Truong, Lan V and Cocco, Giuseppe and Font-Segura, Josep and Guillén i Fàbregas, Albert (2023) Concentration Properties of Random Codes. IEEE Transactions on Information Theory, 69 (12). pp. 7499-7537. DOI https://doi.org/10.1109/tit.2023.3312326 (In Press)
Truong, Lan V and Cocco, Giuseppe and Font-Segura, Josep and Guillén i Fàbregas, Albert (2023) Concentration Properties of Random Codes. IEEE Transactions on Information Theory, 69 (12). pp. 7499-7537. DOI https://doi.org/10.1109/tit.2023.3312326 (In Press)
Truong, Lan V and Cocco, Giuseppe and Font-Segura, Josep and Guillén i Fàbregas, Albert (2023) Concentration Properties of Random Codes. IEEE Transactions on Information Theory, 69 (12). pp. 7499-7537. DOI https://doi.org/10.1109/tit.2023.3312326 (In Press)
Abstract
This paper shows that, for discrete memoryless channels, the error exponent of a randomly generated code with independent codewords converges in probability to its expectation—the typical error exponent. For high rates, the result follows from the fact that the random-coding error exponent and the sphere-packing error exponent coincide. For low rates, instead, the convergence is based on the fact that the union bound accurately characterizes the error probability. The paper also zooms into the behavior at asymptotically low rates, and shows that the normalized error exponent converges in distribution to the standard Gaussian or a Gaussian-like distribution. We also state several results on the convergence of the error probability and error exponent for generic ensembles and channels.
Item Type: | Article |
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Uncontrolled Keywords: | Error exponent; typical error exponent; random coding; concentrations; maximum likelihood decoder |
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: | 08 Nov 2023 14:25 |
Last Modified: | 07 Aug 2024 18:43 |
URI: | http://repository.essex.ac.uk/id/eprint/36351 |
Available files
Filename: Final.pdf