We consider the problem of estimating an upper bound on the capacity of a
memoryless channel with unknown channel law and continuous output alphabet. A
novel data-driven algorithm is proposed that exploits the dual representation
of capacity where the maximization over the input distribution is replaced with
a minimization over a reference distribution on the channel output. To
efficiently compute the required divergence maximization between the
conditional channel and the reference distribution, we use a modified mutual
information neural estimator that takes the channel input as an additional
parameter. We numerically evaluate our approach on different memoryless
channels and show empirically that the estimated upper bounds closely converge
either to the channel capacity or to best-known lower bounds.

提出一种基于数据驱动的算法，利用最小化通道输出上的参考分布来估算未知通道法和连续输出字母表上通道容量上界的估算方法，并使用修改的互信息神经估计器来计算所需的条件通道和参考分布之间的散度最大化，在不同的无记忆通道上进行数字评估，证明了该方法估算的上界要么接近通道容量，要么接近最佳已知下界。

基于数据的容量上限估计

Data-Driven Estimation of Capacity Upper Bounds

Recently, several methods have been proposed for estimating the mutual
information from sample data using deep neural networks and without the knowing
closed form distribution of the data. This class of estimators is referred to
as neural mutual information estimators. Although very promising, such
techniques have yet to be rigorously bench-marked so as to establish their
efficacy, ease of implementation, and stability for capacity estimation which
is joint maximization frame-work. In this paper, we compare the different
techniques proposed in the literature for estimating capacity and provide a
practitioner perspective on their effectiveness. In particular, we study the
performance of mutual information neural estimator (MINE), smoothed mutual
information lower-bound estimator (SMILE), and directed information neural
estimator (DINE) and provide insights on InfoNCE. We evaluated these algorithms
in terms of their ability to learn the input distributions that are capacity
approaching for the AWGN channel, the optical intensity channel, and peak
power-constrained AWGN channel. For both scenarios, we provide insightful
comments on various aspects of the training process, such as stability,
sensitivity to initialization.

本研究对目前文献提出的神经互信息估计器如 MINE、SMILE、DINE 进行了对比评估，以探讨它们在容量估计方面的表现和应用效果。