The benefits offered by ubiquitous communication networks are now mitigated by the relative ease with which malicious users can interfere or tamper with sensitive data. The past decade has thus witnessed a growing concern for the issues of privacy, confidentiality, and integrity of communications. In particular, the users in a communication network now often find themselves in a position in which they wish to communicate without being detected by others.
In this talk, we will revisit recent results regarding the fundamental limits of covert communication over noisy channels from the perspective of source and channel resolvability. Source and channel resolvability are canonical information-theoretic problems that exploit error-control codes as a means to shape the distribution of stochastic processes. This conceptual approach allows us to develop three coding schemes that generalize and extend prior work in two directions. First, we show that, irrespective of the quality of the channels, it is possible to communicate O(sqrt(n)) reliable and covert bits over n channel uses if the transmitter and the receiver share a key of size O(sqrt(n)); this improves upon earlier results requiring a key of size O(sqrt(n) log n) bits. Second, we show that, under certain conditions, it is possible to communicate O(sqrt(n)) reliable and covert bits over n channel uses without a secret key; this generalizes an earlier result established for binary symmetric channels.
The main technical problem that we address is how to develop concentration inequalities for "low-weight" sequences; the crux of our approach is to define suitably modified typical sets that are amenable to concentration inequalities. We will also discuss how the conceptual approach allows us to analyze the fundamental limits of covert communication in multi-terminal problems.
Matthieu Bloch is an Assistant Professor in the School of Electrical and Computer Engineering at Georgia Tech, where he received the Ph.D. degree in Electrical Engineering in 2008. His research interests are in the areas of information theory, error-control coding, wireless communications, and cryptography. He is the co-recipient of the IEEE Communications Society and IEEE Information Theory Society 2011 Joint Paper Award and the co-author of the textbook Physical-Layer Security: From Information Theory to Security Engineering published by Cambridge University Press.