Recent experiments have shown that the capacity of DNA storage systems may be significantly increased by synthesizing composite DNA letters. In this work, we model a DNA storage channel with composite inputs as a \textit{multinomial channel}, and propose an optimization algorithm for its capacity achieving input distribution, for an arbitrary number of output reads. The algorithm is termed multidimensional dynamic assignment Blahut-Arimoto (M-DAB), and is a generalized version of the DAB algorithm, proposed by Wesel et al. developed for the binomial channel. We also empirically observe a scaling law behavior of the capacity as a function of the support size of the capacity-achieving input distribution.

翻译：近期实验表明，通过合成复合DNA碱基可显著提升DNA存储系统的容量。本文将复合输入下的DNA存储信道建模为\textit{多项信道}，并提出一种针对任意输出读取次数下容量实现输入分布的优化算法。该算法称为多维动态分配Blahut-Arimoto算法（M-DAB），是Wesel等人针对二项信道提出的DAB算法的泛化版本。我们通过实验还观察到，容量随容量实现输入分布支撑集大小变化的标度律行为。