The rate-distortion function for the quadratic Gaussian CEO problem
A new multiterminal source coding problem called the CEO problem was presented and investigated by Berger, Zhang, and Viswanathan. Recently, Viswanathan and Berger have investigated an extension of the CEO problem to Gaussian sources and call it the quadratic Gaussian CEO problem. They considered th...
Uloženo v:
| Vydáno v: | IEEE transactions on information theory Ročník 44; číslo 3; s. 1057 - 1070 |
|---|---|
| Hlavní autor: | |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
New York
IEEE
01.05.1998
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Témata: | |
| ISSN: | 0018-9448, 1557-9654 |
| On-line přístup: | Získat plný text |
| Tagy: |
Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
|
| Abstract | A new multiterminal source coding problem called the CEO problem was presented and investigated by Berger, Zhang, and Viswanathan. Recently, Viswanathan and Berger have investigated an extension of the CEO problem to Gaussian sources and call it the quadratic Gaussian CEO problem. They considered this problem from a statistical viewpoint, deriving some interesting results. In this paper, we consider the quadratic Gaussian CEO problem from a standpoint of multiterminal rate-distortion theory. We regard the CEO problem as a certain multiterminal remote source coding problem with infinitely many separate encoders whose observations are conditionally independent if the remote source is given. This viewpoint leads us to a complete solution to the problem. We determine the tradeoff between the total amount of rate and squared distortion, deriving an explicit formula of the rate-distortion function. The derived function has the form of a sum of two nonnegative functions. One is a classical rate-distortion function for single Gaussian source and the other is a new rate-distortion function which dominates the performance of the system for a relatively small distortion. It follows immediately from our result that the conjecture of Viswanathan and Berger on the asymptotic behavior of minimum squared distortion for large rates is true. |
|---|---|
| AbstractList | A new multiterminal source coding problem called the CEO problem was presented and investigated by Berger, Zhang, and Viswanathan. Recently, Viswanathan and Berger have investigated an extension of the CEO problem to Gaussian sources and call it the quadratic Gaussian CEO problem. They considered this problem from a statistical viewpoint, deriving some interesting results. In this paper, we consider the quadratic Gaussian CEO problem from a standpoint of multiterminal rate-distortion theory. We regard the CEO problem as a certain multiterminal remote source coding problem with infinitely many separate encoders whose observations are conditionally independent if the remote source is given. This viewpoint leads us to a complete solution to the problem. We determine the tradeoff between the total amount of rate and squared distortion, deriving an explicit formula of the rate-distortion function. The derived function has the form of a sum of two nonnegative functions. One is a classical rate-distortion function for single Gaussian source and the other is a new rate-distortion function