Zero-Error Capacity of Multiple Access Channels via Nonstochastic Information

The problem of characterising the zero-error capacity region for multiple access channels even in the noiseless case has remained an open problem for over three decades. Motivated by this challenging question, a recently developed theory of nonstochastic information is applied to characterise the zero-error capacity region for the case of two correlated transmitters. Unlike previous contributions, this analysis does not assume that the blocklength is asymptotically large. Finally, a new notion of nonstochastic information is proposed for a non-cooperative problem involving three agents. These results are preliminary steps towards understanding information flows in worst-case distributed estimation and control problems.