Universally attainable error exponents for rate-distortion coding of noisy sources
Consider the problem of rate-constrained reconstruction of a finite-alphabet discrete memoryless signal X/sup n/=(X/sub 1/,...,X/sub n/), based on a noise-corrupted observation sequence Z/sup n/, which is the finite-alphabet output of a discrete memoryless channel (DMC) whose input is X/sup n/. Supp...
Gespeichert in:
| Veröffentlicht in: | IEEE transactions on information theory Jg. 50; H. 6; S. 1229 - 1246 |
|---|---|
| 1. Verfasser: | |
| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
New York
IEEE
01.06.2004
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Schlagworte: | |
| ISSN: | 0018-9448, 1557-9654 |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Abstract | Consider the problem of rate-constrained reconstruction of a finite-alphabet discrete memoryless signal X/sup n/=(X/sub 1/,...,X/sub n/), based on a noise-corrupted observation sequence Z/sup n/, which is the finite-alphabet output of a discrete memoryless channel (DMC) whose input is X/sup n/. Suppose that there is some uncertainty in the source distribution, in the channel characteristics, or in both. Equivalently, suppose that the distribution of the pairs (X/sub i/,Z/sub i/), rather than completely being known, is only known to belong to a set /spl Theta/. Suppose further that the relevant performance criterion is the probability of excess distortion, i.e., letting X/spl circ//sup n/(Z/sup n/) denote the reconstruction, we are interested in the behavior of P/sub /spl theta//(/spl rho/(X/sup n/,X/spl circ//sup n/(Z/sup n/))>d/sub /spl theta//), where /spl rho/ is a (normalized) block distortion induced by a single-letter distortion measure and P/sub /spl theta// denotes the probability measure corresponding to the case where (X/sub i/,Z/sub i/)/spl sim//spl theta/, /spl theta//spl isin//spl Theta/. Since typically this probability will either not decay at all or do so at an exponential rate, it is the rate of this decay which we focus on. More concretely, for a given rate R /spl ges/ 0 and a family of distortion levels {d/sub /spl theta//}/sub /spl theta//spl isin//spl Theta//, we are interested in families of exponential levels {I/sub /spl theta//}/sub /spl theta//spl isin//spl Theta// which are achievable in the sense that for large n there exist rate-R schemes satisfying -1/nlog P/sub /spl theta// (/spl rho/(X/sup n/, X/spl circ//sup n/(Z/sup n/)) > d/sub /spl theta//) /spl ges/ I/sub /spl theta//, for all /spl theta/ /spl isin/ /spl Theta/. Our main result is a complete "single-letter" characterization of achievable levels {I/sub /spl theta//}/sub /spl theta//spl isin//spl Theta// per any given triple (/spl Theta/,R,{d/sub /spl theta//}/sub /spl theta//spl isin//spl Theta//). Equipped with this result, we later turn to addressing the question of the "right" choice of {I/sub /spl theta//}/spl theta//spl isin//spl Theta/. Relying on methodology recently put forth by Feder and Merhav in the context of the composite hypothesis testing problem, we propose a competitive minimax approach for the choice of these levels and apply our main result for characterizing the associated key quantities. Subsequently, we apply the main result to characterize optimal performance in a Neyman-Pearson-like setting, where there are two possible noise-corrupted signals. In this problem, the goal of the observer of the noisy signal, rather than having to determine which of the two it is (as in the hypothesis testing problem), is to reproduce the underlying clean signal with as high a fidelity as possible (e.g., lowest number of symbol errors when distortion measure is Hamming), under the assumption that one source is active, while operating at a limited information rate R and subject to a constraint on the fidelity of reconstruction when the other source is active. Finally, we apply our result to characterize a sufficient condition for the source class /spl Theta/ to be universally encodable in the sense of the existence of schemes attaining the optimal distribution-dependent exponent, simultaneously for all sources in the class. This condition was shown in an earlier work to suffice for universality in expectation. |
