Lossless Coding for Distributed Streaming Sources
Distributed source coding is traditionally viewed in a block coding context wherein all source symbols are known in advance by the encoders. However, many modern applications to which distributed source coding ideas are applied, are better modeled as having streaming data. In a streaming setting, so...
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| Veröffentlicht in: | IEEE transactions on information theory Jg. 60; H. 3; S. 1447 - 1474 |
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| Sprache: | Englisch |
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IEEE
01.03.2014
Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
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| Abstract | Distributed source coding is traditionally viewed in a block coding context wherein all source symbols are known in advance by the encoders. However, many modern applications to which distributed source coding ideas are applied, are better modeled as having streaming data. In a streaming setting, source symbol pairs are revealed to separate encoders in real time and need to be reconstructed at the decoder with subject to some tolerable end-to-end delay. In this paper, a causal sequential random binning encoder is introduced and paired with maximum likelihood (ML) and universal decoders. The latter uses a novel weighted empirical suffix entropy decoding rule. We derive a lower bounds on the error exponent with delay for each decoder. We also provide upper bounds for the special case of streaming with decoder side information and discuss when upper and lower bounds match. We show that both ML and universal decoders achieve the same (positive) error exponents for all rate pairs inside the Slepian-Wolf achievable rate region. The dominant error events in streaming are different from those in block-coding and result in different exponents. Because the sequential random binning scheme is also universal over delays, the resulting code eventually reconstructs every source symbol correctly with probability one. |
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| AbstractList | Distributed source coding is traditionally viewed in a block coding context wherein all source symbols are known in advance by the encoders. However, many modern applications to which distributed source coding ideas are applied, are better modeled as having streaming data. In a streaming setting, source symbol pairs are revealed to separate encoders in real time and need to be reconstructed at the decoder with subject to some tolerable end-to-end delay. In this paper, a causal sequential random binning encoder is introduced and paired with maximum likelihood (ML) and universal decoders. The latter uses a novel weighted empirical suffix entropy decoding rule. We derive a lower bounds on the error exponent with delay for each decoder. We also provide upper bounds for the special case of streaming with decoder side information and discuss when upper and lower bounds match. We show that both ML and universal decoders achieve the same (positive) error exponents for all rate pairs inside the Slepian-Wolf achievable rate region. The dominant error events in streaming are different from those in block-coding and result in different exponents. Because the sequential random binning scheme is also universal over delays, the resulting code eventually reconstructs every source symbol correctly with probability one. Distributed source coding is traditionally viewed in a block coding context wherein all source symbols are known in advance by the encoders. However, many modern applications to which distributed source coding ideas are applied, are better modeled as having streaming data. In a streaming setting, source symbol pairs are revealed to separate encoders in real time and need to be reconstructed at the decoder with subject to some tolerable end-to-end delay. In this paper, a causal sequential random binning encoder is introduced and paired with maximum likelihood (ML) and universal decoders. The latter uses a novel weighted empirical suffix entropy decoding rule. We derive a lower bounds on the error exponent with delay for each decoder. We also provide upper bounds for the special case of streaming with decoder side information and discuss when upper and lower bounds match. We show that both ML and universal decoders achieve the same (positive) error exponents for all rate pairs inside the Slepian-Wolf achievable rate region. The dominant error events in streaming are different from those in block-coding and result in different exponents. Because the sequential random binning scheme is also universal over delays, the resulting code eventually reconstructs every source symbol correctly with probability one. [PUBLICATION ABSTRACT] |
| Author | Sahai, Anant Cheng Chang Draper, Stark C. |
