随机码对数错误概率的大偏差行为
Large Deviations Behavior of the Logarithmic Error Probability of Random Codes
摘要：
本文研究了常成分码集合的误差指数在其期望值附近的偏差，称为典型随机码的误差指数。特别是，它表明，随机绘制码本的误差指数小于TRC指数的概率是指数小，这个指数的上限和下限，在某些情况下，这是一致的。此外，随机抽取码本的错误指数大于TRC指数的概率被证明是双指数小，双指数指数的上限和下限给出。结果表明，码本的错误指数大于TRC的错误指数是非常罕见的。证明中的关键部分是一个新的含因变量的类型类枚举数的大偏差结果。
英文摘要：
This work studies the deviations of the error exponent of the constant composition code ensemble around its expectation, known as the error exponent of the typical random code (TRC). In particular, it is shown that the probability of randomly drawing a codebook whose error exponent is smaller than the TRC exponent is exponentially small; upper and lower bounds for this exponent are given, which coincide in some cases. In addition, the probability of randomly drawing a codebook whose error exponent is larger than the TRC exponent is shown to be double-exponentially small; upper and lower bounds to the double-exponential exponent are given. The results suggest that codebooks whose error exponent is larger than the error exponent of the TRC are extremely rare. The key ingredient in the proofs is a new large deviations result of type class enumerators with dependent variables.
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