Explicit codes for the wiretap channel with uncertainty on the eavesdropper's channel

Abstract

We develop explicit codes for the wiretap channel when uncertainties hold on the eavesdropper's channel statistics. We do not require any symmetry or degradation assumptions on the channel and we do not require a pre-shared secret between the legitimate users. Our code construction achieves the best known achievable communication rate derived with non-constructive proofs. The underlying idea of our code design is an efficient emulation of random binning via polar codes to obtain reliability, along with an appropriate combination of universal hashing implemented via invertible extractors to ensure secrecy. Our code construction does not follow from previous constructions with polar codes that cannot support uncertainties on the eavesdropper's channel and require a pre-shared secret, and conceptually differs from known explicit codes relying on invertible extractors that are not optimal for asymmetric or non-degraded channels.