10,736 research outputs found
Controlled Sensing for Multihypothesis Testing
The problem of multiple hypothesis testing with observation control is
considered in both fixed sample size and sequential settings. In the fixed
sample size setting, for binary hypothesis testing, the optimal exponent for
the maximal error probability corresponds to the maximum Chernoff information
over the choice of controls, and a pure stationary open-loop control policy is
asymptotically optimal within the larger class of all causal control policies.
For multihypothesis testing in the fixed sample size setting, lower and upper
bounds on the optimal error exponent are derived. It is also shown through an
example with three hypotheses that the optimal causal control policy can be
strictly better than the optimal open-loop control policy. In the sequential
setting, a test based on earlier work by Chernoff for binary hypothesis
testing, is shown to be first-order asymptotically optimal for multihypothesis
testing in a strong sense, using the notion of decision making risk in place of
the overall probability of error. Another test is also designed to meet hard
risk constrains while retaining asymptotic optimality. The role of past
information and randomization in designing optimal control policies is
discussed.Comment: To appear in the Transactions on Automatic Contro
Strong Converse for a Degraded Wiretap Channel via Active Hypothesis Testing
We establish an upper bound on the rate of codes for a wiretap channel with
public feedback for a fixed probability of error and secrecy parameter. As a
corollary, we obtain a strong converse for the capacity of a degraded wiretap
channel with public feedback. Our converse proof is based on a reduction of
active hypothesis testing for discriminating between two channels to coding for
wiretap channel with feedback.Comment: This paper was presented at Allerton 201
Distributed Binary Detection with Lossy Data Compression
Consider the problem where a statistician in a two-node system receives
rate-limited information from a transmitter about marginal observations of a
memoryless process generated from two possible distributions. Using its own
observations, this receiver is required to first identify the legitimacy of its
sender by declaring the joint distribution of the process, and then depending
on such authentication it generates the adequate reconstruction of the
observations satisfying an average per-letter distortion. The performance of
this setup is investigated through the corresponding rate-error-distortion
region describing the trade-off between: the communication rate, the error
exponent induced by the detection and the distortion incurred by the source
reconstruction. In the special case of testing against independence, where the
alternative hypothesis implies that the sources are independent, the optimal
rate-error-distortion region is characterized. An application example to binary
symmetric sources is given subsequently and the explicit expression for the
rate-error-distortion region is provided as well. The case of "general
hypotheses" is also investigated. A new achievable rate-error-distortion region
is derived based on the use of non-asymptotic binning, improving the quality of
communicated descriptions. Further improvement of performance in the general
case is shown to be possible when the requirement of source reconstruction is
relaxed, which stands in contrast to the case of general hypotheses.Comment: to appear on IEEE Trans. Information Theor
Asymptotic Estimates in Information Theory with Non-Vanishing Error Probabilities
This monograph presents a unified treatment of single- and multi-user
problems in Shannon's information theory where we depart from the requirement
that the error probability decays asymptotically in the blocklength. Instead,
the error probabilities for various problems are bounded above by a
non-vanishing constant and the spotlight is shone on achievable coding rates as
functions of the growing blocklengths. This represents the study of asymptotic
estimates with non-vanishing error probabilities.
In Part I, after reviewing the fundamentals of information theory, we discuss
Strassen's seminal result for binary hypothesis testing where the type-I error
probability is non-vanishing and the rate of decay of the type-II error
probability with growing number of independent observations is characterized.
In Part II, we use this basic hypothesis testing result to develop second- and
sometimes, even third-order asymptotic expansions for point-to-point
communication. Finally in Part III, we consider network information theory
problems for which the second-order asymptotics are known. These problems
include some classes of channels with random state, the multiple-encoder
distributed lossless source coding (Slepian-Wolf) problem and special cases of
the Gaussian interference and multiple-access channels. Finally, we discuss
avenues for further research.Comment: Further comments welcom
The asymptotic spectrum of LOCC transformations
We study exact, non-deterministic conversion of multipartite pure quantum
states into one-another via local operations and classical communication (LOCC)
and asymptotic entanglement transformation under such channels. In particular,
we consider the maximal number of copies of any given target state that can be
extracted exactly from many copies of any given initial state as a function of
the exponential decay in success probability, known as the converese error
exponent. We give a formula for the optimal rate presented as an infimum over
the asymptotic spectrum of LOCC conversion. A full understanding of exact
asymptotic extraction rates between pure states in the converse regime thus
depends on a full understanding of this spectrum. We present a characterisation
of spectral points and use it to describe the spectrum in the bipartite case.
This leads to a full description of the spectrum and thus an explicit formula
for the asymptotic extraction rate between pure bipartite states, given a
converse error exponent. This extends the result on entanglement concentration
in [Hayashi et al, 2003], where the target state is fixed as the Bell state. In
the limit of vanishing converse error exponent the rate formula provides an
upper bound on the exact asymptotic extraction rate between two states, when
the probability of success goes to 1. In the bipartite case we prove that this
bound holds with equality.Comment: v1: 21 pages v2: 21 pages, Minor corrections v3: 17 pages, Minor
corrections, new reference added, parts of Section 5 and the Appendix
removed, the omitted material can be found in an extended form in
arXiv:1808.0515
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