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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Bibliographic Details
Published in:IEEE transactions on information theory Vol. 70; no. 2; p. 1
Main Authors: Truong, Lan V., Fabregas, Albert Guillen i
Format: Journal Article
Language:English
Published: New York IEEE 01.02.2024
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Channel coding
Codes
Decay rate
Decoding
Error probability
Errors
Maximum likelihood decoding
Memoryless systems
Monte Carlo methods
Tail
ISSN:0018-9448, 1557-9654
Online Access:Get full text
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Summary: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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ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2023.3310117