Polar Coding for the Broadcast Channel with Confidential Messages: A Random Binning Analogy

TL;DR

This paper introduces a low-complexity polar coding scheme for secure broadcast channels that achieves strong secrecy without assuming channel symmetry, using shared secret seeds and chaining techniques.

Contribution

It extends polar coding methods to non-symmetric channels with confidentiality, employing an optimal randomness rate and linking to random binning proofs.

Findings

Achieves strong secrecy in broadcast channels

Uses minimal shared secret seed

Employs chaining to improve coding performance

Abstract

We develop a low-complexity polar coding scheme for the discrete memoryless broadcast channel with confidential messages under strong secrecy and randomness constraints. Our scheme extends previous work by using an optimal rate of uniform randomness in the stochastic encoder, and avoiding assumptions regarding the symmetry or degraded nature of the channels. The price paid for these extensions is that the encoder and decoders are required to share a secret seed of negligible size and to increase the block length through chaining. We also highlight a close conceptual connection between the proposed polar coding scheme and a random binning proof of the secrecy capacity region.