5,833 research outputs found
On the Evaluation of the Polyanskiy-Poor-Verdu Converse Bound for Finite Blocklength Coding in AWGN
A tight converse bound to channel coding rate in the finite block-length
regime and under AWGN conditions was recently proposed by Polyanskiy, Poor, and
Verdu (PPV). The bound is a generalization of a number of other classical
results, and it was also claimed to be equivalent to Shannon's 1959 cone
packing bound. Unfortunately, its numerical evaluation is troublesome even for
not too large values of the block-length n. In this paper we tackle the
numerical evaluation by compactly expressing the PPV converse bound in terms of
non-central chi-squared distributions, and by evaluating those through a an
integral expression and a corresponding series expansion which exploit a method
proposed by Temme. As a result, a robust evaluation method and new insights on
the bound's asymptotics, as well as new approximate expressions, are given.Comment: 13 pages, 10 figures. Matlab code available from
http://dgt.dei.unipd.it section Download->Finite Blocklength Regim
Laplace deconvolution and its application to Dynamic Contrast Enhanced imaging
In the present paper we consider the problem of Laplace deconvolution with
noisy discrete observations. The study is motivated by Dynamic Contrast
Enhanced imaging using a bolus of contrast agent, a procedure which allows
considerable improvement in {evaluating} the quality of a vascular network and
its permeability and is widely used in medical assessment of brain flows or
cancerous tumors. Although the study is motivated by medical imaging
application, we obtain a solution of a general problem of Laplace deconvolution
based on noisy data which appears in many different contexts. We propose a new
method for Laplace deconvolution which is based on expansions of the
convolution kernel, the unknown function and the observed signal over Laguerre
functions basis. The expansion results in a small system of linear equations
with the matrix of the system being triangular and Toeplitz. The number of
the terms in the expansion of the estimator is controlled via complexity
penalty. The advantage of this methodology is that it leads to very fast
computations, does not require exact knowledge of the kernel and produces no
boundary effects due to extension at zero and cut-off at . The technique
leads to an estimator with the risk within a logarithmic factor of of the
oracle risk under no assumptions on the model and within a constant factor of
the oracle risk under mild assumptions. The methodology is illustrated by a
finite sample simulation study which includes an example of the kernel obtained
in the real life DCE experiments. Simulations confirm that the proposed
technique is fast, efficient, accurate, usable from a practical point of view
and competitive
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