|---|---|
| AbstractList | Consider the problem of rate-constrained reconstruction of a finite-alphabet discrete memoryless signal Xn = (X1,..., Xn.), based on a noise-corrupted observation sequence Zn, which is the finite-alphabet output of a discrete memoryless channel (DMC) whose input is Xn. Suppose that there is some uncertainty in the source distribution, in the channel characteristics, or in both. Equivalently, suppose that the distribution of the pairs (Xi, Zi), rather than completely being known, is only known to belong to a set theta. Suppose further that the relevant performance criterion is the probability of excess distortion, i.e., letting Xn(Zn) denote the reconstruction, we are interested in the behavior of P theta (rho(Xn, Xn(Zn)) > d theta), where rho is a (normalized) block distortion induced by a single-letter distortion measure and P theta denotes the probability measure corresponding to the case where (Xi, Zi) ~ theta, theta belongs to theta. Since typically this probability will either not decay at all or do so at an exponential rate, it is the rate of this decay which we focus on. More concretely, for a given rate R >= 0 and a family of distortion levels {d theta} theta belongs to theta, we are interested in families of exponential levels {I theta} theta belongs to theta which are achievable in the sense that for large n there exist rate-R schemes satisfying - 1/n log P theta (rho(Xn, Xn (Zn)) > d theta) >= I theta, for all theta belongs to theta. Our main result is a complete "single-letter" characterization of achievable levels {I theta} theta belongs to theta per any given triple (theta, R, {d theta} theta belongs to theta). Equipped with this result, we later turn to addressing the question of the "right" choice of {I theta} theta belongs to theta. Relying on methodology recently put forth by Feder and Merhav in the context of the composite hypothesis testing problem, we propose a competitive minimax approach for the choice of these levels and apply our main result for characterizing the associated key quantities. Subsequently, we apply the main result to characterize optimal performance in a Neyman-Pearson-like setting, where there are two possible noise-corrupted signals. In this problem, the goal of the observer of the noisy signal, rather than having to determine which of the two it is (as in the hypothesis testing problem), is to reproduce the underlying clean signal with as high a fidelity as possible (e.g., lowest number of symbol errors when distortion measure is Hamming), under the assumption that one source is active, while operating at a limited information rate R and subject to a constraint on the fidelity of reconstruction when the other source is active. Finally, we apply our result to characterize a sufficient condition for the source class theta to be universally encodable in the sense of the existence of schemes attaining the optimal distribution-dependent exponent, simultaneously for all sources in the class. This condition was shown in an earlier work to suffice for universality in expectation. [PUBLICATION ABSTRACT] Consider the problem of rate-constrained reconstruction of a finite-alphabet discrete memoryless signal X/sup n/=(X/sub 1/,...,X/sub n/), based on a noise-corrupted observation sequence Z/sup n/, which is the finite-alphabet output of a discrete memoryless channel (DMC) whose input is X/sup n/. Suppose that there is some uncertainty in the source distribution, in the channel characteristics, or in both. Equivalently, suppose that the distribution of the pairs (X/sub i/,Z/sub i/), rather than completely being