Truong, Lan V and Fàbregas, Albert Guillén I (2024) Generalized Random Gilbert-Varshamov Codes: Typical Error Exponent and Concentration Properties. IEEE Transactions on Information Theory, 70 (2). pp. 820-853. DOI https://doi.org/10.1109/tit.2023.3310117
Truong, Lan V and Fàbregas, Albert Guillén I (2024) Generalized Random Gilbert-Varshamov Codes: Typical Error Exponent and Concentration Properties. IEEE Transactions on Information Theory, 70 (2). pp. 820-853. DOI https://doi.org/10.1109/tit.2023.3310117
Truong, Lan V and Fàbregas, Albert Guillén I (2024) Generalized Random Gilbert-Varshamov Codes: Typical Error Exponent and Concentration Properties. IEEE Transactions on Information Theory, 70 (2). pp. 820-853. DOI https://doi.org/10.1109/tit.2023.3310117
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.
Item Type: | Article |
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Uncontrolled Keywords: | Codes; Tail; Channel coding; Error probability; Monte Carlo methods; Memoryless systems; Maximum likelihood decoding; Random coding; error exponent; typical error exponent; gilbert-Varshamov codes; concentration properties |
Divisions: | Faculty of Science and Health Faculty of Science and Health > Mathematics, Statistics and Actuarial Science, School of |
SWORD Depositor: | Unnamed user with email elements@essex.ac.uk |
Depositing User: | Unnamed user with email elements@essex.ac.uk |
Date Deposited: | 20 Sep 2023 15:07 |
Last Modified: | 07 Aug 2024 17:44 |
URI: | http://repository.essex.ac.uk/id/eprint/36353 |
Available files
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