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 Paper ID D4-S5-T1.2 Paper Title Channel Coding Theorems in Non-stochastic Information Theory Authors Anshuka Rangi, Massimo Franceschetti, University of California, San Diego, United States Session D4-S5-T1: Information Measures II Chaired Session: Thursday, 15 July, 23:20 - 23:40 Engagement Session: Thursday, 15 July, 23:40 - 00:00 Abstract Recently, the $\delta$-mutual information between uncertain variables has been introduced as a generalization of Nair's non-stochastic mutual information functional~\cite{lim2017information,rangi2019towards}. Within this framework, we introduce four different notions of capacity and present corresponding coding theorems. Our definitions include an analogue of Shannon's capacity in a non-stochastic setting and a generalization of the zero-error capacity. The associated coding theorems hold for stationary, memoryless, non-stochastic uncertain channels. These results establish the relationship between the $\delta$-mutual information and our operational definitions, providing a step towards the development of a complete non-stochastic information theory.