Information-Theoretic
Secure Broadcasting
Ghadamali Bagheri-Karam
Coding and Signal Transmission (CST)
Laboratory
University of Waterloo
Friday, January 22, 2pm
Location: BA 4287
Abstract:
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 Cover’s
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 Costa’s 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 receivers’ 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.
Bio:
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-Karam’s 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
(akhisti@comm.utoronto.ca)