Explicit Wiretap Channel Codes via Source Coding, Universal Hashing, and Distribution Approximation, When the Channels' Statistics are Uncertain

Abstract: We consider wiretap channels with uncertainty on the eavesdropper channel under (i) noisy blockwise type II, (ii) compound, or (iii) arbitrarily varying models. We present explicit wiretap codes that can handle these models in a unified manner and only rely on three primitives, namely source coding with side information, universal hashing, and distribution approximation. Our explicit wiretap codes achieve the best known single-letter achievable rates, previously obtained non-constructively, for the models considered. Our results are obtained for strong secrecy, do not require a pre-shared secret between the legitimate users, and do not require any symmetry properties on the channel. An extension of our results to compound main channels is also derived via new capacity-achieving polar coding schemes for compound settings.