known, is only known to belong to a set /spl Theta/. Suppose further that the relevant performance criterion is the probability of excess distortion, i.e., letting X/spl circ//sup n/(Z/sup n/) denote the reconstruction, we are interested in the behavior of P/sub /spl theta//(/spl rho/(X/sup n/,X/spl circ//sup n/(Z/sup n/))>d/sub /spl theta//), where /spl rho/ is a (normalized) block distortion induced by a single-letter distortion measure and P/sub /spl theta// denotes the probability measure corresponding to the case where (X/sub i/,Z/sub i/)/spl sim//spl theta/, /spl theta//spl isin//spl Theta/. Since typically this probability will either not decay at all or do so at an exponential rate, it is the rate of this decay which we focus on. More concretely, for a given rate R /spl ges/ 0 and a family of distortion levels {d/sub /spl theta//}/sub /spl theta//spl isin//spl Theta//, we are interested in families of exponential levels {I/sub /spl theta//}/sub /spl theta//spl isin//spl Theta// which are achievable in the sense that for large n there exist rate-R schemes satisfying -1/nlog P/sub /spl theta// (/spl rho/(X/sup n/, X/spl circ//sup n/(Z/sup n/)) > d/sub /spl theta//) /spl ges/ I/sub /spl theta//, for all /spl theta/ /spl isin/ /spl Theta/. Our main result is a complete "single-letter" characterization of achievable levels {I/sub /spl theta//}/sub /spl theta//spl isin//spl Theta// per any given triple (/spl Theta/,R,{d/sub /spl theta//}/sub /spl theta//spl isin//spl Theta//). Equipped with this result, we later turn to addressing the question of the "right" choice of {I/sub /spl theta//}/spl theta//spl isin//spl Theta/. Relying on methodology recently put forth by Feder and Merhav in the context of the composite hypothesis testing problem, we propose a competitive minimax approach for the choice of these levels and apply our main result for characterizing the associated key quantities. Subsequently, we apply the main result to characterize optimal performance in a Neyman-Pearson-like setting, where there are two possible noise-corrupted signals. In this problem, the goal of the observer of the noisy signal, rather than having to determine which of the two it is (as in the hypothesis testing problem), is to reproduce the underlying clean signal with as high a fidelity as possible (e.g., lowest number of symbol errors when distortion measure is Hamming), under the assumption that one source is active, while operating at a limited information rate R and subject to a constraint on the fidelity of reconstruction when the other source is active. Finally, we apply our result to characterize a sufficient condition for the source class /spl Theta/ to be universally encodable in the sense of the existence of schemes attaining the optimal distribution-dependent exponent, simultaneously for all sources in the class. This condition was shown in an earlier work to suffice for universality in expectation. Consider the problem of rate-constrained reconstruction of a finite-alphabet discrete memoryless signal X super(n)=(X sub(1),...,X sub(n)), based on a noise-corrupted observation sequence Z super(n), which is the finite-alphabet output of a discrete memoryless channel (DMC) whose input is X super(n). Suppose that there is some uncertainty in the source distribution, in the channel characteristics, or in both. Equivalently, suppose that the distribution of the pairs (X sub(i),Z sub(i)), rather than completely being known, is only known to belong to a set Theta . Suppose further that the relevant performance criterion is the probability of excess distortion, i.e., letting X[circumflex] super(n)(Z super(n) ) denote the reconstruction, we are interested in the behavior of P sub([thetas])( rho (X super(n) ,X[circumflex] super(n)(Z super(n)))>d sub([thetas])), where rho is a (normalized) block distortion induced by a single-letter distortion measure and P sub([thetas]) denotes the