Improved upper bounds on the capacity of binary channels with causal adversaries

Abstract—In this work we consider the communication of information in the presence of a causal adversarial jammer. In the setting under study, a sender wishes to communicate a message to a receiver by transmitting a codeword x = (x1,..., xn) bit-by-bit over a communication channel. The adversarial jammer can view the transmitted bits xi one at a time, and can change up to a p-fraction of them. However, the decisions of the jammer must be made in a causal manner. Namely, for each bit xi the jammer’s decision on whether to corrupt it or not (and on how to change it) must depend only on xj for j ≤ i. This is in contrast to the “classical ” adversarial jammer which may base its decisions on its complete knowledge of x. Binary channels with causal adversarial jammers have seen recent studies in which both lower bounds and upper bounds on their capacity is derived. In this work, we present improved upper bounds on the capacity which hold for both deterministic and stochastic encoding schemes. I