Title: Mutual Information Estimation via Score-to-Fisher Bridge for Nonlinear Gaussian Noise Channels Show Chinese title

Title: 通过分数到费舍尔桥的互信息估计用于非线性高斯噪声信道

Abstract: We present a numerical method to evaluate mutual information (MI) in nonlinear Gaussian noise channels by using denoising score matching (DSM) learning for estimating the score function of channel output. Via de Bruijn's identity, Fisher information estimated from the learned score function yields accurate estimates of MI through a Fisher integral representation for a variety of priors and channel nonlinearities. In this work, we propose a comprehensive theoretical foundation for the Score-to-Fisher bridge methodology, along with practical guidelines for its implementation. We also conduct extensive validation experiments, comparing our approach with closed-form solutions and a kernel density estimation baseline. The results of our numerical experiments demonstrate that the proposed method is both practical and efficient for MI estimation in nonlinear Gaussian noise channels. Show Chinese abstract

Abstract: 我们提出了一种数值方法，通过使用去噪得分匹配（DSM）学习来估计信道输出的得分函数，从而评估非线性高斯噪声信道中的互信息（MI）。 通过 de Bruijn 的恒等式，从学习得到的得分函数中估计的费舍尔信息可通过费舍尔积分表示法对多种先验和信道非线性情况提供准确的 MI 估计。 在本工作中，我们提出了 Score-to-Fisher 桥接方法的全面理论基础，并提供了其实施的实用指南。 我们还进行了广泛的验证实验，将我们的方法与闭式解和核密度估计基线进行比较。 我们数值实验的结果表明，所提出的方法在非线性高斯噪声信道中的 MI 估计中既实用又高效。