Toronto Networking Seminar

Organized by Department of Computer Science and Department of Electrical and Computer Engineering, University of Toronto

Information-Theoretic Secure Broadcasting

Ghadamali Bagheri-Karam
Coding and Signal Transmission (CST) Laboratory
University of Waterloo


Friday, January 22, 2pm
Location: BA 4287 


In this talk, a secure broadcast channel is considered. In the secure broadcast scenario, a source node wishes to broadcast two confidential messages to two receivers, while a wire-tapper also receives the transmitted signal. This model is motivated by wireless communications, where individual secure messages are broadcast over open media and can be received by any illegitimate receiver. The secrecy level is measured by the equivocation rate at the eavesdropper. An inner bound on the secrecy capacity region for the general broadcast channel is presented. This inner bound is based on a combination of random binning, and the Gelfand-Pinsker binning. A situation in which the channels are degraded is studied. For the degraded broadcast channel with an eavesdropper, the secrecy capacity region is presented. The achievable coding scheme is based on Coverís superposition scheme and random binning which is refereed as the Secret Superposition Scheme. The converse proof is based on a combination of the converse proof of the conventional degraded broadcast channel and Csiszar Lemma. The Additive White Gaussian Noise (AWGN) channel case is evaluated and is showed that the Secret Superposition Scheme with Gaussian codebook is optimal. The converse proof is based on Costaís entropy power inequality. The capacity region of the degraded MIMO secure broadcast channel is derived. For the outerbound, the notion of the enhanced channels is used to show that the secret superposition of Gaussian codes is optimal. The channels of the legitimate receivers are needed to be enhanced, and the channel of the eavesdropper remains unchanged. The result of the degraded case then is extended to a non-degraded case. It is proved that the secret superposition of Gaussian codes, along with successive decoding, cannot work when the channels are not degraded. A Secret Dirty Paper Coding (SDPC) scheme is developed to show that SDPC is optimal for this channel. A corollary generalizing the capacity region of the two receivers case to the case of multiple receivers then is presented. Finally, a scenario which frequently occurs in the practice of wireless networks is investigated. In this scenario, the transmitter and the eavesdropper have multiple antennae, while both intended receivers have a single antenna (representing resource limited mobile units). The secrecy capacity region in terms of generalized eigenvalues of the receiversí channels and the eavesdropper channel is characterized. A corollary generalizing the results of the two receivers case to multiple receivers then is presented and in the high SNR region the capacity region is evaluated.


Ghadamali Bagheri-Karam is a final-semester Ph.D student at the Coding and Signal Transmission (CST) Laboratory in Electrical and Computer Engineering, University of Waterloo. Mr. Bagheri-Karam received his B.Sc and M.Sc. degrees from Isfahan University of Technology in Isfahan, Iran in 2000 and 2003, respectively. He joined the Department of Electrical and Computer Engineering, University of Waterloo, in 2005. Mr. Bagheri-Karamís current research interests are in the Physical Layer of Wireless Systems with emphasis on Information-Theoretic secrecy in multi-terminal communication systems including Broadcast Channels, Multiple-Access Channels, Multiple Antenna Systems, and Co-operative Networking. He has published/submitted several conference/jornal papers of his works.

Host of Talk:

Ashish Khisti (