which dominates the performance of the system for a relatively small distortion. It follows immediately from our result that the conjecture of Viswanathan and Berger on the asymptotic behavior of minimum squared distortion for large rates is true. A new multiterminal source coding problem called the CEO problem was presented and investigated by Berger, Zhang, and Viswanathan. Recently, Viswanathan and Berger have investigated an extension of the CEO problem to Gaussian sources and call it the quadratic Gaussian CEO problem. They considered this problem from a statistical viewpoint, deriving some interesting results. A new multiterminal source coding problem called the CEO problem was presented and investigated by Berger, Zhang, and Viswanathan. Recently, Viswanathan and Berger have investigated an extension of the CEO problem to Gaussian sources and call it the quadratic Gaussian CEO problem. They considered this problem from a statistical viewpoint, deriving some interesting results. In this paper, we consider the quadratic Gaussian CEO problem from a standpoint of multiterminal rate-distortion theory. We regard the CEO problem as a certain multiterminal remote source coding problem with infinitely many separate encoders whose observations are conditionally independent if the remote source is given. This viewpoint leads us to a complete solution to the problem. We determine the tradeoff between the total amount of rate and squared distortion, deriving an explicit formula of the rate-distortion function. The derived function has the form of a sum of two nonnegative functions. One is a classical rate-distortion function for single Gaussian source and the other is a new rate-distortion function which dominates the performance of the system for a relatively small distortion. It follows immediately from our result that the conjecture of Viswanathan and Berger on the asymptotic behavior of minimum squared distortion for large rates is true |
| Author | Oohama, Y. |
| Author_xml | – sequence: 1 givenname: Y. surname: Oohama fullname: Oohama, Y. organization: Graduate Sch. of Inf. Sci. & Electr. Eng., Kyushu Univ., Fukuoka, Japan |
| BookMark | eNptkDFrwzAQhUVJoUnaoWsn06HQwYlOlmR5LCZNC4Es6Wxk-UQVHDuR7KH_vg4OHUKnu-O-9-54MzJp2gYJeQS6AKDZEtRCygwkuyFTECKNMyn4hEwpBRVnnKs7MgthP4xcAJuSfPeNkdcdxpULXes71zaR7RszNq2PugE49boaIGeite5DcLqJ8tU2Ovq2rPFwT26trgM-XOqcfL2vdvlHvNmuP_O3TWySlHZxCgkHphKbGmkqCzJjWmoJyEprtEgZUltyKBOGpVBVirKkqRBoecIqDSaZk5fRd7h76jF0xcEFg3WtG2z7UDAlhUo5DODzFbhve98MvxWQiYwqnsgBeh0h49sQPNri6N1B-58CaHHOsgBVjFkO7PKKNa7T54g6r139r-JpVDhE_HO-LH8BhAV-9w |
| CODEN | IETTAW |
| CitedBy_id | crossref_primary_10_1109_TCOMM_2015_2499179 crossref_primary_10_1109_JSAC_2010_100920 crossref_primary_10_1109_JSAC_2004_830888 crossref_primary_10_1109_TIT_2018_2854545 crossref_primary_10_1109_TIT_2005_855584 crossref_primary_10_3390_e24040438 crossref_primary_10_1109_TCOMM_2020_2977288 crossref_primary_10_1109_TIT_2021_3073533 crossref_primary_10_1109_TSP_2004_833860 crossref_primary_10_1109_TIT_2014_2317692 crossref_primary_10_1109_TSP_2021_3083985 crossref_primary_10_1109_TIT_2006_885449 crossref_primary_10_1109_TIT_2022_3227794 crossref_primary_10_1109_TIT_2015_2497410 crossref_primary_10_1109_TIT_2013_2245397 