A Tight Upper Bound for the Third-Order Asymptotics for Most Discrete Memoryless Channels
A Tight Upper Bound for the Third-Order Asymptotics for Most Discrete Memoryless Channels
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DOI：
10.1109/tit.2013.2276077
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发表时间：
2012-12
影响因子：
2.5
通讯作者：
M. Tomamichel;V. Tan
中科院分区：
文献类型：
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作者：
M. Tomamichel;V. Tan
本文证明了当离散无记忆信道（DMC）的ε-色散为正时，n次使用的ε-错误容量（平均错误概率）的对数的上界是正态近似加上不超过[ 1/ 2] logn +O（1）的三阶项.这与Y的下界匹配。Polyanskiy（2010），用于具有正反向色散的DMC。若ε-色散为零，则ε-误差容量的对数的上界为n倍容量加上一个常数项（除了一小类DMC且ε ≥ [ 1/ 2]）.
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/ 2] logn +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-error capacity is upper bounded by n times the capacity plus a constant term except for a small class of DMCs and ε ≥ [ 1/ 2].