On exact asymptotics of the error probability in channel coding: symmetric channels
Y\"ucel Altu\u{g}, Aaron B. Wagner

TL;DR
This paper precisely characterizes the sub-exponential decay factors in error probabilities for symmetric channels, revealing a dichotomy and advancing the understanding of normal approximation terms.
Contribution
It determines the exact order of the sub-exponential factor in error bounds for symmetric channels, with and without feedback, and establishes the third-order term in normal approximation.
Findings
Sub-exponential factor exhibits a dichotomy in symmetric channels.
Exact order of the sub-exponential decay factor is identified.
Third-order term in normal approximation is derived.
Abstract
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. 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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