crossref_primary_10_1155_2008_318704 crossref_primary_10_1109_TIT_2013_2245394 crossref_primary_10_1109_TWC_2007_05824 crossref_primary_10_1109_TIT_2008_920249 crossref_primary_10_1109_TIT_2014_2348573 crossref_primary_10_1109_TIT_2004_842566 crossref_primary_10_1109_TIT_2014_2361332 crossref_primary_10_1109_TIT_2022_3174409 crossref_primary_10_3390_e21020213 crossref_primary_10_1109_JSAC_2005_843544 crossref_primary_10_1109_JSAC_2005_843542 crossref_primary_10_1109_TIT_2006_889016 crossref_primary_10_1109_TIT_2016_2621749 crossref_primary_10_1109_TSP_2004_842160 crossref_primary_10_1109_JSTSP_2007_901511 crossref_primary_10_1109_TCOMM_2023_3317916 crossref_primary_10_1145_2489253_2489269 crossref_primary_10_1109_TIT_2009_2034791 crossref_primary_10_1109_TIT_2007_904782 crossref_primary_10_1109_TIT_2005_850110 crossref_primary_10_1109_TCOMM_2018_2863377 crossref_primary_10_1109_TIT_2014_2333473 crossref_primary_10_1049_iet_com_2011_0799 crossref_primary_10_1109_TIT_2013_2274514 crossref_primary_10_1109_TIT_2017_2723396 crossref_primary_10_1109_TIT_2008_929967 crossref_primary_10_1109_TIFS_2015_2407153 crossref_primary_10_1109_JSEN_2024_3407480 crossref_primary_10_1209_0295_5075_87_48003 crossref_primary_10_1109_TIT_2007_894680 crossref_primary_10_1109_MSP_2006_1657818 crossref_primary_10_1109_18_817521 crossref_primary_10_1109_JSAC_2004_830875 crossref_primary_10_1109_18_746775 crossref_primary_10_1155_2008_748605 crossref_primary_10_1109_TCOMM_2022_3194978 crossref_primary_10_1109_TCOMM_2015_2466547 crossref_primary_10_1109_TWC_2011_041311_100259 crossref_primary_10_1109_TIT_2012_2188273 crossref_primary_10_1109_TCOMM_2022_3218822 crossref_primary_10_1109_MSP_2006_1657815 crossref_primary_10_1109_MSP_2006_1657814 crossref_primary_10_1109_TIT_2004_836707 crossref_primary_10_1109_TIP_2008_2010148 crossref_primary_10_1109_TIT_2005_847692 crossref_primary_10_1016_j_jfranklin_2015_12_011 crossref_primary_10_1109_TIT_2012_2184667 crossref_primary_10_1109_TWC_2012_121712_111968 crossref_primary_10_1109_TIT_2007_899484 crossref_primary_10_1109_TIT_2013_2288257 crossref_primary_10_1109_18_720552 crossref_primary_10_1109_TIT_2015_2417154 crossref_primary_10_1109_TIT_2013_2287722 crossref_primary_10_1049_iet_com_2018_5704 crossref_primary_10_1016_j_sigpro_2007_05_006 crossref_primary_10_1109_TIT_2011_2161915 crossref_primary_10_1109_TIT_2010_2050960 crossref_primary_10_1109_TSP_2010_2089622 crossref_primary_10_1109_TIT_2008_924659 crossref_primary_10_1109_TIT_2016_2616135 crossref_primary_10_1109_TCOMM_2016_2523516 crossref_primary_10_1109_TIT_2016_2531080 crossref_primary_10_1109_79_985684 crossref_primary_10_1109_TWC_2009_071296 crossref_primary_10_1109_TIT_2007_903142 crossref_primary_10_1109_TIT_2008_917687 crossref_primary_10_1109_TIT_2006_876355 crossref_primary_10_1109_TIT_2010_2044058 crossref_primary_10_1109_TAC_2021_3110430 crossref_primary_10_1109_TIT_2010_2090193 crossref_primary_10_1587_transinf_2018EDP7138 crossref_primary_10_1109_TIT_2008_926389 crossref_primary_10_1109_TSP_2016_2595491 crossref_primary_10_1109_TIT_2008_920204 crossref_primary_10_1109_TIT_2011_2146070 crossref_primary_10_1109_TIT_2011_2132990 crossref_primary_10_1109_TSP_2007_898755 crossref_primary_10_1109_LCOMM_2013_042313_130361 crossref_primary_10_1109_TIT_2009_2027579 