two special cases of this problem are the interactive function computation studied by Ma and Ishwar, and the tradeoff curve between one-way communication and shared randomness studied by Cuff. The latter work had inspired Gohari and Anantharam to study the general problem of channel simulation via interactive communication stated above. However only inner and outer bounds for the special case of no shared randomness were obtained in their work. In this paper we settle this problem by providing an exact computable characterization of the multi-round problem. To show this we employ the technique of "output statistics of random binning" that has been recently developed by the authors.

Achievability Proof via Output Statistics of Random Binning

“…The proposed method has a simple structure (using only random binning), and can solve some problems much easier than the traditional techniques; see [35,36] for two examples that are not included in this manuscript. These examples consider the problems of channel simulation and coordination.…”

“…These examples consider the problems of channel simulation and coordination. In [35], we find an exact computable characterization of a multi-round channel simulation problem for which only inner and outer bounds were known previously. In coordination problems [6], we want to generate random variables whose joint distribution is close to a desired i.i.d.…”

Information Complexity Density and Simulation of Protocols

“…A general version of the simulation problem was considered in [55], but only bounded round simulation protocols were considered. Interestingly, it was shown in [8] that the amortized 3 distributional communication complexity of simulating n copies of a protocol π for vanishing simulation error is bounded above by 4 IC(π).…”

“…On the other hand, the arguments in 6 [8] or [55] give us D ε (π n ) ≥ nIC(π) − nε[|π| + log |X ||Y|] − ε log(1/ε).…”

Assisted sampling of correlated sources

“…In channel synthesis [10], [11], Alice sends rate-limited messages to Bob to simulate a noisy channel between them. Recent work has generalized this setup to interactive communication [12] and a general characterization was been recently obtained by Yassaee et al [13]. A number of different scenarios for three terminals trying to coordinate actions was studied by Cuff et al [14], and a recent relay model was considered by Haddadpour et al [15] that also recovers some of the channel synthesis results [6], [11].…”