Capacity-based random codes cannot achieve strong secrecy over symmetric wiretap channels

Authors:
Laura Luzzi;Matthieu R. Bloch
Affiliations:
Supélec, Gif-sur-Yvette, France;School of ECE, Georgia Institute of Technology, Atlanta, GA
Venue:
Proceedings of the 5th International ICST Conference on Performance Evaluation Methodologies and Tools
Year:
2011

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Abstract

In this paper, we investigate the limitations of capacity-based random code constructions for the wiretap channel, i.e., constructions that associate to each confidential message a subcode whose rate approaches the capacity of the eavesdropper's channel. Generalizing a previous result for binary symmetric channels, we show that random capacity-based codes do not achieve the strong secrecy capacity over the symmetric discrete memoryless channels they were designed for. However, we also show that these codes can achieve strong secrecy rates provided they are used over degraded wiretap channels.