Efficient Encoding/Decoding of GC-Balanced Codes Correcting Tandem Duplications
Tandem duplication is the process of inserting a copy of a segment of DNA adjacent to the original position. Motivated by applications that store data in living organisms, Jain et al. (2017) proposed the study of codes that correct tandem duplications. All code constructions are based on irreducible...
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| Veröffentlicht in: | IEEE transactions on information theory Jg. 66; H. 8; S. 4892 - 4903 |
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| Sprache: | Englisch |
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IEEE
01.08.2020
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
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| ISSN: | 0018-9448, 1557-9654 |
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| Abstract | Tandem duplication is the process of inserting a copy of a segment of DNA adjacent to the original position. Motivated by applications that store data in living organisms, Jain et al. (2017) proposed the study of codes that correct tandem duplications. All code constructions are based on irreducible words . Such code constructions are almost optimal to combat tandem duplications of length at most <inline-formula> <tex-math notation="LaTeX">k </tex-math></inline-formula> where <inline-formula> <tex-math notation="LaTeX">k\leq 3 </tex-math></inline-formula>. However, the problem of designing efficient encoder/decoder for such codes has not been investigated. In addition, the method cannot be extended to deal with the case of arbitrary <inline-formula> <tex-math notation="LaTeX">k </tex-math></inline-formula>, where <inline-formula> <tex-math notation="LaTeX">k\geq 4 </tex-math></inline-formula>. In this work, we study efficient encoding/decoding methods for irreducible words over general <inline-formula> <tex-math notation="LaTeX">q </tex-math></inline-formula>-ary alphabet. Our methods provide the first known efficient encoder/decoder for <inline-formula> <tex-math notation="LaTeX">q </tex-math></inline-formula>-ary codes correcting tandem duplications of length at most <inline-formula> <tex-math notation="LaTeX">k </tex-math></inline-formula>, where <inline-formula> <tex-math notation="LaTeX">k\leq 3 </tex-math></inline-formula>. In particular, we describe an <inline-formula> <tex-math notation="LaTeX">(\ell,m) </tex-math></inline-formula>-finite state encoder and show that when <inline-formula> <tex-math notation="LaTeX">m=\Theta (1/\epsilon) </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">\ell =\Theta (1/\epsilon) </tex-math></inline-formula>, the encoder achieves rate that is <inline-formula> <tex-math notation="LaTeX">\epsilon </tex-math></inline-formula> away from the optimal rate. We also provide ranking/unranking algorithms for irreducible words and modify the algorithms to reduce the space requirements for the finite state encoder. Over the DNA alphabet (or quaternary alphabet), we also impose weight constraint on the codewords. In particular, a quaternary word is <inline-formula> <tex-math notation="LaTeX">{\tt GC} </tex-math></inline-formula>-balanced if exactly half of the symbols of are either <inline-formula> <tex-math notation="LaTeX">{\tt C} </tex-math></inline-formula> or <inline-formula> <tex-math notation="LaTeX">{\tt G} </tex-math></inline-formula>. Via a modification of Knuth's balancing technique, we provide an efficient method that translates quaternary messages into <inline-formula> <tex-math notation="LaTeX">{\tt GC} </tex-math></inline-formula>-balanced codewords and the resulting codebook is able to correct tandem duplications of length at most <inline-formula> <tex-math notation="LaTeX">k </tex-math></inline-formula>, where <inline-formula> <tex-math notation="LaTeX">k\leq 3 </tex-math></inline-formula>. In addition, we provide the first known construction of codes to combat tandem duplications of length at most <inline-formula> <tex-math notation="LaTeX">k </tex-math></inline-formula>, where <inline-formula> <tex-math notation="LaTeX">k \geq 4 </tex-math></inline-formula>. Such codes can correct duplication errors in linear-time and they are almost optimal in terms of rate. |
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| AbstractList | Tandem duplication is the process of inserting a copy of a segment of DNA adjacent to the original position. Motivated by applications that store data in living organisms, Jain et al. (2017) proposed the study of codes that correct tandem duplications. All code constructions are based on irreducible words . Such code constructions are almost optimal to combat tandem duplications of length at most <inline-formula> <tex-math notation="LaTeX">k </tex-math></inline-formula> where <inline-formula> <tex-math notation="LaTeX">k\leq 3 </tex-math></inline-formula>. However, the problem of designing efficient encoder/decoder for such codes has not been investigated. In addition, the method cannot be extended to deal with the case of arbitrary <inline-formula> <tex-math notation="LaTeX">k </tex-math></inline-formula>, where <inline-formula> <tex-math notation="LaTeX">k\geq 4 </tex-math></inline-formula>. In this work, we study efficient encoding/decoding methods for irreducible words over general <inline-formula> <tex-math notation="LaTeX">q </tex-math></inline-formula>-ary alphabet. Our methods provide the first known efficient encoder/decoder for <inline-formula> <tex-math notation="LaTeX">q </tex-math></inline-formula>-ary codes correcting