Coding against delayed adversaries

In this work we consider the communication of information in the presence of a delayed adversarial jammer. In the setting under study, a sender wishes to communicate a message to a receiver by transmitting a codeword x = (x₁, ..., x_n) over a communication channel. The adversarial jammer can view the transmitted symbols xi one at a time, but must base its action (when changing x_i) on x_j for j ≤ i - Δ_n, where Δ ∈ [0, 1] is a delay parameter. In this work, we study codes for a class of delayed adversaries, and for any delay Δ > 0 present a single letter characterization of the achievable communication rate in the presence of such adversaries.