We address the challenge of optimizing the capacity-achieving input distribution for a multinomial channel under the constraint of limited input support size, which is a crucial aspect in the design of DNA storage systems. We propose an algorithm that further elaborates the Multidimensional Dynamic Assignment Blahut-Arimoto (M-DAB) algorithm. Our proposed algorithm integrates variational autoencoder for determining the optimal locations of input distribution, into the alternating optimization of the input distribution locations and weights.

翻译：我们解决了在输入支持集大小受限的条件下，优化多项通道容量可达输入分布的挑战，这是DNA存储系统设计中的一个关键方面。我们提出了一种算法，该算法进一步阐述了多维动态分配Blahut-Arimoto（M-DAB）算法。我们提出的算法将用于确定输入分布最优位置的变分自编码器，集成到输入分布位置与权重的交替优化过程中。