tandem duplications of length at most <inline-formula> <tex-math notation="LaTeX">k </tex-math></inline-formula>, where <inline-formula> <tex-math notation="LaTeX">k\leq 3 </tex-math></inline-formula>. In particular, we describe an <inline-formula> <tex-math notation="LaTeX">(\ell,m) </tex-math></inline-formula>-finite state encoder and show that when <inline-formula> <tex-math notation="LaTeX">m=\Theta (1/\epsilon) </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">\ell =\Theta (1/\epsilon) </tex-math></inline-formula>, the encoder achieves rate that is <inline-formula> <tex-math notation="LaTeX">\epsilon </tex-math></inline-formula> away from the optimal rate. We also provide ranking/unranking algorithms for irreducible words and modify the algorithms to reduce the space requirements for the finite state encoder. Over the DNA alphabet (or quaternary alphabet), we also impose weight constraint on the codewords. In particular, a quaternary word is <inline-formula> <tex-math notation="LaTeX">{\tt GC} </tex-math></inline-formula>-balanced if exactly half of the symbols of are either <inline-formula> <tex-math notation="LaTeX">{\tt C} </tex-math></inline-formula> or <inline-formula> <tex-math notation="LaTeX">{\tt G} </tex-math></inline-formula>. Via a modification of Knuth's balancing technique, we provide an efficient method that translates quaternary messages into <inline-formula> <tex-math notation="LaTeX">{\tt GC} </tex-math></inline-formula>-balanced codewords and the resulting codebook is able to correct tandem duplications of length at most <inline-formula> <tex-math notation="LaTeX">k </tex-math></inline-formula>, where <inline-formula> <tex-math notation="LaTeX">k\leq 3 </tex-math></inline-formula>. In addition, we provide the first known construction of codes to combat tandem duplications of length at most <inline-formula> <tex-math notation="LaTeX">k </tex-math></inline-formula>, where <inline-formula> <tex-math notation="LaTeX">k \geq 4 </tex-math></inline-formula>. Such codes can correct duplication errors in linear-time and they are almost optimal in terms of rate. Tandem duplication is the process of inserting a copy of a segment of DNA adjacent to the original position. Motivated by applications that store data in living organisms, Jain et al. (2017) proposed the study of codes that correct tandem duplications. All code constructions are based on irreducible words . Such code constructions are almost optimal to combat tandem duplications of length at most [Formula Omitted] where [Formula Omitted]. However, the problem of designing efficient encoder/decoder for such codes has not been investigated. In addition, the method cannot be extended to deal with the case of arbitrary [Formula Omitted], where [Formula Omitted]. In this work, we study efficient encoding/decoding methods for irreducible words over general [Formula Omitted]-ary alphabet. Our methods provide the first known efficient encoder/decoder for [Formula Omitted]-ary codes correcting tandem duplications of length at most [Formula Omitted], where [Formula Omitted]. In particular, we describe an [Formula Omitted]-finite state encoder and show that when [Formula Omitted] and [Formula Omitted], the encoder achieves rate that is [Formula Omitted] away from the optimal rate. We also provide ranking/unranking algorithms for irreducible words and modify the algorithms to reduce the space requirements for the finite state encoder. Over the DNA alphabet (or quaternary alphabet), we also impose weight constraint on the codewords. In particular, a quaternary word is [Formula Omitted]-balanced if exactly half of the symbols of are either [Formula Omitted] or [Formula Omitted]. Via a modification of Knuth’s balancing technique, we provide an efficient method that translates quaternary messages into [Formula Omitted]-balanced codewords and the resulting codebook is able to correct tandem duplications of length at most [Formula Omitted], where [Formula Omitted]. In addition, we provide the first known construction of codes to combat tandem duplications of length at most [Formula Omitted], where [Formula Omitted]. Such codes can correct duplication errors in linear-time and they are almost optimal in terms of rate. |
| Author | Chee, Yeow Meng Chrisnata, Johan Kiah, Han Mao Nguyen, Tuan Thanh |
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| Cites_doi | 10.1093/nar/gkj454 10.1109/TIT.1986.1057136 10.1038/35057062 10.1109/ISIT.2018.8437789 10.1186/gb-2013-14-5-r51 10.1109/TIT.2017.2688361 10.1109/TMBMC.2016.2537305 10.1109/ISIT.2017.8007104 10.1145/3338514 10.1109/LCOMM.2018.2868666 10.1038/s41598-017-05188-1 10.1038/nbt.4079 10.1109/TIT.1973.1054929 10.1007/s00239-004-2619-6 |
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| References | ref13 ref15 ref20 marcus (ref17) 2001 ref22 nijenhuis (ref14) 2014 ref21 sipser (ref18) 2013 lenz (ref12) 2018 ref2 ref1 kova?evi? (ref9) 2019 ref16 ref8 lander (ref11) 2001; 409 ref7 ref4 ref3 immink (ref6) 2018 kova?evi? (ref10) 2019 ref5 weisstein (ref19) 2020 |
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| SubjectTerms | 3G mobile communication Algorithms Alphabets Biological information theory Coders Codes DNA DNA storage Encoders-Decoders Encoding Encoding-Decoding Error-correction codes GC-balanced codes In vivo Organisms Reproduction (copying) Sequential analysis tandem duplication Words (language) |
| Title | Efficient Encoding/Decoding of GC-Balanced Codes Correcting Tandem Duplications |
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