Secure Nested Codes for Type II Wiretap Channels

TL;DR

This paper introduces secure nested coding schemes for type II wiretap channels, achieving near-secrecy capacity and improving known secrecy rates for binary symmetric channels through innovative code constructions.

Contribution

It proposes two novel secure nested coding schemes for type II wiretap channels, expanding the achievable rate-equivocation region and enhancing secrecy rate bounds.

Findings

Achievable rate-equivocation region nearly covers the secrecy capacity.

New perfect secrecy rate surpasses previous results for binary symmetric channels.

Extension of coding schemes to various channel models demonstrates versatility.

Abstract

This paper considers the problem of secure coding design for a type II wiretap channel, where the main channel is noiseless and the eavesdropper channel is a general binary-input symmetric-output memoryless channel. The proposed secure error-correcting code has a nested code structure. Two secure nested coding schemes are studied for a type II Gaussian wiretap channel. The nesting is based on cosets of a good code sequence for the first scheme and on cosets of the dual of a good code sequence for the second scheme. In each case, the corresponding achievable rate-equivocation pair is derived based on the threshold behavior of good code sequences. The two secure coding schemes together establish an achievable rate-equivocation region, which almost covers the secrecy capacity-equivocation region in this case study. The proposed secure coding scheme is extended to a type II binary symmetric wiretap channel. A new achievable perfect secrecy rate, which improves upon the previously reported result by Thangaraj et al., is derived for this channel.