37,103 research outputs found
On Pseudocodewords and Improved Union Bound of Linear Programming Decoding of HDPC Codes
In this paper, we present an improved union bound on the Linear Programming
(LP) decoding performance of the binary linear codes transmitted over an
additive white Gaussian noise channels. The bounding technique is based on the
second-order of Bonferroni-type inequality in probability theory, and it is
minimized by Prim's minimum spanning tree algorithm. The bound calculation
needs the fundamental cone generators of a given parity-check matrix rather
than only their weight spectrum, but involves relatively low computational
complexity. It is targeted to high-density parity-check codes, where the number
of their generators is extremely large and these generators are spread densely
in the Euclidean space. We explore the generator density and make a comparison
between different parity-check matrix representations. That density effects on
the improvement of the proposed bound over the conventional LP union bound. The
paper also presents a complete pseudo-weight distribution of the fundamental
cone generators for the BCH[31,21,5] code
Learning the dependence structure of rare events: a non-asymptotic study
Assessing the probability of occurrence of extreme events is a crucial issue
in various fields like finance, insurance, telecommunication or environmental
sciences. In a multivariate framework, the tail dependence is characterized by
the so-called stable tail dependence function (STDF). Learning this structure
is the keystone of multivariate extremes. Although extensive studies have
proved consistency and asymptotic normality for the empirical version of the
STDF, non-asymptotic bounds are still missing. The main purpose of this paper
is to fill this gap. Taking advantage of adapted VC-type concentration
inequalities, upper bounds are derived with expected rate of convergence in
O(k^-1/2). The concentration tools involved in this analysis rely on a more
general study of maximal deviations in low probability regions, and thus
directly apply to the classification of extreme data
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