Channel Coding Theorems in Non-stochastic Information Theory

Recently, the
$\delta$
-mutual information between uncertain variables has been introduced as a generalization of Nair's non-stochastic mutual information functional [1], [2]. 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.