69 research outputs found
Capacity Results for Relay Channels with Confidential Messages
We consider a communication system where a relay helps transmission of
messages from {a} sender to {a} receiver. The relay is considered not only as a
helper but as a wire-tapper who can obtain some knowledge about transmitted
messages. In this paper we study a relay channel with confidential
messages(RCC), where a sender attempts to transmit common information to both a
receiver and a relay and also has private information intended for the receiver
and confidential to the relay. The level of secrecy of private information
confidential to the relay is measured by the equivocation rate, i.e., the
entropy rate of private information conditioned on channel outputs at the
relay. The performance measure of interest for the RCC is the rate triple that
includes the common rate, the private rate, and the equivocation rate as
components. The rate-equivocation region is defined by the set that consists of
all these achievable rate triples. In this paper we give two definitions of the
rate-equivocation region. We first define the rate-equivocation region in the
case of deterministic encoder and call it the deterministic rate-equivocation
region. Next, we define the rate-equivocation region in the case of stochastic
encoder and call it the stochastic rate-equivocation region. We derive explicit
inner and outer bounds for the above two regions. On the
deterministic/stochastic rate-equivocation region we present two classes of
relay channels where inner and outer bounds match. We also evaluate the
deterministic and stochastic rate-equivocation regions of the Gaussian RCC.Comment: 31 pages, 8 figure
The Wiretap Channel with Feedback: Encryption over the Channel
In this work, the critical role of noisy feedback in enhancing the secrecy
capacity of the wiretap channel is established. Unlike previous works, where a
noiseless public discussion channel is used for feedback, the feed-forward and
feedback signals share the same noisy channel in the present model. Quite
interestingly, this noisy feedback model is shown to be more advantageous in
the current setting. More specifically, the discrete memoryless modulo-additive
channel with a full-duplex destination node is considered first, and it is
shown that the judicious use of feedback increases the perfect secrecy capacity
to the capacity of the source-destination channel in the absence of the
wiretapper. In the achievability scheme, the feedback signal corresponds to a
private key, known only to the destination. In the half-duplex scheme, a novel
feedback technique that always achieves a positive perfect secrecy rate (even
when the source-wiretapper channel is less noisy than the source-destination
channel) is proposed. These results hinge on the modulo-additive property of
the channel, which is exploited by the destination to perform encryption over
the channel without revealing its key to the source. Finally, this scheme is
extended to the continuous real valued modulo- channel where it is
shown that the perfect secrecy capacity with feedback is also equal to the
capacity in the absence of the wiretapper.Comment: Submitted to IEEE Transactions on Information Theor
Secure Beamforming for MIMO Two-Way Communications with an Untrusted Relay
This paper studies the secure beamforming design in a multiple-antenna
three-node system where two source nodes exchange messages with the help of an
untrusted relay node. The relay acts as both an essential signal forwarder and
a potential eavesdropper. Both two-phase and three-phase two-way relay
strategies are considered. Our goal is to jointly optimize the source and relay
beamformers for maximizing the secrecy sum rate of the two-way communications.
We first derive the optimal relay beamformer structures. Then, iterative
algorithms are proposed to find source and relay beamformers jointly based on
alternating optimization. Furthermore, we conduct asymptotic analysis on the
maximum secrecy sum-rate. Our analysis shows that when all transmit powers
approach infinity, the two-phase two-way relay scheme achieves the maximum
secrecy sum rate if the source beamformers are designed such that the received
signals at the relay align in the same direction. This reveals an important
advantage of signal alignment technique in against eavesdropping. It is also
shown that if the source powers approach zero the three-phase scheme performs
the best while the two-phase scheme is even worse than direct transmission.
Simulation results have verified the efficiency of the secure beamforming
algorithms as well as the analytical findings.Comment: 10 figures, Submitted to IEEE Transactions on Signal Processin
The Relay-Eavesdropper Channel: Cooperation for Secrecy
This paper establishes the utility of user cooperation in facilitating secure
wireless communications. In particular, the four-terminal relay-eavesdropper
channel is introduced and an outer-bound on the optimal rate-equivocation
region is derived. Several cooperation strategies are then devised and the
corresponding achievable rate-equivocation region are characterized. Of
particular interest is the novel Noise-Forwarding (NF) strategy, where the
relay node sends codewords independent of the source message to confuse the
eavesdropper. This strategy is used to illustrate the deaf helper phenomenon,
where the relay is able to facilitate secure communications while being totally
ignorant of the transmitted messages. Furthermore, NF is shown to increase the
secrecy capacity in the reversely degraded scenario, where the relay node fails
to offer performance gains in the classical setting. The gain offered by the
proposed cooperation strategies is then proved theoretically and validated
numerically in the additive White Gaussian Noise (AWGN) channel.Comment: 33 pages, submitted to IEEE Transactions on Information Theor
- …