probability measure corresponding to the case where (X sub(i),Z sub(i)) similar to ; 8; , [thetas][isin] Theta . Since typically this probability will either not decay at all or do so at an exponential rate, it is the rate of this decay which we focus on. More concretely, for a given rate R greater than or equal to 0 and a family of distortion levels {d sub([thetas])} sub([thetas][isin]9 8; ), we are interested in families of exponential levels {I sub([thetas])} sub([thetas][isin]9 8; ) which are achievable in the sense that for large n there exist rate-R schemes satisfying -1/nlog P sub([thetas]) ( rho (X super(n), X[circumflex] super(n)(Z super(n) )) > d sub([thetas])) greater than or equal to I sub([thetas]), for all [thetas] [isin] Theta . Our main result is a complete "single-letter" characterization of achievable levels {I sub([thetas])} sub([thetas][isin]9 8; ) per any given triple ( Theta ,R,{d sub([thetas])} sub([thetas]&# x2208; Theta )). Equipped with this result, we later turn to addressing the question of the "right" choice of {I sub([thetas])}[thetas][isin] Theta . Relying on methodology recently put forth by Feder and Merhav in the context of the composite hypothesis testing problem, we propose a- competitive minimax approach for the choice of these levels and apply our main result for characterizing the associated key quantities. Subsequently, we apply the main result to characterize optimal performance in a Neyman-Pearson-like setting, where there are two possible noise-corrupted signals. In this problem, the goal of the observer of the noisy signal, rather than having to determine which of the two it is (as in the hypothesis testing problem), is to reproduce the underlying clean signal with as high a fidelity as possible (e.g., lowest number of symbol errors when distortion measure is Hamming), under the assumption that one source is active, while operating at a limited information rate R and subject to a constraint on the fidelity of reconstruction when the other source is active. Finally, we apply our result to characterize a sufficient condition for the source class Theta to be universally encodable in the sense of the existence of schemes attaining the optimal distribution-dependent exponent, simultaneously for all sources in the class. This condition was shown in an earlier work to suffice for universality in expectation. Consider the problem of rate-constrained reconstruction of a finite-alphabet discrete memoryless signal X/n/=(X(1),...,X/n/), based on a noise-corrupted observation sequence Z/n/, which is the finite-alphabet output of a discrete memoryless channel (DMC) whose input is X/n/. Suppose that there is some uncertainty in the source distribution, in the channel characteristics, or in both. Equivalently, suppose that the distribution of the pairs (X/i/,Z/i/), rather than completely being known, is only known to belong to a set /Theta/. Suppose further that the relevant performance criterion is the probability of excess distortion, i.e., letting Xo/n/(Z/n/) denote the reconstruction, we are interested in the behavior of P//theta//(rho(X/n/,Xo/n/(Z/n/)) > d//theta//), where rho is a (normalized) block distortion induced by a single-letter distortion measure and P//theta// denotes the probability measure corresponding to the case where (X/i/,Z/i/)~/theta/, /theta//isin//Theta/. Since typically this probability will either not decay at all or do so at an exponential rate, it is the rate of this decay which we focus on. More concretely, for a given rate R /ges/ 0 and a family of distortion levels {d//theta//}//theta//isin//Theta//, we are interested in families of exponential levels {I//theta//}//theta//isin//Theta// which are achievable in the sense that for large n there exist rate-R schemes satisfying -1/nlog P//theta// (rho(X/n/, Xo/n/(Z/n/)) > d//theta//) /ges/ I//theta//, for all /theta/ /isin/ /Theta/. Our main result is a complete "single-letter" characterization of achievable levels {I//theta//}//theta//isin//Theta// per any given triple (/Theta/,R,{d//theta//}//theta//isin//Theta//). Equipped with this result, we later turn to addressing the question of the "right" choice of {I//theta//}/theta//isin//Theta/. Relying on methodology recently put forth by Feder and Merhav in the context of the composite hypothesis testing problem, we propose a- competitive minimax approach for the choice of these levels and apply our main result for characterizing the associated key quantities. Subsequently, we apply the main result to characterize optimal performance in a Neyman-Pearson-like setting, where there are two possible noise-corrupted signals. In this problem, the goal of the observer of the noisy signal, rather than having to determine which of the two it is (as in the hypothesis testing problem), is to reproduce the underlying clean signal with as high a fidelity as possible (e.g., lowest number of symbol errors when distortion measure is Hamming), under the assumption that one source is active, while operating at a limited information rate R and subject to a constraint on the fidelity of reconstruction when the other source is active. Finally, we apply our result to characterize a sufficient condition for the source class /Theta/ to be universally encodable in the sense of the existence of schemes attaining the optimal distribution-dependent exponent, simultaneously for all sources in the class. This condition was shown in an earlier work to suffice for universality in expectation. |
| Author | Weissman, T. |
| Author_xml | – sequence: 1 givenname: T. surname: Weissman fullname: Weissman, T. organization: Dept. of Electr. Eng., Stanford Univ., CA, USA |
| BookMark | eNp9kc1LAzEQxYNUsK2ePXhZPOhp23zuZo9S_CgUBGnPIZtNJGWb1CQV-9-bUkHooadhht97w8wbgYHzTgNwi-AEIdhMl_PlBENIJxxzWKELMESM1WVTMToAQwgRLxtK-RUYxbjOLWUID8HHytlvHaLs-30hU5LWybbXhQ7Bh0L_bPMSl2Jhchdk0mVnY_IhWe8K5TvrPgtvCudt3BfR74LS8RpcGtlHffNXx2D18rycvZWL99f57GlRKkKbVDJuSN1hRVtckRaSGvHKMMK6PFayJbJWhkkjCWZ5rqGhqDM1U5JD1PKOkTF4PPpug__a6ZjExkal-1467XdRNNkXU4RoJh_OkphTTurqYHl_Aq7zTS5fIVDDeEMbXmVoeoRU8DEGbcQ22I0Me4GgOEQhchTiEIU4RpEV7EShbJKHH6YgbX9Gd3fUWa31_xYCMYGI_AJ6PZh2 |
| CODEN | IETTAW |
| CitedBy_id | crossref_primary_10_1109_TIT_2004_839518 crossref_primary_10_1109_TIT_2006_878234 crossref_primary_10_1109_TIT_2018_2857829 crossref_primary_10_1109_TIT_2018_2881738 crossref_primary_10_1109_TIT_2019_2903152 crossref_primary_10_1109_TWC_2023_3238463 crossref_primary_10_4103_0256_4602_64599 crossref_primary_10_1109_TIT_2016_2562008 crossref_primary_10_1109_TIT_2005_860432 crossref_primary_10_1109_TIT_2007_892772 crossref_primary_10_1109_TIT_2021_3083271 |
| Cites_doi | 10.1109/TIT.1968.1054147 10.1109/18.720535 10.1109/18.481803 10.1109/TIT.2002.1003837 10.1109/18.508836 10.1109/18.9780 10.1109/TIT.1975.1055439 10.1109/TIT.1974.1055254 10.1109/TIT.1984.1056936 10.1109/18.720554 10.1109/DCC.1993.253144 10.1137/0127048 10.1007/978-3-7091-2945-6 10.1109/TIT.2002.800478 10.1109/TIT.1976.1055576 10.1109/TIT.1972.1054831 10.1109/18.986015 10.1109/TIT.1981.1056322 10.1109/18.978747 10.1109/18.669153 10.1109/18.79912 10.1109/TIT.1980.1056164 10.1109/TIT.1974.1055204 10.1002/0471219282.eot142 10.1109/18.720552 10.1109/TIT.1970.1054469 10.1109/18.75244 10.1109/TIT.2002.808137 10.1109/18.481794 10.1109/18.382015 10.1109/18.481776 10.1109/18.259634 10.1109/TIT.1980.1056251 10.1109/18.340451 10.1109/TIT.2003.819336 10.1109/18.887861 |
| ContentType | Journal Article |
| Copyright | Copyright Institute of Electrical and Electronics Engineers, Inc. (IEEE) Jun 2004 |
| Copyright_xml | – notice: Copyright Institute of Electrical and Electronics Engineers, Inc. (IEEE) Jun 2004 |
| DBID | RIA RIE AAYXX CITATION 7SC 7SP 8FD JQ2 L7M L~C L~D F28 FR3 |
| DOI | 10.1109/TIT.2004.828061 |
| 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 ANTE: Abstracts in New Technology & Engineering Engineering Research Database |