| Author_xml | – sequence: 1 givenname: Stark C. surname: Draper fullname: Draper, Stark C. email: stark.draper@utoronto.ca organization: Dept. of Electr. & Comput. Eng., Univ. of Toronto, Toronto, ON, Canada – sequence: 2 surname: Cheng Chang fullname: Cheng Chang email: cchang@eecs.berkeley.edu organization: Dept. of Electr. Eng. & Comput. Sci., Univ. of California Berkeley, Berkeley, CA, USA – sequence: 3 givenname: Anant surname: Sahai fullname: Sahai, Anant email: sahai@eecs.berkeley.edu organization: Dept. of Electr. Eng. & Comput. Sci., Univ. of California Berkeley, Berkeley, CA, USA |
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| Keywords | Streaming Lower bound Block code Lossless circuit streaming data Source coding Coding circuit Distributed source signal Entropy Slepian-Wolf coding lossless source coding Information transmission Maximum likelihood decoding Distributed source coding Upper bound Delay time Maximum likelihood Causality universal decoding |
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| References | ref13 ref15 ref31 ref30 ref11 ref32 ref10 chang (ref2) 2007 ref1 ref17 ref19 meng (ref18) 2011 sahai (ref25) 2005 shulman (ref26) 2002 sahai (ref24) 0 ref23 girod (ref14) 2005; 93 ref22 ref21 dragotti (ref6) 2009 ref28 koshelev (ref16) 1977; 13 ref27 csisz r (ref5) 1981 draper (ref7) 2004 ref29 ref8 ref9 puri (ref20) 2002 ref4 ref3 gallager (ref12) 1976 |
| References_xml | – year: 1981 ident: ref5 publication-title: Information Theory Coding Theorems for Discrete Memoryless Systems – ident: ref30 doi: 10.1109/TIT.2008.924691 – ident: ref9 doi: 10.1155/2009/508167 – ident: ref19 doi: 10.1109/ICME.2008.4607512 – ident: ref4 doi: 10.1002/0471200611 – volume: 13 start-page: 26 year: 1977 ident: ref16 article-title: On a problem of separate coding of two dependent sources publication-title: Prob Peredachi Inf – ident: ref31 doi: 10.1109/TIT.1976.1055508 – ident: ref28 doi: 10.1109/CDC.2011.6161478 – ident: ref22 doi: 10.1109/TIT.2008.920339 – year: 2007 ident: ref2 publication-title: Streaming source coding with delay – volume: 93 start-page: 71 year: 2005 ident: ref14 article-title: Distributed video coding publication-title: Proc IEEE doi: 10.1109/JPROC.2004.839619 – ident: ref27 doi: 10.1109/TIT.1973.1055037 – ident: ref8 doi: 10.1109/ISIT.2005.1523572 – ident: ref32 doi: 10.1109/TIT.2010.2040867 – ident: ref29 doi: 10.1109/TIT.2006.885500 – year: 0 ident: ref24 article-title: Source coding and channel requirements for unstable processes publication-title: IEEE Trans Inf Theory 2006 – ident: ref11 doi: 10.1016/S0019-9958(74)90876-6 – start-page: 538 year: 2005 ident: ref25 article-title: A simple encoding and decoding strategy for stabilization over discrete memoryless channels publication-title: Proc Allerton Conf – ident: ref21 doi: 10.1145/195058.195462 – ident: ref13 doi: 10.1109/SFCS.1984.715906 – start-page: 127 year: 2002 ident: ref26 article-title: Source broadcasting with an unknown amount of receiver side information publication-title: Proc Inf Theory Workshop – year: 2009 ident: ref6 publication-title: Distributed source coding Theory algorithms and applications – year: 1976 ident: ref12 publication-title: Source coding with side information and universal coding – start-page: 262 year: 2002 ident: ref20 article-title: <formula formulatype="inline"><tex Notation="TeX">$n$</tex></formula>-channel multiple descriptions: Theory and construction publication-title: Proc Data Compress Conf – ident: ref10 doi: 10.1109/ACSSC.2005.1600071 – ident: ref15 doi: 10.1109/TIT.2009.2032803 – ident: ref17 doi: 10.1109/TIT.2003.819334 – start-page: 1 year: 2011 ident: ref18 article-title: Tree interactive encoding and decoding: Conditionally <formula formulatype="inline"> <tex Notation="TeX">$\phi$</tex></formula>-mixing sources publication-title: Proc Int Symp Inf Theory – ident: ref3 doi: 10.1109/TIT.1975.1055356 – start-page: 1332 year: 2004 ident: ref7 article-title: Universal incremental Slepian-Wolf coding publication-title: Proc Allerton Conf – ident: ref1 doi: 10.1017/CBO9780511804441 – ident: ref23 doi: 10.1109/TIT.2006.878169 |
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| SubjectTerms | Applied sciences Codes Coding, codes Delays Distributed source coding Entropy Exact sciences and technology Information theory Information, signal and communications theory Joints lossless source coding Maximum likelihood decoding Maximum likelihood method Probability distribution Signal and communications theory Slepian-Wolf coding Source coding streaming data Systems, networks and services of telecommunications Telecommunications Telecommunications and information theory Transmission and modulation (techniques and equipments) universal decoding |
| Title | Lossless Coding for Distributed Streaming Sources |
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