On the capacity of the binary adversarial wiretap channel

Abstract: New bounds on the semantic secrecy capacity of the binary adversarial wiretap channel are established . Against an adversary which reads a $\rho_r$ fraction of the transmitted codeword and modifies a $\rho_w$ fraction of the codeword, we show an achievable rate of $1-h(\rho_w)-\rho_r$, where $h(\cdot)$ is the binary entropy function. We also give an upper bound which is nearly matching when $\rho_r$ is small.