Date & Time: Wednesday, April 27, 2011 , 16:30-17:30
Venue: Ramanujan Hall
Title: On Gaussian Wiretap Lattice Codes
Speaker: : Prof. Frederique Oggier, NTU, Singapore
In coding theory, information is transmitted over a noisy channel, and is encoded so as to provide redundancy to help the receiver to retrieve the intended message despite the noise. A wiretap channel is a communication channel where the information is sent to a legitimate receiver in the presence of an eavesdropper, and the goal of a wiretap code is to ensure reliability for the legitimate receiver, but also confidentiality, namely, the eavesdropper should only get a legitimate amount of the information. It has been shown that such wiretap codes exist when the two channels (the legimitate one and the one of the eavesdropper) are different, however, this is really an existence result, and very few such codes are known.
In this talk, we consider a wiretap channel where both channels experience a Gaussian noise, and propose wiretap lattice codes. We introduce a new lattice invariant called "secrecy gain", which is closely related to the theta series of the lattice, and captures the confusion at the eavesdropper. We then study the secrecy gain of unimodular lattices, and show how they can be used to construct wiretap lattice codes.