# Toward Optimal ANC: Establishing Mutual Information Lower Bound

arXiv: https://arxiv.org/abs/2505.17877 · HTML: https://mlsanity.com/paper/2505.17877/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 45 references that are in the map.
- First posted on arXiv 23 May 2025.

## Builds on (most cited first, 6 of 6)

- [Self-attending RNN for Speech Enhancement to Improve Cross-corpus Generalization](https://mlsanity.com/paper/2105.12831/) (2021)
- [A Hybrid SFANC-FxNLMS Algorithm for Active Noise Control based on Deep Learning](https://mlsanity.com/paper/2208.08082/) (2022)
- [Deep Generative Fixed-filter Active Noise Control](https://mlsanity.com/paper/2303.05788/) (2023)
- [Spatially Selective Active Noise Control Systems](https://mlsanity.com/paper/2208.09997/) (2022)
- [Unsupervised learning based end-to-end delayless generative fixed-filter active noise control](https://mlsanity.com/paper/2402.09460/) (2024)
- [Deep Active Speech Cancellation with Mamba-Masking Network](https://mlsanity.com/paper/2502.01185/) (2025)

## Abstract (arXiv)

Active Noise Cancellation (ANC) algorithms aim to suppress unwanted acoustic disturbances by generating anti-noise signals that destructively interfere with the original noise in real time. Although recent deep learning-based ANC algorithms have set new performance benchmarks, there remains a shortage of theoretical limits to rigorously assess their improvements. To address this, we derive a unified lower bound on cancellation performance composed of two components. The first component is information-theoretic: it links residual error power to the fraction of disturbance entropy captured by the anti-noise signal, thereby quantifying limits imposed by information-processing capacity. The second component is support-based: it measures the irreducible error arising in frequency bands that the cancellation path cannot address, reflecting fundamental physical constraints. By taking the maximum of these two terms, our bound establishes a theoretical ceiling on the Normalized Mean Squared Error (NMSE) attainable by any ANC algorithm. We validate its tightness empirically on the NOISEX dataset under varying reverberation times, demonstrating robustness across diverse acoustic conditions.