Using tools developed in a recent work by Shen and the second author, in this paper we carry out an in-depth study on the average decoding error probability of the random matrix ensemble over the erasure channel under three decoding principles, namely unambiguous decoding, maximum likelihood decoding and list decoding. We obtain explicit formulas for the average decoding error probabilities of the random matrix ensemble under these three decoding principles and compute the error exponents. Moreover, for unambiguous decoding, we compute the variance of the decoding error probability of the random matrix ensemble and the error exponent of the variance, which imply a strong concentration result, that is, roughly speaking, the ratio of the decoding error probability of a random code in the ensemble and the average decoding error probability of the ensemble converges to 1 with high probability when the code length goes to infinity.

翻译：利用Shen与第二作者近期工作中发展的工具，本文深入研究了删除信道下随机矩阵系综在三种译码原则——即无歧义译码、最大似然译码及列表译码——下的平均译码错误概率。我们获得了这三种译码原则下随机矩阵系综平均译码错误概率的显式公式，并计算了错误指数。此外，针对无歧义译码，我们计算了随机矩阵系综译码错误概率的方差及其错误指数，由此导出了一个强集中结果：大致而言，当码长趋于无穷时，系综中随机码的译码错误概率与系综平均译码错误概率之比以高概率收敛于1。