Expurgated Random-Coding Ensembles: Exponents, Refinements, and Connections
This paper studies expurgated random-coding bounds and exponents for channel coding with a given (possibly suboptimal) decoding rule. Variations of Gallager's analysis are presented, yielding several asymptotic and nonasymptotic bounds on the error probability for an arbitrary codeword distribu...
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| Published in: | IEEE transactions on information theory Vol. 60; no. 8; pp. 4449 - 4462 |
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| Main Authors: | , , , , |
| Format: | Journal Article Conference Proceeding |
| Language: | English |
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New York, NY
IEEE
01.08.2014
Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE) Institute of Electrical and Electronics Engineers (IEEE) |
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| ISSN: | 0018-9448, 1557-9654 |
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| Abstract | This paper studies expurgated random-coding bounds and exponents for channel coding with a given (possibly suboptimal) decoding rule. Variations of Gallager's analysis are presented, yielding several asymptotic and nonasymptotic bounds on the error probability for an arbitrary codeword distribution. A simple nonasymptotic bound is shown to attain an exponent of Csiszár and Körner under constant-composition coding. Using Lagrange duality, this exponent is expressed in several forms, one of which is shown to permit a direct derivation via cost-constrained coding that extends to infinite and continuous alphabets. The method of type class enumeration is studied, and it is shown that this approach can yield improved exponents and better tightness guarantees for some codeword distributions. A generalization of this approach is shown to provide a multiletter exponent that extends immediately to channels with memory. |
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| AbstractList | This paper studies expurgated random-coding bounds and exponents for channel coding with a given (possibly suboptimal) decoding rule. Variations of Gallager's analysis are presented, yielding several asymptotic and nonasymptotic bounds on the error probability for an arbitrary codeword distribution. A simple nonasymptotic bound is shown to attain an exponent of Csiszar and Korner under constant-composition coding. Using Lagrange duality, this exponent is expressed in several forms, one of which is shown to permit a direct derivation via cost-constrained coding that extends to infinite and continuous alphabets. The method of type class enumeration is studied, and it is shown that this approach can yield improved exponents and better tightness guarantees for some codeword distributions. A generalization of this approach is shown to provide a multiletter exponent that extends immediately to channels with memory. This paper studies expurgated random-coding bounds and exponents for channel coding with a given (possibly suboptimal) decoding rule. Variations of Gallager's analysis are presented, yielding several asymptotic and nonasymptotic bounds on the error probability for an arbitrary codeword distribution. A simple nonasymptotic bound is shown to attain an exponent of Csiszár and Körner under constant-composition coding. Using Lagrange duality, this exponent is expressed in several forms, one of which is shown to permit a direct derivation via cost-constrained coding that extends to infinite and continuous alphabets. The method of type class enumeration is studied, and it is shown that this approach can yield improved exponents and better tightness guarantees for some codeword distributions. A generalization of this approach is shown to provide a multiletter exponent that extends immediately to channels with memory. This paper studies expurgated random-coding bounds and exponents for channel coding with a given (possibly suboptimal) decoding rule. Variations of Gallager's analysis are presented, yielding several asymptotic and nonasymptotic bounds on the error probability for an arbitrary codeword distribution. A simple nonasymptotic bound is shown to attain an exponent of Csiszár and Körner under constant-composition coding. Using Lagrange duality, this exponent is expressed in several forms, one of which is shown to permit a direct derivation via cost-constrained coding that extends to infinite and continuous alphabets. The method of type class enumeration is studied, and it is shown that this approach can yield improved exponents and better tightness guarantees for some codeword distributions. A generalization of this approach is shown to provide a multiletter exponent that extends immediately to channels with memory. This work was supported in part by the European Research Council under Grant 259663, in part by the European Union’s 7th Framework Programme under Grant 303633, and in part by the Spanish Ministry of Economy and Competitiveness under Grant RYC-2011-08150 and Grant TEC2012-38800-C03-03. The work of N. Merhav was supported by the Israel Science Foundation under Grant 412/12. |
| Author | Guillen i Fabregas, Albert Scarlett, Jonathan Martinez, Alfonso Merhav, Neri Peng, Li |
| Author_xml | – sequence: 1 givenname: Jonathan surname: Scarlett fullname: Scarlett, Jonathan email: jmscarlett@gmail.com organization: Department of Engineering, University of Cambridge, Cambridge, U.K – sequence: 2 givenname: Li surname: Peng fullname: Peng, Li email: lp327@cam.ac.uk organization: Department of Engineering, University of Cambridge, Cambridge, U.K – sequence: 3 givenname: Neri surname: Merhav fullname: Merhav, Neri email: merhav@ee.technion.ac.il organization: Department of Electrical Engineering, Technion-Israel Institute of Technology, Haifa, Israel – sequence: 4 givenname: Alfonso surname: Martinez fullname: Martinez, Alfonso email: alfonso.martinez@ieee.org organization: Department of Information and Communication Technologies, Universitat Pompeu Fabra, Barcelona – sequence: 5 givenname: Albert surname: Guillen i Fabregas fullname: Guillen i Fabregas, Albert email: guillen@ieee.org organization: Department of Information and Communication TechnologiesInstitució Catalana de Recerca i Estudis Avançats, Universitat Pompeu Fabra, Barcelona, Spain |
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| Cites_doi | 10.1109/TIT.1977.1055792 10.1109/ITA.2013.6502939 10.1109/TIT.2009.2034892 10.1016/S0019-9958(74)80060-4 10.1109/TIT.2010.2043769 10.1109/18.370121 10.1109/TIT.1968.1054148 10.1109/18.340469 10.1109/TIT.2008.929004 10.1109/TIT.1956.1056798 10.1109/TIT.1981.1056281 10.1017/CBO9780511804441 10.1109/TIT.2014.2322033 10.1109/TIT.1982.1056585 10.1002/0471200611 10.1109/TIT.2014.2310453 10.1109/Allerton.2013.6736628 10.1002/j.1538-7305.1948.tb01338.x 10.1073/pnas.39.1.42 10.1561/0100000052 10.1017/CBO9780511921889 10.1109/18.887846 |
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| Keywords | maximum-likelihood decoding reliability function random coding type class enumeration mismatched decoding Expurgated error exponents Alphabet Channel with memory Error probability Refinement method Random coding Channel coding Mismatching Maximum likelihood decoding Reliability |
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| References | ref13 ref12 ref15 ref14 ref11 ref10 ref1 ref17 ref16 ref19 ref18 d’yachkov (ref22) 1980; 16 csiszár (ref4) 1977 gallager (ref2) 1968 cover (ref20) 2001 ref24 ref23 ref21 merhav (ref9) 2009; 6 ref27 altu? (ref26) 2014 scarlett (ref25) 2014 ref8 ref7 ref3 ref6 ref5 de bruijn (ref28) 1981 |
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| Snippet | This paper studies expurgated random-coding bounds and exponents for channel coding with a given (possibly suboptimal) decoding rule. Variations of Gallager's... |
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| SubjectTerms | Applied sciences Asymptotic methods Asymptotic properties Channels Codes Coding Coding, codes Decoding Derivation Electronic mail Encoding Error analysis Error probability Exact sciences and technology Exponents Expurgated error exponents Information theory Information, signal and communications theory IP networks Joints Lagrange multiplier Maximum-likelihood decoding Measurement Mismatched decoding Permissible error Probability distribution Random coding Reliability function Signal and communications theory Telecommunications and information theory Type class enumeration |
| Title | Expurgated Random-Coding Ensembles: Exponents, Refinements, and Connections |
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