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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 2014-08, Vol.60 (8), p.4449-4462 |
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| Main Authors: | , , , , |
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| container_title | IEEE transactions on information theory |
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| creator | Scarlett, Jonathan Peng, Li Merhav, Neri Martinez, Alfonso Guillen i Fabregas, Albert |
| description | 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. |
| doi_str_mv | 10.1109/TIT.2014.2322033 |
| format | article |
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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.</description><identifier>ISSN: 0018-9448</identifier><identifier>EISSN: 1557-9654</identifier><identifier>DOI: 10.1109/TIT.2014.2322033</identifier><identifier>CODEN: IETTAW</identifier><language>eng</language><publisher>New York, NY: IEEE</publisher><subject>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</subject><ispartof>IEEE transactions on information theory, 2014-08, Vol.60 (8), p.4449-4462</ispartof><rights>2015 INIST-CNRS</rights><rights>Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) Aug 2014</rights><rights>info:eu-repo/semantics/openAccess © 2014 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. The final published article can be found at <a href="http://dx.doi.org/10.1109/TIT.2014.2322033">http://dx.doi.org/10.1109/TIT.2014.2322033</a></rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c396t-fade143a9ab02bcdbb99bc251521cfa5aa86e2c14a9b063d972453a0e13c1ee43</citedby><cites>FETCH-LOGICAL-c396t-fade143a9ab02bcdbb99bc251521cfa5aa86e2c14a9b063d972453a0e13c1ee43</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/6810903$$EHTML$$P50$$Gieee$$H</linktohtml><link.rule.ids>230,309,310,314,780,784,789,790,885,23930,23931,25140,27924,27925,54796</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=28722000$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Scarlett, Jonathan</creatorcontrib><creatorcontrib>Peng, Li</creatorcontrib><creatorcontrib>Merhav, Neri</creatorcontrib><creatorcontrib>Martinez, Alfonso</creatorcontrib><creatorcontrib>Guillen i Fabregas, Albert</creatorcontrib><title>Expurgated Random-Coding Ensembles: Exponents, Refinements, and Connections</title><title>IEEE transactions on information theory</title><addtitle>TIT</addtitle><description>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.</description><subject>Applied sciences</subject><subject>Asymptotic methods</subject><subject>Asymptotic properties</subject><subject>Channels</subject><subject>Codes</subject><subject>Coding</subject><subject>Coding, codes</subject><subject>Decoding</subject><subject>Derivation</subject><subject>Electronic mail</subject><subject>Encoding</subject><subject>Error analysis</subject><subject>Error probability</subject><subject>Exact sciences and technology</subject><subject>Exponents</subject><subject>Expurgated error exponents</subject><subject>Information theory</subject><subject>Information, signal and communications theory</subject><subject>IP networks</subject><subject>Joints</subject><subject>Lagrange multiplier</subject><subject>Maximum-likelihood decoding</subject><subject>Measurement</subject><subject>Mismatched decoding</subject><subject>Permissible error</subject><subject>Probability distribution</subject><subject>Random coding</subject><subject>Reliability function</subject><subject>Signal and communications theory</subject><subject>Telecommunications and information theory</subject><subject>Type class enumeration</subject><issn>0018-9448</issn><issn>1557-9654</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2014</creationdate><recordtype>article</recordtype><recordid>eNpdkc1r3DAQxUVpodu090IuhlDIod5q9GFbuZVl04QECmF7FmN5HBxsaSPZkP731bJLCjkMw0O_9xjxGPsKfA3AzY_d7W4tOKi1kEJwKd-xFWhdl6bS6j1bcQ5NaZRqPrJPKT1lqTSIFbvbvuyX-IgzdcUD-i5M5SZ0g38stj7R1I6UrorMBE9-Tt-LB-oHT9NRZL7YBO_JzUPw6TP70OOY6Mtpn7E_19vd5qa8__3rdvPzvnTSVHPZY0egJBpsuWhd17bGtE5o0AJcjxqxqUg4UGhaXsnO1EJpiZxAOiBS8ozBMdelxdlIjqLD2QYc_ovDCF4LK2VdSZM9l0fPPobnhdJspyE5Gkf0FJZkodZSC1PVB_TiDfoUlujzjyxoVWVOSsgUPx0RQ0qReruPw4TxrwVuD43Y3Ig9NGJPjWTLt1MwJodjH9G7Ib36RFNnjvPMnR-5gYhen6smh-aYf-dykwM</recordid><startdate>20140801</startdate><enddate>20140801</enddate><creator>Scarlett, Jonathan</creator><creator>Peng, Li</creator><creator>Merhav, Neri</creator><creator>Martinez, Alfonso</creator><creator>Guillen i Fabregas, Albert</creator><general>IEEE</general><general>Institute of Electrical and Electronics Engineers</general><general>The Institute of Electrical and Electronics Engineers, Inc. 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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.</abstract><cop>New York, NY</cop><pub>IEEE</pub><doi>10.1109/TIT.2014.2322033</doi><tpages>14</tpages><oa>free_for_read</oa></addata></record> |
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| language | eng |
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| subjects | 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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