This paper presents an achievability bound that evaluates the exact probability of error of an ensemble of random codes that are decoded by a minimum distance decoder. Compared to the state-of-the-art which demands exponential computation time, this bound is evaluated in polynomial time. This improvement in complexity is also attainable for the original random coding bound that utilizes an information density decoder. The general bound is particularized for the binary symmetric channel, the binary erasure channel, and the Gaussian channel.

翻译：本文提出一种可达性界，用于评估采用最小距离译码器的随机码集的精确错误概率。与现有需要指数计算时间的先进方法相比，该界可在多项式时间内完成评估。这种复杂度的提升同样适用于采用信息密度译码器的原始随机编码界。该通用界被具体应用于二元对称信道、二元删除信道及高斯信道。