On the Limits of Distributed Agreement between Correlated Sources
2022 58th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2022
The work of Witsenhausen explores conditions under which two non-interactive users observing different coordinates of an i.i.d random process, can reach asymptotic agreement. Witsenhausen considers two scenarios: one in which both users observe a finite sequence with an error probability in the limit, and the second in which both users observe infinite-length sequences. In both cases, it turns out that perfect agreement is possible if and only if the joint distribution has a special decomposable structure known as a Gács-Körner common part. This paper revisits Witsenhausen's work and makes two contributions. First, we show that both results are equivalent, that each implies the other. Second, we offer a new proof of the second result, that unlike the others, avoids any tensorizing arguments or manipulations of multi-letter information measures. We explain how this new converse might overcome some of the obstacles commonly encountered in the classical converse arguments.
Jonathan Ponniah. "On the Limits of Distributed Agreement between Correlated Sources" 2022 58th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2022 (2022). https://doi.org/10.1109/Allerton49937.2022.9929402