602 research outputs found
Secrecy in the 2-User Symmetric Deterministic Interference Channel with Transmitter Cooperation
This work presents novel achievable schemes for the 2-user symmetric linear
deterministic interference channel with limited-rate transmitter cooperation
and perfect secrecy constraints at the receivers. The proposed achievable
scheme consists of a combination of interference cancelation, relaying of the
other user's data bits, time sharing, and transmission of random bits,
depending on the rate of the cooperative link and the relative strengths of the
signal and the interference. The results show, for example, that the proposed
scheme achieves the same rate as the capacity without the secrecy constraints,
in the initial part of the weak interference regime. Also, sharing random bits
through the cooperative link can achieve a higher secrecy rate compared to
sharing data bits, in the very high interference regime. The results highlight
the importance of limited transmitter cooperation in facilitating secure
communications over 2-user interference channels.Comment: 5 pages, submitted to SPAWC 201
On Finding a Subset of Healthy Individuals from a Large Population
In this paper, we derive mutual information based upper and lower bounds on
the number of nonadaptive group tests required to identify a given number of
"non defective" items from a large population containing a small number of
"defective" items. We show that a reduction in the number of tests is
achievable compared to the approach of first identifying all the defective
items and then picking the required number of non-defective items from the
complement set. In the asymptotic regime with the population size , to identify non-defective items out of a population
containing defective items, when the tests are reliable, our results show
that measurements are
sufficient, where is a constant independent of and , and
is a bounded function of and . Further, in the nonadaptive group
testing setup, we obtain rigorous upper and lower bounds on the number of tests
under both dilution and additive noise models. Our results are derived using a
general sparse signal model, by virtue of which, they are also applicable to
other important sparse signal based applications such as compressive sensing.Comment: 32 pages, 2 figures, 3 tables, revised version of a paper submitted
to IEEE Trans. Inf. Theor
Cramer Rao-Type Bounds for Sparse Bayesian Learning
In this paper, we derive Hybrid, Bayesian and Marginalized Cram\'{e}r-Rao
lower bounds (HCRB, BCRB and MCRB) for the single and multiple measurement
vector Sparse Bayesian Learning (SBL) problem of estimating compressible
vectors and their prior distribution parameters. We assume the unknown vector
to be drawn from a compressible Student-t prior distribution. We derive CRBs
that encompass the deterministic or random nature of the unknown parameters of
the prior distribution and the regression noise variance. We extend the MCRB to
the case where the compressible vector is distributed according to a general
compressible prior distribution, of which the generalized Pareto distribution
is a special case. We use the derived bounds to uncover the relationship
between the compressibility and Mean Square Error (MSE) in the estimates.
Further, we illustrate the tightness and utility of the bounds through
simulations, by comparing them with the MSE performance of two popular
SBL-based estimators. It is found that the MCRB is generally the tightest among
the bounds derived and that the MSE performance of the Expectation-Maximization
(EM) algorithm coincides with the MCRB for the compressible vector. Through
simulations, we demonstrate the dependence of the MSE performance of SBL based
estimators on the compressibility of the vector for several values of the
number of observations and at different signal powers.Comment: Accepted for publication in the IEEE Transactions on Signal
Processing, 11 pages, 10 figure
Computationally Tractable Algorithms for Finding a Subset of Non-defective Items from a Large Population
In the classical non-adaptive group testing setup, pools of items are tested
together, and the main goal of a recovery algorithm is to identify the
"complete defective set" given the outcomes of different group tests. In
contrast, the main goal of a "non-defective subset recovery" algorithm is to
identify a "subset" of non-defective items given the test outcomes. In this
paper, we present a suite of computationally efficient and analytically
tractable non-defective subset recovery algorithms. By analyzing the
probability of error of the algorithms, we obtain bounds on the number of tests
required for non-defective subset recovery with arbitrarily small probability
of error. Our analysis accounts for the impact of both the additive noise
(false positives) and dilution noise (false negatives). By comparing with the
information theoretic lower bounds, we show that the upper bounds on the number
of tests are order-wise tight up to a factor, where is the number
of defective items. We also provide simulation results that compare the
relative performance of the different algorithms and provide further insights
into their practical utility. The proposed algorithms significantly outperform
the straightforward approaches of testing items one-by-one, and of first
identifying the defective set and then choosing the non-defective items from
the complement set, in terms of the number of measurements required to ensure a
given success rate.Comment: In this revision: Unified some proofs and reorganized the paper,
corrected a small mistake in one of the proofs, added more reference
On the DMT of TDD-SIMO Systems with Channel-Dependent Reverse Channel Training
This paper investigates the Diversity-Multiplexing gain Trade-off (DMT) of a
training based reciprocal Single Input Multiple Output (SIMO) system, with (i)
perfect Channel State Information (CSI) at the Receiver (CSIR) and noisy CSI at
the Transmitter (CSIT), and (ii) noisy CSIR and noisy CSIT. In both the cases,
the CSIT is acquired through Reverse Channel Training (RCT), i.e., by sending a
training sequence from the receiver to the transmitter. A channel-dependent
fixed-power training scheme is proposed for acquiring CSIT, along with a
forward-link data transmit power control scheme. With perfect CSIR, the
proposed scheme is shown to achieve a diversity order that is quadratically
increasing with the number of receive antennas. This is in contrast with
conventional orthogonal RCT schemes, where the diversity order is known to
saturate as the number of receive antennas is increased, for a given channel
coherence time. Moreover, the proposed scheme can achieve a larger DMT compared
to the orthogonal training scheme. With noisy CSIR and noisy CSIT, a three-way
training scheme is proposed and its DMT performance is analyzed. It is shown
that nearly the same diversity order is achievable as in the perfect CSIR case.
The time-overhead in the training schemes is explicitly accounted for in this
work, and the results show that the proposed channel-dependent RCT and data
power control schemes offer a significant improvement in terms of the DMT,
compared to channel-agnostic orthogonal RCT schemes. The outage performance of
the proposed scheme is illustrated through Monte-Carlo simulations.Comment: Accepted for publication in IEEE Transactions on Communication
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