Comparative Study of Generalized Quantitative-Qualitative Inaccuracy Fuzzy Measures for Noiseless Coding Theorem and 1:1 Codes
In coding theory, we study various properties of codes for application in data compression, cryptography, error correction, and network coding. The study of codes is introduced in Information Theory, electrical engineering, mathematics, and computer sciences for the transmission of data through reli...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2015/258675 |
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| author | H. D. Arora Anjali Dhiman |
| author_facet | H. D. Arora Anjali Dhiman |
| author_sort | H. D. Arora |
| collection | DOAJ |
| description | In coding theory, we study various properties of codes for application in data compression, cryptography, error correction, and network coding. The study of codes is introduced in Information Theory, electrical engineering, mathematics, and computer sciences for the transmission of data through reliable and efficient methods. We have to consider how coding of messages can be done efficiently so that the maximum number of messages can be sent over a noiseless channel in a given time. Thus, the minimum value of mean codeword length subject to a given constraint on codeword lengths has to be founded. In this paper, we have introduced mean codeword length of order α and type β for 1:1 codes and analyzed the relationship between average codeword length and fuzzy information measures for binary 1:1 codes. Further, noiseless coding theorem associated with fuzzy information measure has been established. |
| format | Article |
| id | doaj-art-d746872b3fb54ff8bf43028071991b19 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-d746872b3fb54ff8bf43028071991b192025-02-03T06:44:45ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252015-01-01201510.1155/2015/258675258675Comparative Study of Generalized Quantitative-Qualitative Inaccuracy Fuzzy Measures for Noiseless Coding Theorem and 1:1 CodesH. D. Arora0Anjali Dhiman1Department of Mathematics, Amity Institute of Applied Sciences, Amity University, Noida 201301, IndiaDepartment of Mathematics, Ideal Institute of Management and Technology, GGSIP University, Delhi 110092, IndiaIn coding theory, we study various properties of codes for application in data compression, cryptography, error correction, and network coding. The study of codes is introduced in Information Theory, electrical engineering, mathematics, and computer sciences for the transmission of data through reliable and efficient methods. We have to consider how coding of messages can be done efficiently so that the maximum number of messages can be sent over a noiseless channel in a given time. Thus, the minimum value of mean codeword length subject to a given constraint on codeword lengths has to be founded. In this paper, we have introduced mean codeword length of order α and type β for 1:1 codes and analyzed the relationship between average codeword length and fuzzy information measures for binary 1:1 codes. Further, noiseless coding theorem associated with fuzzy information measure has been established.http://dx.doi.org/10.1155/2015/258675 |
| spellingShingle | H. D. Arora Anjali Dhiman Comparative Study of Generalized Quantitative-Qualitative Inaccuracy Fuzzy Measures for Noiseless Coding Theorem and 1:1 Codes International Journal of Mathematics and Mathematical Sciences |
| title | Comparative Study of Generalized Quantitative-Qualitative Inaccuracy Fuzzy Measures for Noiseless Coding Theorem and 1:1 Codes |
| title_full | Comparative Study of Generalized Quantitative-Qualitative Inaccuracy Fuzzy Measures for Noiseless Coding Theorem and 1:1 Codes |
| title_fullStr | Comparative Study of Generalized Quantitative-Qualitative Inaccuracy Fuzzy Measures for Noiseless Coding Theorem and 1:1 Codes |
| title_full_unstemmed | Comparative Study of Generalized Quantitative-Qualitative Inaccuracy Fuzzy Measures for Noiseless Coding Theorem and 1:1 Codes |
| title_short | Comparative Study of Generalized Quantitative-Qualitative Inaccuracy Fuzzy Measures for Noiseless Coding Theorem and 1:1 Codes |
| title_sort | comparative study of generalized quantitative qualitative inaccuracy fuzzy measures for noiseless coding theorem and 1 1 codes |
| url | http://dx.doi.org/10.1155/2015/258675 |
| work_keys_str_mv | AT hdarora comparativestudyofgeneralizedquantitativequalitativeinaccuracyfuzzymeasuresfornoiselesscodingtheoremand11codes AT anjalidhiman comparativestudyofgeneralizedquantitativequalitativeinaccuracyfuzzymeasuresfornoiselesscodingtheoremand11codes |