Recent Progresses in Characterising Information Inequalities
In this paper, we present a revision on some of the recent progresses made in characterising and understanding information inequalities, which are the fundamental physical laws in communications and compression. We will begin with the introduction of a geometric framework for information inequalitie...
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| Format: | Article |
| Language: | English |
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MDPI AG
2011-01-01
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| Series: | Entropy |
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| Online Access: | http://www.mdpi.com/1099-4300/13/2/379/ |
| _version_ | 1811184763888730112 |
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| author | Terence Chan |
| author_facet | Terence Chan |
| author_sort | Terence Chan |
| collection | DOAJ |
| description | In this paper, we present a revision on some of the recent progresses made in characterising and understanding information inequalities, which are the fundamental physical laws in communications and compression. We will begin with the introduction of a geometric framework for information inequalities, followed by the first non-Shannon inequality proved by Zhang et al. in 1998 [1]. The discovery of this non-Shannon inequality is a breakthrough in the area and has led to the subsequent discovery of many more non-Shannon inequalities. We will also review the close relations between information inequalities and other research areas such as Kolmogorov complexity, determinantal inequalities, and group-theoretic inequalities. These relations have led to non-traditional techniques in proving information inequalities and at the same time made impacts back onthose related areas by the introduction of information-theoretic tools. |
| first_indexed | 2024-04-11T13:17:58Z |
| format | Article |
| id | doaj.art-47742c6248d8468f8684764ad7d66599 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-11T13:17:58Z |
| publishDate | 2011-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-47742c6248d8468f8684764ad7d665992022-12-22T04:22:19ZengMDPI AGEntropy1099-43002011-01-0113237940110.3390/e13020379Recent Progresses in Characterising Information InequalitiesTerence ChanIn this paper, we present a revision on some of the recent progresses made in characterising and understanding information inequalities, which are the fundamental physical laws in communications and compression. We will begin with the introduction of a geometric framework for information inequalities, followed by the first non-Shannon inequality proved by Zhang et al. in 1998 [1]. The discovery of this non-Shannon inequality is a breakthrough in the area and has led to the subsequent discovery of many more non-Shannon inequalities. We will also review the close relations between information inequalities and other research areas such as Kolmogorov complexity, determinantal inequalities, and group-theoretic inequalities. These relations have led to non-traditional techniques in proving information inequalities and at the same time made impacts back onthose related areas by the introduction of information-theoretic tools.http://www.mdpi.com/1099-4300/13/2/379/determinantal inequalitiesGreene’s TheoremKolmogorov complexityquasi-uniformityShannon entropiessubspace rank inequalities |
| spellingShingle | Terence Chan Recent Progresses in Characterising Information Inequalities Entropy determinantal inequalities Greene’s Theorem Kolmogorov complexity quasi-uniformity Shannon entropies subspace rank inequalities |
| title | Recent Progresses in Characterising Information Inequalities |
| title_full | Recent Progresses in Characterising Information Inequalities |
| title_fullStr | Recent Progresses in Characterising Information Inequalities |
| title_full_unstemmed | Recent Progresses in Characterising Information Inequalities |
| title_short | Recent Progresses in Characterising Information Inequalities |
| title_sort | recent progresses in characterising information inequalities |
| topic | determinantal inequalities Greene’s Theorem Kolmogorov complexity quasi-uniformity Shannon entropies subspace rank inequalities |
| url | http://www.mdpi.com/1099-4300/13/2/379/ |
| work_keys_str_mv | AT terencechan recentprogressesincharacterisinginformationinequalities |