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arXiv · 1212.3689

A Tight Upper Bound for the Third-Order Asymptotics for Most Discrete Memoryless Channels

Marco Tomamichel·Vincent Y. F. Tan
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Abstract

This paper shows that the logarithm of the epsilon-error capacity (average error probability) for n uses of a discrete memoryless channel is upper bounded by the normal approximation plus a third-order term that does not exceed 1/2 log n + O(1) if the epsilon-dispersion of the channel is positive. This matches a lower bound by Y. Polyanskiy (2010) for discrete memoryless channels with positive reverse dispersion. If the epsilon-dispersion vanishes, the logarithm of the epsilon-error capacity is upper bounded by the n times the capacity plus a constant term except for a small class of DMCs and epsilon >= 1/2.

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Marco Tomamichel, Vincent Y. F. Tan. 2013-10-24. A Tight Upper Bound for the Third-Order Asymptotics for Most Discrete Memoryless Channels. https://doi.org/10.1109/tit.2013.2276077

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