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On exact asymptotics of the error probability in channel coding: symmetric channels (1908.11419v1)
Published 29 Aug 2019 in cs.IT and math.IT
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.