| 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 Engineering Research Database ANTE: Abstracts in New Technology & Engineering |
| DatabaseTitleList | Technology Research Database Technology Research Database Computer and Information Systems Abstracts |
| Database_xml | – sequence: 1 dbid: RIE name: IEEE Xplore url: https://ieeexplore.ieee.org/ sourceTypes: Publisher |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Engineering Computer Science |
| EISSN | 1557-9654 |
| EndPage | 1246 |
| ExternalDocumentID | 689268921 10_1109_TIT_2004_828061 1302301 |
| Genre | orig-research |
| 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 F28 FR3 |
| ID | FETCH-LOGICAL-c349t-58f37d2c4b263b037186f535df37cab3a7cf5afa3256f5e0f41df75ca801b8d53 |
| IEDL.DBID | RIE |
| ISICitedReferencesCount | 20 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000221803300019&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 | Sun Sep 28 01:09:27 EDT 2025 Thu Oct 02 11:08:20 EDT 2025 Fri Jul 25 04:29:15 EDT 2025 Tue Nov 18 21:18:39 EST 2025 Sat Nov 29 08:07:34 EST 2025 Tue Aug 26 16:39:07 EDT 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 6 |
| Language | English |
| License | https://ieeexplore.ieee.org/Xplorehelp/downloads/license-information/IEEE.html |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c349t-58f37d2c4b263b037186f535df37cab3a7cf5afa3256f5e0f41df75ca801b8d53 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 ObjectType-Article-2 ObjectType-Feature-1 content type line 23 |
| PQID | 195894986 |
| PQPubID | 23500 |
| PageCount | 18 |
| ParticipantIDs | proquest_miscellaneous_926324114 crossref_primary_10_1109_TIT_2004_828061 ieee_primary_1302301 crossref_citationtrail_10_1109_TIT_2004_828061 proquest_journals_195894986 proquest_miscellaneous_28483765 |
| PublicationCentury | 2000 |
| PublicationDate | 2004-06-01 |
| PublicationDateYYYYMMDD | 2004-06-01 |
| PublicationDate_xml | – month: 06 year: 2004 text: 2004-06-01 day: 01 |
| PublicationDecade | 2000 |
| PublicationPlace | New York |
| PublicationPlace_xml | – name: New York |
| PublicationTitle | IEEE transactions on information theory |
| PublicationTitleAbbrev | TIT |
| PublicationYear | 2004 |
| 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 ref35 ref12 ref34 ref15 ref37 ref14 ref36 ref30 ref33 ref10 ref32 ref2 ref1 ref17 ref39 ref16 ref38 Donoho (ref11) ref19 ref18 Shannon (ref31); 7 ref24 ref23 ref26 ref25 ref20 ref22 ref21 Csiszár (ref9) 1981 ref28 ref27 ref29 ref8 ref4 Blahut (ref7) 1987 ref3 ref6 ref5 ref40 |
| References_xml | – ident: ref17 doi: 10.1109/TIT.1968.1054147 – ident: ref20 doi: 10.1109/18.720535 – ident: ref18 doi: 10.1109/18.481803 – ident: ref14 doi: 10.1109/TIT.2002.1003837 – ident: ref8 doi: 10.1109/18.508836 – volume-title: Information Theory: Coding Theorems for Discrete Memoryless Systems year: 1981 ident: ref9 – ident: ref12 doi: 10.1109/18.9780 – ident: ref27 doi: 10.1109/TIT.1975.1055439 – ident: ref5 doi: 10.1109/TIT.1974.1055254 – ident: ref28 doi: 10.1109/TIT.1984.1056936 – ident: ref1 doi: 10.1109/18.720554 – ident: ref26 doi: 10.1109/DCC.1993.253144 – ident: ref36 doi: 10.1137/0127048 – ident: ref15 doi: 10.1007/978-3-7091-2945-6 – ident: ref21 doi: 10.1109/TIT.2002.800478 – ident: ref6 doi: 10.1109/TIT.1976.1055576 – ident: ref39 doi: 10.1109/TIT.1972.1054831 – volume: 7 start-page: 142 volume-title: IRE Conv. Rec. ident: ref31 article-title: Coding theorems for a discrete source with a fidelity criterion – ident: ref32 doi: 10.1109/18.986015 – ident: ref16 doi: 10.1109/TIT.1981.1056322 – ident: ref33 doi: 10.1109/18.978747 – ident: ref13 doi: 10.1109/18.669153 – ident: ref24 doi: 10.1109/18.79912 – ident: ref40 doi: 10.1109/TIT.1980.1056164 – ident: ref23 doi: 10.1109/TIT.1974.1055204 – volume-title: The Kolmogorov sampler ident: ref11 – ident: ref3 doi: 10.1002/0471219282.eot142 – ident: ref4 doi: 10.1109/18.720552 – ident: ref35 doi: 10.1109/TIT.1970.1054469 – ident: ref38 doi: 10.1109/18.75244 – ident: ref25 doi: 10.1109/TIT.2002.808137 – ident: ref37 doi: 10.1109/18.481794 – ident: ref2 doi: 10.1109/18.382015 – ident: ref29 doi: 10.1109/18.481776 – ident: ref19 doi: 10.1109/18.259634 – ident: ref34 doi: 10.1109/TIT.1980.1056251 – ident: ref22 doi: 10.1109/18.340451 – volume-title: Principles and Practice of Information Theory year: 1987 ident: ref7 – ident: ref10 doi: 10.1109/TIT.2003.819336 – ident: ref30 doi: 10.1109/18.887861 |
