A tight upper bound for the third-order asymptotics for most discrete memoryless channels

Publication Type:
Journal Article
IEEE Transactions on Information Theory, 2013, 59 (11), pp. 7041 - 7051
Issue Date:
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This paper shows that the logarithm of the ε-error capacity (average error probability) for n uses of a discrete memoryless channel (DMC) is upper bounded by the normal approximation plus a third-order term that does not exceed 1/2log n +O(1) if the ε-dispersion of the channel is positive. This matches a lower bound by Y. Polyanskiy (2010) for DMCs with positive reverse dispersion. If the ε-dispersion vanishes, the logarithm of the ε-dispersion capacity is upper bounded by n times the capacity plus a constant term except for a small class of DMCs and ε≥1/2. © 1963-2012 IEEE.
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