On the Generalized Gaussian CEO Problem
This paper considers a distributed source coding (DSC) problem where L encoders observe noisy linear combinations of K correlated remote Gaussian sources, and separately transmit the compressed observations to the decoder to reconstruct the remote sources subject to a sum-distortion constraint. This...
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| Vydané v: | IEEE transactions on information theory Ročník 58; číslo 6; s. 3350 - 3372 |
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| Hlavní autori: | , |
| Médium: | Journal Article |
| Jazyk: | English |
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New York
IEEE
01.06.2012
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 considers a distributed source coding (DSC) problem where L encoders observe noisy linear combinations of K correlated remote Gaussian sources, and separately transmit the compressed observations to the decoder to reconstruct the remote sources subject to a sum-distortion constraint. This DSC problem is referred to as the generalized Gaussian CEO problem since it can be viewed as a generalization of the quadratic Gaussian CEO problem where the number of remote source K =1. First, we provide a new outer region obtained using the entropy power inequality and an equivalent argument (in the sense of having the same rate-distortion region and Berger-Tung inner region) among a certain class of generalized Gaussian CEO problems. We then give two sufficient conditions for our new outer region to match the inner region achieved by Berger-Tung schemes, where the second matching condition implies that in the low-distortion regime, the Berger-Tung inner rate region is always tight, while in the high-distortion regime, the same region is tight if a certain condition holds. The sum-rate part of the outer region is also studied and shown to meet the Berger-Tung sum-rate upper bound under a certain condition, which is obtained using the Karush-Kuhn-Tucker conditions of the underlying convex semidefinite optimization problem, and is in general weaker than the aforesaid two for rate region tightness. |
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| AbstractList | This paper considers a distributed source coding (DSC) problem where L encoders observe noisy linear combinations of K correlated remote Gaussian sources, and separately transmit the compressed observations to the decoder to reconstruct the remote sources subject to a sum-distortion constraint. This DSC problem is referred to as the generalized Gaussian CEO problem since it can be viewed as a generalization of the quadratic Gaussian CEO problem where the number of remote source K =1. First, we provide a new outer region obtained using the entropy power inequality and an equivalent argument (in the sense of having the same rate-distortion region and Berger-Tung inner region) among a certain class of generalized Gaussian CEO problems. We then give two sufficient conditions for our new outer region to match the inner region achieved by Berger-Tung schemes, where the second matching condition implies that in the low-distortion regime, the Berger-Tung inner rate region is always tight, while in the high-distortion regime, the same region is tight if a certain condition holds. The sum-rate part of the outer region is also studied and shown to meet the Berger-Tung sum-rate upper bound under a certain condition, which is obtained using the Karush-Kuhn-Tucker conditions of the underlying convex semidefinite optimization problem, and is in general weaker than the aforesaid two for rate region tightness. This paper considers a distributed source coding (DSC) problem where $L$ encoders observe noisy linear combinations of $K$ correlated remote Gaussian sources, and separately transmit the compressed observations to the decoder to reconstruct the remote sources subject to a sum-distortion constraint. This DSC problem is referred to as the generalized Gaussian CEO problem since it can be viewed as a generalization of the quadratic Gaussian CEO problem where the number of remote source $K=1$. First, we provide a new outer region obtained using the entropy power inequality and an equivalent argument (in the sense of having the same rate-distortion region and Berger-Tung inner region) among a certain class of generalized Gaussian CEO problems. We then give two sufficient conditions for our new outer region to match the inner region achieved by Berger-Tung schemes, where the second matching condition implies that in the low-distortion regime, the Berger-Tung inner rate region is always tight, while in the high-distortion regime, the same region is tight if a certain condition holds. The sum-rate part of the outer region is also studied and shown to meet the Berger-Tung sum-rate upper bound under a certain condition, which is obtained using the Karush-Kuhn-Tucker conditions of the underlying convex semidefinite optimization problem, and is in general weaker than the aforesaid two for rate region tightness. [PUBLICATION ABSTRACT] |
| Author | Yang Yang Zixiang Xiong |
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| Cites_doi | 10.1109/ITWKSPS.2010.5503203 10.1109/TIT.2011.2173706 10.1109/18.669162 10.1002/0471787779 10.1109/ISIT.2004.1365154 10.1109/TIT.2012.2201347 10.1145/320941.320947 10.1109/TIT.2008.920343 10.1109/TIT.2005.850110 10.1109/TIT.2010.2050960 10.1109/ISIT.2010.5513305 10.1017/CBO9780511810800 10.1109/18.490552 10.1109/18.623151 |
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| References | ref13 ref15 ref14 ref20 kvasnica (ref21) 2004 oohama (ref12) 2009 ref10 price (ref19) 2005 tung (ref2) 1978 pandya (ref11) 2004 ref16 ref18 ref8 ref7 ref9 ref4 ref3 ref6 ltkepohl (ref17) 1996 ref5 berger (ref1) 1977 |
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| Snippet | This paper considers a distributed source coding (DSC) problem where L encoders observe noisy linear combinations of K correlated remote Gaussian sources, and... This paper considers a distributed source coding (DSC) problem where $L$ encoders observe noisy linear combinations of $K$ correlated remote Gaussian sources,... |
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| SubjectTerms | Coding theory Compressed Covariance matrix Decoding Differential scanning calorimetry Distributed source coding (DSC) Encoders Entropy Equivalence Gaussian Gaussian CEO problem Inequalities Joints multiterminal source coding Noise measurement Normal distribution Optimization rate region remote sources Source coding sum rate Transforms Upper bound |
| Title | On the Generalized Gaussian CEO Problem |
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