On Exact Asymptotics of the Error Probability in Channel Coding: Symmetric Channels

The exact order of the optimal sub-exponentially decaying factor in the classical bounds on the error probability of fixed-length codes over a Gallager-symmetric discrete memoryless channel with and without ideal feedback is determined for rates above the critical rate. Regardless of the availabilit...

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Bibliographic Details
Published in:IEEE transactions on information theory Vol. 67; no. 2; pp. 844 - 868
Main Authors: Altug, Yucel, Wagner, Aaron B.
Format: Journal Article
Language:English
Published: New York IEEE 01.02.2021
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Channel coding
Channels
Codes
Conferences
Decoding
error exponents
Error probability
exact asymptotics
Feedback
Random variables
Reliability
reliable communication
symmetric channels
ISSN:0018-9448, 1557-9654
Online Access:Get full text
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Summary:The exact order of the optimal sub-exponentially decaying factor in the classical bounds on the error probability of fixed-length codes over a Gallager-symmetric discrete memoryless channel with and without ideal feedback is determined for rates above the critical rate. Regardless of the availability of feedback, it is shown that the order of the optimal sub-exponential factor exhibits a dichotomy. Moreover, the proof technique is used to establish the third-order term in the normal approximation for symmetric channels, where a similar dichotomy is shown to exist.
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ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2020.3042592