crossref_primary_10_1109_TIFS_2015_2404134 crossref_primary_10_1109_TIT_2014_2317181 crossref_primary_10_1109_TIT_2009_2032730 crossref_primary_10_1109_TIT_2012_2201347 crossref_primary_10_1109_TIFS_2024_3522775 crossref_primary_10_1109_TSP_2013_2264465 crossref_primary_10_1109_JSAC_2011_110515 crossref_primary_10_1002_wcm_723 crossref_primary_10_1109_TCOMM_2018_2885800 crossref_primary_10_1109_TVT_2024_3373812 crossref_primary_10_1109_TWC_2019_2923399 crossref_primary_10_1109_TIT_2019_2897842 crossref_primary_10_3390_s150202737 crossref_primary_10_1109_TIT_2021_3111658 crossref_primary_10_1109_TIT_2020_3002756 crossref_primary_10_1109_TIT_2012_2204722 crossref_primary_10_1109_TIT_2019_2948848 crossref_primary_10_3390_e15062129 crossref_primary_10_1109_TIT_2009_2032853 crossref_primary_10_1109_TCOMM_2022_3224977 crossref_primary_10_1109_JSEN_2010_2066557 crossref_primary_10_1109_JSAIT_2024_3499012 crossref_primary_10_1109_TIT_2010_2040879 crossref_primary_10_1109_TSP_2007_894412 |
| Cites_doi | 10.1109/18.119685 10.1109/TIT.1980.1056192 10.1109/18.2629 10.1109/18.42171 10.1109/18.476308 10.1109/TIT.1987.1057384 10.1109/18.490552 10.1214/aos/1176347496 10.1109/18.623151 10.1109/18.641555 10.1109/TIT.1982.1056560 10.1109/TIT.1986.1057194 10.1109/18.32118 10.1109/TIT.1974.1055184 10.1109/18.312162 10.1002/0471200611 10.1109/TIT.1987.1057383 10.1007/BF00057730 10.1109/TIT.1985.1057085 |
| ContentType | Journal Article |
| Copyright | Copyright Institute of Electrical and Electronics Engineers, Inc. (IEEE) May 1998 |
| Copyright_xml | – notice: Copyright Institute of Electrical and Electronics Engineers, Inc. (IEEE) May 1998 |
| DBID | RIA RIE AAYXX CITATION 7SC 7SP 8FD JQ2 L7M L~C L~D |
| DOI | 10.1109/18.669162 |
| DatabaseName | IEEE All-Society Periodicals Package (ASPP) 1998–Present IEEE Electronic Library (IEL) CrossRef Computer and Information Systems Abstracts Electronics & Communications Abstracts Technology Research Database ProQuest Computer Science Collection Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional |
| DatabaseTitle | CrossRef Technology Research Database Computer and Information Systems Abstracts – Academic Electronics & Communications Abstracts ProQuest Computer Science Collection Computer and Information Systems Abstracts Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Professional |
| DatabaseTitleList | Technology Research Database Computer and Information Systems Abstracts |
| Database_xml | – sequence: 1 dbid: RIE name: IEEE Electronic Library (IEL) url: https://ieeexplore.ieee.org/ sourceTypes: Publisher |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Engineering Statistics Computer Science |
| EISSN | 1557-9654 |
| EndPage | 1070 |
| ExternalDocumentID | 30450049 10_1109_18_669162 669162 |
| Genre | Feature |
| GroupedDBID | -~X .DC 0R~ 29I 3EH 4.4 5GY 5VS 6IK 97E AAJGR AARMG AASAJ AAWTH ABAZT ABFSI ABQJQ ABVLG ACGFO ACGFS ACGOD ACIWK AENEX AETEA AETIX AGQYO AGSQL AHBIQ AI. AIBXA AKJIK AKQYR ALLEH ALMA_UNASSIGNED_HOLDINGS ASUFR ATWAV BEFXN BFFAM BGNUA BKEBE BPEOZ CS3 DU5 E.L EBS EJD F5P HZ~ H~9 IAAWW IBMZZ ICLAB IDIHD IFIPE IFJZH IPLJI JAVBF LAI M43 MS~ O9- OCL P2P PQQKQ RIA RIE RNS RXW TAE TN5 VH1 VJK AAYXX CITATION 7SC 7SP 8FD JQ2 L7M L~C L~D RIG |
