1,933 research outputs found
Optimal Detection for Diffusion-Based Molecular Timing Channels
This work studies optimal detection for communication over diffusion-based
molecular timing (DBMT) channels. The transmitter simultaneously releases
multiple information particles, where the information is encoded in the time of
release. The receiver decodes the transmitted information based on the random
time of arrival of the information particles, which is modeled as an additive
noise channel. For a DBMT channel without flow, this noise follows the L\'evy
distribution. Under this channel model, the maximum-likelihood (ML) detector is
derived and shown to have high computational complexity. It is also shown that
under ML detection, releasing multiple particles improves performance, while
for any additive channel with -stable noise where (such as
the DBMT channel), under linear processing at the receiver, releasing multiple
particles degrades performance relative to releasing a single particle. Hence,
a new low-complexity detector, which is based on the first arrival (FA) among
all the transmitted particles, is proposed. It is shown that for a small number
of released particles, the performance of the FA detector is very close to that
of the ML detector. On the other hand, error exponent analysis shows that the
performance of the two detectors differ when the number of released particles
is large.Comment: 16 pages, 9 figures. Submitted for publicatio
Information Extraction Under Privacy Constraints
A privacy-constrained information extraction problem is considered where for
a pair of correlated discrete random variables governed by a given
joint distribution, an agent observes and wants to convey to a potentially
public user as much information about as possible without compromising the
amount of information revealed about . To this end, the so-called {\em
rate-privacy function} is introduced to quantify the maximal amount of
information (measured in terms of mutual information) that can be extracted
from under a privacy constraint between and the extracted information,
where privacy is measured using either mutual information or maximal
correlation. Properties of the rate-privacy function are analyzed and
information-theoretic and estimation-theoretic interpretations of it are
presented for both the mutual information and maximal correlation privacy
measures. It is also shown that the rate-privacy function admits a closed-form
expression for a large family of joint distributions of . Finally, the
rate-privacy function under the mutual information privacy measure is
considered for the case where has a joint probability density function
by studying the problem where the extracted information is a uniform
quantization of corrupted by additive Gaussian noise. The asymptotic
behavior of the rate-privacy function is studied as the quantization resolution
grows without bound and it is observed that not all of the properties of the
rate-privacy function carry over from the discrete to the continuous case.Comment: 55 pages, 6 figures. Improved the organization and added detailed
literature revie
Entropy Production of Doubly Stochastic Quantum Channels
We study the entropy increase of quantum systems evolving under primitive,
doubly stochastic Markovian noise and thus converging to the maximally mixed
state. This entropy increase can be quantified by a logarithmic-Sobolev
constant of the Liouvillian generating the noise. We prove a universal lower
bound on this constant that stays invariant under taking tensor-powers. Our
methods involve a new comparison method to relate logarithmic-Sobolev constants
of different Liouvillians and a technique to compute logarithmic-Sobolev
inequalities of Liouvillians with eigenvectors forming a projective
representation of a finite abelian group. Our bounds improve upon similar
results established before and as an application we prove an upper bound on
continuous-time quantum capacities. In the last part of this work we study
entropy production estimates of discrete-time doubly-stochastic quantum
channels by extending the framework of discrete-time logarithmic-Sobolev
inequalities to the quantum case.Comment: 24 page
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