Coding against a limited-view adversary: The effect of causality and feedback

We consider the problem of communication over a multi-path network in the presence of a causal adversary. The limited-view causal adversary is able to, based on the current and past observations, eavesdrop on a subset of links and also jam on a potentially overlapping subset of links. The goal is to ensure that the communication takes place reliably and secretly. We study two adversarial models - additive and overwrite jamming. For both adversarial models, we consider communication models both without and with passive feedback from decoder to encoder, i.e., the encoder sees everything that the decoder sees. The problem assumes transmissions are in the large alphabet regime. For both types of jamming models, we find the capacity under three scenarios - reliability without feedback, reliability and secrecy without feedback, and reliability with feedback. We observe that in comparison to the non-causal setting the capacity with a causal adversary is strictly increased for a wide variety of parameter settings, and present our intuition through several examples.