| ID | FETCH-LOGICAL-c370t-71341283f7c6cdf1692a6a61e2bfca572e0fb41b32eb58d7e6b0755ef432da1c3 |
| IEDL.DBID | RIE |
| ISICitedReferencesCount | 241 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000073200100010&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 0018-9448 |
| IngestDate | Sat Sep 27 22:16:17 EDT 2025 Fri Jul 25 05:15:54 EDT 2025 Sat Nov 29 02:54:42 EST 2025 Tue Nov 18 22:37:41 EST 2025 Tue Aug 26 21:00:16 EDT 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 3 |
| Language | English |
| License | https://ieeexplore.ieee.org/Xplorehelp/downloads/license-information/IEEE.html |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c370t-71341283f7c6cdf1692a6a61e2bfca572e0fb41b32eb58d7e6b0755ef432da1c3 |
| Notes | SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 ObjectType-Article-2 content type line 23 |
| PQID | 195908436 |
| PQPubID | 36024 |
| PageCount | 14 |
| ParticipantIDs | ieee_primary_669162 proquest_journals_195908436 proquest_miscellaneous_28658741 crossref_primary_10_1109_18_669162 crossref_citationtrail_10_1109_18_669162 |
| PublicationCentury | 1900 |
| PublicationDate | 1998-05-01 |
| PublicationDateYYYYMMDD | 1998-05-01 |
| PublicationDate_xml | – month: 05 year: 1998 text: 1998-05-01 day: 01 |
| PublicationDecade | 1990 |
| PublicationPlace | New York |
| PublicationPlace_xml | – name: New York |
| PublicationTitle | IEEE transactions on information theory |
| PublicationTitleAbbrev | TIT |
| PublicationYear | 1998 |
| Publisher | IEEE The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Publisher_xml | – name: IEEE – name: The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| References | ref13 ref15 han (ref12) 1995; 41 ref11 ref10 ref21 ref1 ref17 ref16 ref19 ref18 ref8 ref7 ref9 ref4 ref3 berger (ref2) 1979 berger (ref23) 1978 yamamoto (ref14) 1980; e63 ref6 cover (ref22) 1991 ref5 tung (ref20) 1978 |
| References_xml | – ident: ref10 doi: 10.1109/18.119685 – ident: ref21 doi: 10.1109/TIT.1980.1056192 – ident: ref5 doi: 10.1109/18.2629 – year: 1979 ident: ref2 article-title: multiterminal estimation and decision theory publication-title: IEEE Shannon Theory Workshop – ident: ref6 doi: 10.1109/18.42171 – volume: 41 start-page: 1802 year: 1995 ident: ref12 article-title: parameter estimation with multiterminal data compression publication-title: IEEE Trans Information Theory doi: 10.1109/18.476308 – ident: ref15 doi: 10.1109/TIT.1987.1057384 – ident: ref1 doi: 10.1109/18.490552 – ident: ref9 doi: 10.1214/aos/1176347496 – ident: ref13 doi: 10.1109/18.623151 – ident: ref19 doi: 10.1109/18.641555 – volume: e63 start-page: 700 year: 1980 ident: ref14 article-title: source coding theory for multiterminal communication systems with a remote source publication-title: Trans IECE Japan – ident: ref16 doi: 10.1109/TIT.1982.1056560 – ident: ref3 doi: 10.1109/TIT.1986.1057194 – start-page: 171 year: 1978 ident: ref23 publication-title: Multiterminal source coding – ident: ref7 doi: 10.1109/18.32118 – ident: ref17 doi: 10.1109/TIT.1974.1055184 – ident: ref11 doi: 10.1109/18.312162 – year: 1978 ident: ref20 publication-title: Multiterminal source coding – year: 1991 ident: ref22 publication-title: Elements of Information Theory doi: 10.1002/0471200611 – ident: ref4 doi: 10.1109/TIT.1987.1057383 – ident: ref8 doi: 10.1007/BF00057730 – ident: ref18 doi: 10.1109/TIT.1985.1057085 |
