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An Optimization Problem Related to the Computation of the Epsilon-entropy of an Ellipsoid in a Hamming Space

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Abstract

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.

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REFERENCES

  1. Pinsker, M.S., Entropy of an Ellipsoid in a Hamming Space, Probl. Peredachi Inf., 2000, vol. 36, no. 4, pp. 47–52 [Probl. Inf. Trans. (Engl. Transl.), 2000, vol. 36, no. 4, pp. 325-330].

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  2. Dumer, I.I., Pinsker, M.S., and Prelov, V.V., Epsilon-entropy of an Ellipsoid in a Hamming Space, Probl. Peredachi Inf., 2002, vol. 38, no. 1, pp. 3–18 [Probl. Inf. Trans. (Engl. Transl.), 2002, vol. 38, no. 1, pp. 1-15].

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Authors
  1. I. I. Dumer
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  2. M. S. Pinsker
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  3. V. V. Prelov
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Dumer, I.I., Pinsker, M.S. & Prelov, V.V. An Optimization Problem Related to the Computation of the Epsilon-entropy of an Ellipsoid in a Hamming Space. Problems of Information Transmission 38, 99–112 (2002). https://doi.org/10.1023/A:1020054525528

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  • DOI: https://doi.org/10.1023/A:1020054525528

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