Monotonic Decrease of the Non-Gaussianness of the Sum of Independent Random Variables: A Simple Proof
Artstein, Ball, Barthe, and Naor have recently shown that the non-Gaussianness (divergence with respect to a Gaussian random variable with identical first and second moments) of the sum of independent and identically distributed (i.i.d.) random variables is monotonically nonincreasing. We give a sim...
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| Veröffentlicht in: | IEEE transactions on information theory 2006-09, Vol.52 (9), p.4295-4297 |
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| container_title | IEEE transactions on information theory |
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| creator | Tulino, A.M. Verdu, S. |
| description | Artstein, Ball, Barthe, and Naor have recently shown that the non-Gaussianness (divergence with respect to a Gaussian random variable with identical first and second moments) of the sum of independent and identically distributed (i.i.d.) random variables is monotonically nonincreasing. We give a simplified proof using the relationship between non-Gaussianness and minimum mean-square error (MMSE) in Gaussian channels. As Artstein , we also deal with the more general setting of nonidentically distributed random variables |
| doi_str_mv | 10.1109/TIT.2006.880066 |
| format | Article |
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We give a simplified proof using the relationship between non-Gaussianness and minimum mean-square error (MMSE) in Gaussian channels. As Artstein , we also deal with the more general setting of nonidentically distributed random variables</description><subject>Applied sciences</subject><subject>Central limit theorem</subject><subject>Channels</subject><subject>Convolution</subject><subject>differential entropy</subject><subject>Divergence</subject><subject>Entropy</subject><subject>entropy power inequality</subject><subject>Errors</subject><subject>Exact sciences and technology</subject><subject>Fasteners</subject><subject>Functional analysis</subject><subject>Gaussian</subject><subject>Gaussian channels</subject><subject>Information theory</subject><subject>Information, signal and communications theory</subject><subject>minimum mean-square error (MMSE)</subject><subject>non-Gaussianness</subject><subject>Power measurement</subject><subject>Proving</subject><subject>Random variables</subject><subject>relative entropy</subject><subject>Signal to noise ratio</subject><subject>Telecommunications and information theory</subject><issn>0018-9448</issn><issn>1557-9654</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2006</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNpFkDtPwzAUhS0EEqUwM7B4QUxpbcd2YraqQKlUHqKFNXKcGxGU2MFOBv49iQrqcp_nnOFD6JKSGaVEzXfr3YwRImdpOlR5hCZUiCRSUvBjNCGEppHiPD1FZyF8DSsXlE0QPDnrOmcrg-_AeNABsCtx9wn42dlopfsQKm0thPB_3_bNOK5tAS0MxXb4TdvCNfhD-0rnNYRbvMDbqmlrwK_eufIcnZS6DnDx16fo_eF-t3yMNi-r9XKxiUzM4i4qgTJBlUjyUoo0YVQSLpOCC66kjglTslBlzCQoUnCSpDwfVqNjagTkwE08RTf73Na77x5ClzVVMFDX2oLrQ6YoH3AwygblfK803oXgocxaXzXa_2SUZCPPbOCZjTyzPc_Bcf2XrYPRdem1NVU42FIiFGdj8tVeVwHA4S3TWAka_wIR-XzQ</recordid><startdate>20060901</startdate><enddate>20060901</enddate><creator>Tulino, A.M.</creator><creator>Verdu, S.</creator><general>IEEE</general><general>Institute of Electrical and Electronics Engineers</general><scope>97E</scope><scope>RIA</scope><scope>RIE</scope><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7SP</scope><scope>8FD</scope><scope>F28</scope><scope>FR3</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20060901</creationdate><title>Monotonic Decrease of the Non-Gaussianness of the Sum of Independent Random Variables: A Simple Proof</title><author>Tulino, A.M. ; 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We give a simplified proof using the relationship between non-Gaussianness and minimum mean-square error (MMSE) in Gaussian channels. As Artstein , we also deal with the more general setting of nonidentically distributed random variables</abstract><cop>New York, NY</cop><pub>IEEE</pub><doi>10.1109/TIT.2006.880066</doi><tpages>3</tpages></addata></record> |
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| source | IEEE Electronic Library (IEL) |
| subjects | Applied sciences Central limit theorem Channels Convolution differential entropy Divergence Entropy entropy power inequality Errors Exact sciences and technology Fasteners Functional analysis Gaussian Gaussian channels Information theory Information, signal and communications theory minimum mean-square error (MMSE) non-Gaussianness Power measurement Proving Random variables relative entropy Signal to noise ratio Telecommunications and information theory |
| title | Monotonic Decrease of the Non-Gaussianness of the Sum of Independent Random Variables: A Simple Proof |
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