Generalized Random Gilbert-Varshamov Codes: Typical Error Exponent and Concentration Properties
We find the exact typical error exponent of constant composition generalized random Gilbert-Varshamov (RGV) codes over discrete memoryless channels with generalized likelihood decoding. We show that the typical error exponent of the RGV ensemble is equal to the expurgated error exponent, provided th...
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| Vydané v: | IEEE transactions on information theory Ročník 70; číslo 2; s. 1 |
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| Hlavní autori: | , |
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| Jazyk: | English |
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New York
IEEE
01.02.2024
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
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| Abstract | We find the exact typical error exponent of constant composition generalized random Gilbert-Varshamov (RGV) codes over discrete memoryless channels with generalized likelihood decoding. We show that the typical error exponent of the RGV ensemble is equal to the expurgated error exponent, provided that the RGV codebook parameters are chosen appropriately. We also prove that the random coding exponent converges in probability to the typical error exponent, and the corresponding non-asymptotic concentration rates are derived. Our results show that the decay rate of the lower tail is exponential while that of the upper tail is double exponential above the expurgated error exponent. The explicit dependence of the decay rates on the RGV distance functions is characterized. |
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| AbstractList | We find the exact typical error exponent of constant composition generalized random Gilbert-Varshamov (RGV) codes over discrete memoryless channels with generalized likelihood decoding. We show that the typical error exponent of the RGV ensemble is equal to the expurgated error exponent, provided that the RGV codebook parameters are chosen appropriately. We also prove that the random coding exponent converges in probability to the typical error exponent, and the corresponding non-asymptotic concentration rates are derived. Our results show that the decay rate of the lower tail is exponential while that of the upper tail is double exponential above the expurgated error exponent. The explicit dependence of the decay rates on the RGV distance functions is characterized. |
| Author | Truong, Lan V. Fabregas, Albert Guillen i |
| Author_xml | – sequence: 1 givenname: Lan V. orcidid: 0000-0002-7756-3464 surname: Truong fullname: Truong, Lan V. organization: School of Mathematics, Statistics and Actuarial Science, University of Essex, Colchester, U.K – sequence: 2 givenname: Albert Guillen i orcidid: 0000-0003-2795-1124 surname: Fabregas fullname: Fabregas, Albert Guillen i organization: Department of Engineering, University of Cambridge, Cambridge, U.K |
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| SubjectTerms | Channel coding Codes Decay rate Decoding Error probability Errors Maximum likelihood decoding Memoryless systems Monte Carlo methods Tail |
| Title | Generalized Random Gilbert-Varshamov Codes: Typical Error Exponent and Concentration Properties |
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