Nested Polar Codes for Wiretap and Relay Channels

TL;DR

This paper demonstrates that nested polar codes can achieve the full capacity-equivocation region for degraded wiretap channels and the capacity of relay channels, with supporting simulation results for moderate block lengths.

Contribution

It introduces a coding scheme using nested polar codes that achieves optimal secrecy and relay channel capacities, extending polar code applications to secure and relay communications.

Findings

Polar codes achieve the capacity-equivocation region for degraded wiretap channels.

The coding scheme attains the capacity of physically degraded relay channels.

Simulation results show competitive performance of polar codes for moderate block lengths.

Abstract

We show that polar codes asymptotically achieve the whole capacity-equivocation region for the wiretap channel when the wiretapper's channel is degraded with respect to the main channel, and the weak secrecy notion is used. Our coding scheme also achieves the capacity of the physically degraded receiver-orthogonal relay channel. We show simulation results for moderate block length for the binary erasure wiretap channel, comparing polar codes and two edge type LDPC codes.