DNA codes for additive stem similarity

DNA codes for additive stem similarity We study two new concepts of combinatorial coding theory: additive stem similarity and additive stem distance between q-ary sequences. For q = 4, the additive stem similarity is applied to describe a mathematical model of thermodynamic similarity, which reflects the “hybridization potential” of two DNA sequences. Codes based on the additive stem distance are called DNA codes. We develop methods to prove upper and lower bounds on the rate of DNA codes analogous to the well-known Plotkin upper bound and random coding lower bound (the Gilbert-Varshamov bound). These methods take into account both the “Markovian” character of the additive stem distance and the structure of a DNA code specified by its invariance under the Watson-Crick transformation. In particular, our lower bound is established with the help of an ensemble of random codes where distribution of independent codewords is defined by a stationary Markov chain. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Problems of Information Transmission Springer Journals

DNA codes for additive stem similarity

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Publisher
SP MAIK Nauka/Interperiodica
Copyright
Copyright © 2009 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/S0032946009020045
Publisher site
See Article on Publisher Site

Abstract

We study two new concepts of combinatorial coding theory: additive stem similarity and additive stem distance between q-ary sequences. For q = 4, the additive stem similarity is applied to describe a mathematical model of thermodynamic similarity, which reflects the “hybridization potential” of two DNA sequences. Codes based on the additive stem distance are called DNA codes. We develop methods to prove upper and lower bounds on the rate of DNA codes analogous to the well-known Plotkin upper bound and random coding lower bound (the Gilbert-Varshamov bound). These methods take into account both the “Markovian” character of the additive stem distance and the structure of a DNA code specified by its invariance under the Watson-Crick transformation. In particular, our lower bound is established with the help of an ensemble of random codes where distribution of independent codewords is defined by a stationary Markov chain.

Journal

Problems of Information TransmissionSpringer Journals

Published: Jul 18, 2009

References

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