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...

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Published in:	Problems of information transmission Vol. 45; no. 2; pp. 124 - 144
Main Authors:	D’yachkov, A. G., Voronina, A. N.
Format:	Journal Article
Language:	English
Published:	Dordrecht SP MAIK Nauka/Interperiodica 01.06.2009
Subjects:	Coding Theory Communications Engineering Control Electrical Engineering Engineering Information Storage and Retrieval Networks Systems Theory Information Transmission Large Deviation Principle Cross Hybridization Moment Generate Function Random Code
ISSN:	0032-9460, 1608-3253
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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.
AbstractList	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.
Author	D’yachkov, A. G. Voronina, A. N.
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Cites_doi	10.1109/18.850695 10.1089/cmb.2007.0083 10.1146/annurev.biophys.32.110601.141800 10.1109/ISIT.2000.866628 10.1109/ISIT.2008.4595399
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Keywords	Information Transmission Large Deviation Principle Cross Hybridization Moment Generate Function Random Code
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References_xml	– volume: 41. start-page: 57 issue: 4 year: 2005 end-page: 77 ident: CR1 article-title: On DNA Codes publication-title: Probl. Peredachi Inf. – volume: 46 start-page: 1558 issue: 4 year: 2000 end-page: 1564 ident: CR7 article-title: On Similarity Codes publication-title: IEEE Trans. Inform. Theory doi: 10.1109/18.850695 – year: 1984 ident: CR12 publication-title: Algebraic Coding Theory – year: 1983 ident: CR13 publication-title: Theory and Practice of Error Control Codes – year: 1977 ident: CR5 publication-title: The Theory of Error-Correcting Codes – year: 1968 ident: CR11 publication-title: Information Theory and Reliable Communication – ident: CR3 – ident: CR4 – volume: 14 start-page: 1088 issue: 8 year: 2007 end-page: 1104 ident: CR2 article-title: Free Energy Gap and Statistical Thermodynamic Fidelity of DNA Codes publication-title: J. Comput. Biol. doi: 10.1089/cmb.2007.0083 – ident: CR6 – year: 1993 ident: CR10 publication-title: Large Deviations Techniques and Applications – volume: 33 start-page: 415 year: 2004 end-page: 440 ident: CR8 article-title: The Thermodynamics of DNA Structural Motifs publication-title: Annu. Rev. Biophys. Biomol. Struct. doi: 10.1146/annurev.biophys.32.110601.141800 – year: 1992 ident: CR9 publication-title: Teoriya veroyatnostei i sluchainykh protsessov – volume: 14 start-page: 1088 issue: 8 year: 2007 ident: 2004_CR2 publication-title: J. Comput. Biol. doi: 10.1089/cmb.2007.0083 – ident: 2004_CR6 doi: 10.1109/ISIT.2000.866628 – volume-title: Theory and Practice of Error Control Codes year: 1983 ident: 2004_CR13 – volume-title: Teoriya veroyatnostei i sluchainykh protsessov year: 1992 ident: 2004_CR9 – volume: 41. start-page: 57 issue: 4 year: 2005 ident: 2004_CR1 publication-title: Probl. Peredachi Inf. – volume-title: Algebraic Coding Theory year: 1984 ident: 2004_CR12 – ident: 2004_CR3 – ident: 2004_CR4 doi: 10.1109/ISIT.2008.4595399 – volume-title: Information Theory and Reliable Communication year: 1968 ident: 2004_CR11 – volume: 46 start-page: 1558 issue: 4 year: 2000 ident: 2004_CR7 publication-title: IEEE Trans. Inform. Theory doi: 10.1109/18.850695 – volume-title: The Theory of Error-Correcting Codes year: 1977 ident: 2004_CR5 – volume: 33 start-page: 415 year: 2004 ident: 2004_CR8 publication-title: Annu. Rev. Biophys. Biomol. Struct. doi: 10.1146/annurev.biophys.32.110601.141800 – volume-title: Large Deviations Techniques and Applications year: 1993 ident: 2004_CR10
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Title	DNA codes for additive stem similarity
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