Empirical Distribution of Good Channel Codes With Nonvanishing Error Probability
Empirical Distribution of Good Channel Codes With Nonvanishing Error Probability
复制标题
具有非零错误概率的良好信道码的经验分布
DOI：
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发表时间：
2014
影响因子：
2.5
通讯作者：
S. Verdú
中科院分区：
文献类型：
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作者：
Yury Polyanskiy;S. Verdú
本文研究了信道码的几个性质，这些信道码接近给定的（离散或高斯）无记忆信道的基本极限，具有非零的错误概率。结果表明，在很强的意义上，由一个可实现容量的代码引起的输出分布接近于可实现容量的输出分布。依靠浓度的措施（isoperimetry）的财产享有后者，它表明，定期（Lipschitz）功能的通道输出可以精确估计，原来是基本上非随机和独立的实际代码。它还表明，一个好的代码的输出分布和实现的能力，不能区分指数可靠性。随机过程产生的输出的通道，以满足渐近均分属性。
This paper studies several properties of channel codes that approach the fundamental limits of a given (discrete or Gaussian) memoryless channel with a nonvanishing probability of error. The output distribution induced by an ϵ-capacity-achieving code is shown to be close in a strong sense to the capacity achieving output distribution. Relying on the concentration of measure (isoperimetry) property enjoyed by the latter, it is shown that regular (Lipschitz) functions of channel outputs can be precisely estimated and turn out to be essentially nonrandom and independent of the actual code. It is also shown that the output distribution of a good code and the capacity achieving one cannot be distinguished with exponential reliability. The random process produced at the output of the channel is shown to satisfy the asymptotic equipartition property.