An Optimization Problem Related to the Computation of the Epsilon-entropy of an Ellipsoid in a Hamming Space
نویسندگان
چکیده
The problem of optimizing (finding the maximin of) the difference between the entropy functions of two n-dimensional vectors under special restrictions on their components is solved. This optimum gives the main term of the asymptotics for the ε-entropy of an ellipsoid in a Hamming space as the dimension of the space grows.
منابع مشابه
Epsilon-entropy of an Ellipsoid in a Hamming Space
i=1 aix 2 i ≤ r). The main goal of this paper is to investigate the asymptotic behavior of the ε-entropy of an ellipsoid Ea(r) as n→ ∞. Recall that the ε-entropy Hε(A) of a set A is defined as the logarithm of the minimal number of points of an ε-net covering the set A, i.e., Hε(A) = logmin |Mε|, (1.2) where the minimum is taken over all sets Mε such that Mε = {y ∈ E 2 | ∀x ∈ A ∃y ∈Mε : d(x, y)...
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عنوان ژورنال:
- Probl. Inf. Transm.
دوره 38 شماره
صفحات -
تاریخ انتشار 2002