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

TL;DR

This paper introduces explicit wiretap codes that achieve optimal rates under uncertain eavesdropper channels using source coding, universal hashing, and distribution approximation, applicable to various models without symmetry or pre-shared secrets.

Contribution

It provides a unified, explicit construction of wiretap codes for uncertain channels, achieving known optimal rates with practical primitives and extending to compound main channels with polar coding.

Findings

Achieves best known single-letter secrecy rates for uncertain wiretap channels.

Constructs explicit codes using only source coding, universal hashing, and distribution approximation.

Extends results to compound main channels with polar coding schemes.

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.