On volumes of spheres for the stem distance

On volumes of spheres for the stem distance For any two q-ary sequences x and y, the stem similarity between them is defined as a total number of stems (blocks of length 2 consisting of adjacent elements of x and y) in their longest common Hamming subsequence. For q = 4 this similarity function and the corresponding distance function arise in molecular biology in describing an additive mathematical model of thermodynamic distance between DNA sequences. In the present paper, we derive explicit formulas for sphere sizes in this metric and consider their asymptotics in the case of spheres of a constant radius. Based on these results, we also obtain a random coding bound and Hamming bound for the optimal size of the so-called DNA codes for the case of a constant distance. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Problems of Information Transmission Springer Journals

On volumes of spheres for the stem distance

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Publisher
Springer Journals
Copyright
Copyright © 2010 by Pleiades Publishing, Ltd.
Subject
Engineering; Systems Theory, Control; Information Storage and Retrieval; Electrical Engineering; Communications Engineering, Networks
ISSN
0032-9460
eISSN
1608-3253
D.O.I.
10.1134/S0032946010010023
Publisher site
See Article on Publisher Site

Abstract

For any two q-ary sequences x and y, the stem similarity between them is defined as a total number of stems (blocks of length 2 consisting of adjacent elements of x and y) in their longest common Hamming subsequence. For q = 4 this similarity function and the corresponding distance function arise in molecular biology in describing an additive mathematical model of thermodynamic distance between DNA sequences. In the present paper, we derive explicit formulas for sphere sizes in this metric and consider their asymptotics in the case of spheres of a constant radius. Based on these results, we also obtain a random coding bound and Hamming bound for the optimal size of the so-called DNA codes for the case of a constant distance.

Journal

Problems of Information TransmissionSpringer Journals

Published: Apr 23, 2010

References

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