| SSID | ssj0014512 |
| Score | 1.8710694 |
| Snippet | Consider the problem of rate-constrained reconstruction of a finite-alphabet discrete memoryless signal X/sup n/=(X/sub 1/,...,X/sub n/), based on a... Consider the problem of rate-constrained reconstruction of a finite-alphabet discrete memoryless signal Xn = (X1,..., Xn.), based on a noise-corrupted... Consider the problem of rate-constrained reconstruction of a finite-alphabet discrete memoryless signal X/n/=(X(1),...,X/n/), based on a noise-corrupted... Consider the problem of rate-constrained reconstruction of a finite-alphabet discrete memoryless signal X super(n)=(X sub(1),...,X sub(n)), based on a... |
| SourceID | proquest crossref ieee |
| SourceType | Aggregation Database Enrichment Source Index Database Publisher |
| StartPage | 1229 |
| SubjectTerms | Block codes Bulk molding compounds Channels Codes Decay rate Distortion Distortion measurement Error analysis Errors Exponents Information rates Information theory Memoryless systems Minimax techniques Noise reduction Rate-distortion Reconstruction Signaling Source coding Testing Uncertainty |
| Title | Universally attainable error exponents for rate-distortion coding of noisy sources |
| URI | https://ieeexplore.ieee.org/document/1302301 https://www.proquest.com/docview/195894986 https://www.proquest.com/docview/28483765 https://www.proquest.com/docview/926324114 |
| Volume | 50 |
| WOSCitedRecordID | wos000221803300019&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 Xplore 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/eLvHCXMwlV3PS8MwFH6oeNCD06lY548cPHiwW7ska3IUUfQyRCZ4K2mawGC00m6C_70vaTcV9eCttCkp_fr68uW99z2AC4sUgzJtQpEhDMzYLMwSEYfWaJVJEUkdK99sIhmPxcuLfFyDq1UtjDHGJ5-Zvjv0sfy81Au3VTZwQTbqirXWkyRparVWEQPG40YZPEYDRs7RyvjEkRxMHiaeCPaFCyPG3zyQb6ny4z_snctd53-PtQs77SKSXDeo78GaKbrQWTZoIK29dmH7i9rgPjy1SRhqNnsnar6smyKmqsqK4MRl4bIqCC5jiROQCHMvIeKQI7p0Po6UlhTltH4nzZ5_fQDPd7eTm_uwbakQasrkPOTC0iQfapYNRzRzcn1iZDnlOZ5GcKhKtOXKKoorIctNZFmc24RrhY4sEzmnh7BR4NMcAeHaxkIJy5REwFmkImORa7NccWuEzQPoL19zqlu9cdf2YpZ63hHJFHFxXTBZ2uASwOXqhtdGauPvofsOhs9hDQIB9JY4pq0p1qlT05FMilEA56uraEMuMKIKUy7qFF008vQRD4D8MUJ6WXvkjse_z9yDrSalx23PnMDGvFqYU9jUb_NpXZ35L_UDUjbpAA |
| linkProvider | IEEE |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV3PT9swFH5CbBLbYQwKWsYvHzhwIG1c2419nBAIBFQIFam3yHFsCalKpqSdxH-_ZyftQNDDblHiyFG-vDx_fu99D-DUIcVg3NhY5ggDty6P81TS2FmjcyUTZagOzSbS8VhOp-phA85XtTDW2pB8Zvv-MMTyi8os_FbZwAfZmC_W-iQ4H9K2WmsVM-CCttrgFE0YWUcn5EMTNZjcTAIV7EsfSKRvfFBoqvLuTxzcy9X2_z3Yd_jWLSPJrxb3Hdiw5S5sL1s0kM5id-HrK73BHjx2aRh6Nnsher6snCK2rqua4MRV6fMqCC5kiZeQiIsgIuKxI6byXo5UjpTVc_NC2l3_Zg-eri4nF9dx11QhNoyreSykY2kxNDwfjljuBfvkyAkmCjyN8DCdGie00wzXQk7YxHFauFQYja4sl4Vg-7BZ4tP8ACKMo1JLx7VCyHmiE-uQbfNCC2elKyLoL19zZjrFcd_4YpYF5pGoDHHxfTB51uISwdnqht-t2Mb6oT0Pw79hLQIRHCxxzDpjbDKvp6O4kqMITlZX0Yp8aESXtlo0GTppZOojEQFZM0IFYXtkjz8_nvkEtq4n93fZ3c349gC-tAk-frPmEDbn9cIewWfzZ_7c1Mfhq_0Lkf7sRw |
| 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=Universally+Attainable+Error+Exponents+for+Rate-Distortion+Coding+of+Noisy+Sources&rft.jtitle=IEEE+transactions+on+information+theory&rft.au=Weissman%2C+T.&rft.date=2004-06-01&rft.issn=0018-9448&rft.volume=50&rft.issue=6&rft.spage=1229&rft.epage=1246&rft_id=info:doi/10.1109%2FTIT.2004.828061&rft.externalDBID=n%2Fa&rft.externalDocID=10_1109_TIT_2004_828061 |
| 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 |