157 research outputs found
Interference Alignment for the Multi-Antenna Compound Wiretap Channel
We study a wiretap channel model where the sender has transmit antennas
and there are two groups consisting of and receivers respectively.
Each receiver has a single antenna. We consider two scenarios. First we
consider the compound wiretap model -- group 1 constitutes the set of
legitimate receivers, all interested in a common message, whereas group 2 is
the set of eavesdroppers. We establish new lower and upper bounds on the secure
degrees of freedom. Our lower bound is based on the recently proposed
\emph{real interference alignment} scheme. The upper bound provides the first
known example which illustrates that the \emph{pairwise upper bound} used in
earlier works is not tight.
The second scenario we study is the compound private broadcast channel. Each
group is interested in a message that must be protected from the other group.
Upper and lower bounds on the degrees of freedom are developed by extending the
results on the compound wiretap channel.Comment: Minor edits. Submitted to IEEE Trans. Inf. Theor
Secure Transmission with Multiple Antennas II: The MIMOME Wiretap Channel
The capacity of the Gaussian wiretap channel model is analyzed when there are
multiple antennas at the sender, intended receiver and eavesdropper. The
associated channel matrices are fixed and known to all the terminals. A
computable characterization of the secrecy capacity is established as the
saddle point solution to a minimax problem. The converse is based on a
Sato-type argument used in other broadcast settings, and the coding theorem is
based on Gaussian wiretap codebooks.
At high signal-to-noise ratio (SNR), the secrecy capacity is shown to be
attained by simultaneously diagonalizing the channel matrices via the
generalized singular value decomposition, and independently coding across the
resulting parallel channels. The associated capacity is expressed in terms of
the corresponding generalized singular values. It is shown that a semi-blind
"masked" multi-input multi-output (MIMO) transmission strategy that sends
information along directions in which there is gain to the intended receiver,
and synthetic noise along directions in which there is not, can be arbitrarily
far from capacity in this regime.
Necessary and sufficient conditions for the secrecy capacity to be zero are
provided, which simplify in the limit of many antennas when the entries of the
channel matrices are independent and identically distributed. The resulting
scaling laws establish that to prevent secure communication, the eavesdropper
needs 3 times as many antennas as the sender and intended receiver have
jointly, and that the optimimum division of antennas between sender and
intended receiver is in the ratio of 2:1.Comment: To Appear, IEEE Trans. Information Theor
The MIMOME Channel
The MIMOME channel is a Gaussian wiretap channel in which the sender,
receiver, and eavesdropper all have multiple antennas. We characterize the
secrecy capacity as the saddle-value of a minimax problem. Among other
implications, our result establishes that a Gaussian distribution maximizes the
secrecy capacity characterization of Csisz{\'a}r and K{\"o}rner when applied to
the MIMOME channel. We also determine a necessary and sufficient condition for
the secrecy capacity to be zero. Large antenna array analysis of this condition
reveals several useful insights into the conditions under which secure
communication is possible.Comment: In Proceedings of the 45th Annual Allerton Conference on
Communication, Control, and Computing, October 2007, 8 page
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