39 research outputs found
Joint Unitary Triangularization for MIMO Networks
This work considers communication networks where individual links can be
described as MIMO channels. Unlike orthogonal modulation methods (such as the
singular-value decomposition), we allow interference between sub-channels,
which can be removed by the receivers via successive cancellation. The degrees
of freedom earned by this relaxation are used for obtaining a basis which is
simultaneously good for more than one link. Specifically, we derive necessary
and sufficient conditions for shaping the ratio vector of sub-channel gains of
two broadcast-channel receivers. We then apply this to two scenarios: First, in
digital multicasting we present a practical capacity-achieving scheme which
only uses scalar codes and linear processing. Then, we consider the joint
source-channel problem of transmitting a Gaussian source over a two-user MIMO
channel, where we show the existence of non-trivial cases, where the optimal
distortion pair (which for high signal-to-noise ratios equals the optimal
point-to-point distortions of the individual users) may be achieved by
employing a hybrid digital-analog scheme over the induced equivalent channel.
These scenarios demonstrate the advantage of choosing a modulation basis based
upon multiple links in the network, thus we coin the approach "network
modulation".Comment: Submitted to IEEE Tran. Signal Processing. Revised versio
Modulation and Estimation with a Helper
The problem of transmitting a parameter value over an additive white Gaussian
noise (AWGN) channel is considered, where, in addition to the transmitter and
the receiver, there is a helper that observes the noise non-causally and
provides a description of limited rate to the transmitter and/or
the receiver. We derive upper and lower bounds on the optimal achievable
-th moment of the estimation error and show that they coincide for
small values of and for low SNR values. The upper bound relies on a
recently proposed channel-coding scheme that effectively conveys
bits essentially error-free and the rest of the rate - over the same AWGN
channel without help, with the error-free bits allocated to the most
significant bits of the quantized parameter. We then concentrate on the setting
with a total transmit energy constraint, for which we derive achievability
results for both channel coding and parameter modulation for several scenarios:
when the helper assists only the transmitter or only the receiver and knows the
noise, and when the helper assists the transmitter and/or the receiver and
knows both the noise and the message. In particular, for the message-informed
helper that assists both the receiver and the transmitter, it is shown that the
error probability in the channel-coding task decays doubly exponentially.
Finally, we translate these results to those for continuous-time power-limited
AWGN channels with unconstrained bandwidth. As a byproduct, we show that the
capacity with a message-informed helper that is available only at the
transmitter can exceed the capacity of the same scenario when the helper knows
only the noise but not the message.Comment: This work has been submitted to the IEEE for possible publication.
Copyright may be transferred without notice, after which this version may no
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Joint Unitary Triangularization for Gaussian Multi-User MIMO Networks
The problem of transmitting a common message to multiple users over the
Gaussian multiple-input multiple-output broadcast channel is considered, where
each user is equipped with an arbitrary number of antennas. A closed-loop
scenario is assumed, for which a practical capacity-approaching scheme is
developed. By applying judiciously chosen unitary operations at the transmit
and receive nodes, the channel matrices are triangularized so that the
resulting matrices have equal diagonals, up to a possible multiplicative scalar
factor. This, along with the utilization of successive interference
cancellation, reduces the coding and decoding tasks to those of coding and
decoding over the single-antenna additive white Gaussian noise channel. Over
the resulting effective channel, any off-the-shelf code may be used. For the
two-user case, it was recently shown that such joint unitary triangularization
is always possible. In this paper, it is shown that for more than two users, it
is necessary to carry out the unitary linear processing jointly over multiple
channel uses, i.e., space-time processing is employed. It is further shown that
exact triangularization, where all resulting diagonals are equal, is still not
always possible, and appropriate conditions for the existence of such are
established for certain cases. When exact triangularization is not possible, an
asymptotic construction is proposed, that achieves the desired property of
equal diagonals up to edge effects that can be made arbitrarily small, at the
price of processing a sufficiently large number of channel uses together.Comment: Extended version of published paper in IEEE Transactions on
Information Theory, vol. 61, no. 5, pp. 2662-2692, May 201
Learning-based attacks in cyber-physical systems
We introduce the problem of learning-based attacks in a simple abstraction of
cyber-physical systems---the case of a discrete-time, linear, time-invariant
plant that may be subject to an attack that overrides the sensor readings and
the controller actions. The attacker attempts to learn the dynamics of the
plant and subsequently override the controller's actuation signal, to destroy
the plant without being detected. The attacker can feed fictitious sensor
readings to the controller using its estimate of the plant dynamics and mimic
the legitimate plant operation. The controller, on the other hand, is
constantly on the lookout for an attack; once the controller detects an attack,
it immediately shuts the plant off. In the case of scalar plants, we derive an
upper bound on the attacker's deception probability for any measurable control
policy when the attacker uses an arbitrary learning algorithm to estimate the
system dynamics. We then derive lower bounds for the attacker's deception
probability for both scalar and vector plants by assuming a specific
authentication test that inspects the empirical variance of the system
disturbance. We also show how the controller can improve the security of the
system by superimposing a carefully crafted privacy-enhancing signal on top of
the "nominal control policy." Finally, for nonlinear scalar dynamics that
belong to the Reproducing Kernel Hilbert Space (RKHS), we investigate the
performance of attacks based on nonlinear Gaussian-processes (GP) learning
algorithms