Strong Functional Representation Lemma and Applications to Coding Theorems
This paper shows that for any random variables <inline-formula> <tex-math notation="LaTeX">X </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">Y </tex-math></inline-formula>, it is possible to represent &l...
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| Vydané v: | IEEE transactions on information theory Ročník 64; číslo 11; s. 6967 - 6978 |
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| Hlavní autori: | , |
| Médium: | Journal Article |
| Jazyk: | English |
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New York
IEEE
01.11.2018
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
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| ISSN: | 0018-9448, 1557-9654 |
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| Abstract | This paper shows that for any random variables <inline-formula> <tex-math notation="LaTeX">X </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">Y </tex-math></inline-formula>, it is possible to represent <inline-formula> <tex-math notation="LaTeX">Y </tex-math></inline-formula> as a function of <inline-formula> <tex-math notation="LaTeX">(X,Z) </tex-math></inline-formula> such that <inline-formula> <tex-math notation="LaTeX">Z </tex-math></inline-formula> is independent of <inline-formula> <tex-math notation="LaTeX">X </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">I(X;Z|Y)\le \log (I(X;Y)+1)+4 </tex-math></inline-formula> bits. We use this strong functional representation lemma (SFRL) to establish a bound on the rate needed for one-shot exact channel simulation for general (discrete or continuous) random variables, strengthening the results by Harsha et al. and Braverman and Garg, and to establish new and simple achievability results for one-shot variable-length lossy source coding, multiple description coding, and Gray-Wyner system. We also show that the SFRL can be used to reduce the channel with state noncausally known at the encoder to a point-to-point channel, which provides a simple achievability proof of the Gelfand-Pinsker theorem. |
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| AbstractList | This paper shows that for any random variables X and Y, it is possible to represent Y as a function of (X, Z) such that Z is independent of X and I(X; Z|Y) ≤ log(I(X; Y)+1)+4 bits. We use this strong functional representation lemma (SFRL) to establish a bound on the rate needed for one-shot exact channel simulation for general (discrete or continuous) random variables, strengthening the results by Harsha et al. and Braverman and Garg, and to establish new and simple achievability results for one-shot variable-length lossy source coding, multiple description coding, and Gray-Wyner system. We also show that the SFRL can be used to reduce the channel with state noncausally known at the encoder to a point-to-point channel, which provides a simple achievability proof of the Gelfand-Pinsker theorem. This paper shows that for any random variables <inline-formula> <tex-math notation="LaTeX">X </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">Y </tex-math></inline-formula>, it is possible to represent <inline-formula> <tex-math notation="LaTeX">Y </tex-math></inline-formula> as a function of <inline-formula> <tex-math notation="LaTeX">(X,Z) </tex-math></inline-formula> such that <inline-formula> <tex-math notation="LaTeX">Z </tex-math></inline-formula> is independent of <inline-formula> <tex-math notation="LaTeX">X </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">I(X;Z|Y)\le \log (I(X;Y)+1)+4 </tex-math></inline-formula> bits. We use this strong functional representation lemma (SFRL) to establish a bound on the rate needed for one-shot exact channel simulation for general (discrete or continuous) random variables, strengthening the results by Harsha et al. and Braverman and Garg, and to establish new and simple achievability results for one-shot variable-length lossy source coding, multiple description coding, and Gray-Wyner system. We also show that the SFRL can be used to reduce the channel with state noncausally known at the encoder to a point-to-point channel, which provides a simple achievability proof of the Gelfand-Pinsker theorem. |
| Author | Gamal, Abbas El Li, Cheuk Ting |
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| Cites_doi | 10.1109/ISIT.2016.7541362 10.1109/TIT.2015.2438831 10.1109/18.567651 10.1109/TIT.1976.1055508 10.1109/TIT.1985.1057042 10.1109/TIT.2013.2283723 10.1109/ISIT.2013.6620306 10.1017/CBO9780511566172 10.1109/TIT.1979.1055989 10.1017/CBO9781139030687 10.1109/TIT.2014.2347282 10.1109/TIT.1975.1055469 10.1109/TIT.2009.2034824 10.1109/TIT.1982.1056588 10.1109/TIT.2011.2104650 10.1214/aop/1176990840 10.1109/TIT.1978.1055880 10.1214/aoms/1177693077 10.1109/TIT.2014.2309968 10.1109/Allerton.2012.6483192 10.1017/9781316104477 10.1109/TIT.1979.1056046 10.1109/ISIT.2014.6874815 10.1109/ISIT.2013.6620434 10.1109/TIT.1976.1055539 10.1109/TIT.2003.815767 10.1109/TIT.2013.2279330 10.1109/TIT.1973.1055037 10.1109/ISIT.2013.6620787 10.1109/TIT.2016.2529657 10.1515/9781400873173 10.1002/j.1538-7305.1974.tb02812.x 10.1109/TIT.2002.802612 10.1109/TIT.1987.1057330 10.1088/1367-2630/15/4/043021 |
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| Snippet | This paper shows that for any random variables <inline-formula> <tex-math notation="LaTeX">X </tex-math></inline-formula> and <inline-formula> <tex-math... This paper shows that for any random variables X and Y, it is possible to represent Y as a function of (X, Z) such that Z is independent of X and I(X; Z|Y) ≤... |
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| SubjectTerms | Channel coding channel simulation channel with state Coding Continuity (mathematics) Electrical engineering Functional representation lemma Indexes lossy source coding one-shot achievability Random variables Representations Source coding Theorems |
| Title | Strong Functional Representation Lemma and Applications to Coding Theorems |
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