| SSID | ssj0014512 |
| Score | 2.0649228 |
| Snippet | A new multiterminal source coding problem called the CEO problem was presented and investigated by Berger, Zhang, and Viswanathan. Recently, Viswanathan and... |
| SourceID | proquest crossref ieee |
| SourceType | Aggregation Database Enrichment Source Index Database Publisher |
| StartPage | 1057 |
| SubjectTerms | Codes Electrical engineering Frequency H infinity control Information Information science Information theory Rate distortion theory Rate-distortion Source coding Statistics Testing Theory |
| Title | The rate-distortion function for the quadratic Gaussian CEO problem |
| URI | https://ieeexplore.ieee.org/document/669162 https://www.proquest.com/docview/195908436 https://www.proquest.com/docview/28658741 |
| Volume | 44 |
| WOSCitedRecordID | wos000073200100010&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVIEE databaseName: IEEE Electronic Library (IEL) customDbUrl: eissn: 1557-9654 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0014512 issn: 0018-9448 databaseCode: RIE dateStart: 19630101 isFulltext: true titleUrlDefault: https://ieeexplore.ieee.org/ providerName: IEEE |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV07T8MwED4BYigDhQKilIeFGFjSxnFiOyOqeAwIGEBii_w4T6iFlvD7seO0AtGFzUouUeTz-b7L-b4DuCilYgLLMlEZs0leCJZo5DKxBerUIRYykiTdi4cH-fpaPrU8200tDCI2h89wGIZNLt9OTR1-lY0492DG77frQvBYqrVMGOQFjcTg1NuvDzlaEiGaliMqh_HBX66n6aXyZwNuvMpN91_fswPbLXgkV1Hbu7CGkx50F40ZSGunPdj6wTLYg04AlJGPeQ_Gfl2QQA-R2IYgJOiFBOcWB9MZ8YiQfNTKhqVhyK2q56HOkoyvH0nbfWYfXm6un8d3SdtIITFMpJ9JqBf1fog5YbixjvIyU1xxipl2RhUiw9TpnGqWoS6kFci1RxIFupxlVlHDDmBjMp3gIRBqvUf3MZL0MCjHDKVz1kdseaqdVE6bPlwu5rgyLct4aHbxVjXRRlpWVFZx3vpwvhR9j9Qaq4R6Yd6XAourg4Xeqtbm5lWgyUllzngfzpZ3vbGEDIia4LSeV6EMV3oMdbTyrQPoxIrDcJzxGDY-ZzWewKb58jqanTbr7RuyJtRM |
| linkProvider | IEEE |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1LT8MwDLYQIAEHHgPEeEaIA5dC06RpekQTLzEGB5C4VXk4J7TBRvn9JE03geDCLWrdqorj-HMdfwY4KaViBZZlojJmE54XLNEoZGJz1KlDzGUkSeoXg4F8eSkfW57tphYGEZvDZ3gWhk0u345MHX6VnQvhwYzfbxdyzrM0FmvNUgY8p5EanHoL9kFHSyNE0_KcyrP46A_n03RT-bUFN37lau1fX7QOqy18JBdR3xswh8MOrE1bM5DWUjuw8o1nsAPLAVJGRuZN6PmVQQJBRGIbipCgGRLcWxyMxsRjQvJeKxsWhyHXqp6ESkvSu3wgbf-ZLXi-unzq3SRtK4XEsCL9SELFqPdEzBVGGOuoKDMllKCYaWdUXmSYOs2pZhnqXNoChfZYIkfHWWYVNWwb5oejIe4Aodb7dB8lSQ-EOGYonbM-ZuOpdlI5bbpwOp3jyrQ846HdxWvVxBtpWVFZxXnrwvFM9C2Sa_wl1AnzPhOYXt2b6q1qrW5SBaKcVHImunA0u-vNJeRA1BBH9aQKhbjSo6jdP996BEs3T_f9qn87uNuD5Vh_GA437sP8x7jGA1g0n15f48Nm7X0B4jPXkw |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=The+rate-distortion+function+for+the+quadratic+Gaussian+CEO+problem&rft.jtitle=IEEE+transactions+on+information+theory&rft.au=Ooohama%2C+Yasutada&rft.date=1998-05-01&rft.pub=The+Institute+of+Electrical+and+Electronics+Engineers%2C+Inc.+%28IEEE%29&rft.issn=0018-9448&rft.eissn=1557-9654&rft.volume=44&rft.issue=3&rft.spage=1057&rft_id=info:doi/10.1109%2F18.669162&rft.externalDBID=NO_FULL_TEXT&rft.externalDocID=30450049 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0018-9448&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0018-9448&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0018-9448&client=summon |