# On the Output Redundancy of LTI Systems: A Geometric Approach with Application to Privacy

arXiv: https://arxiv.org/abs/2409.17705 · HTML: https://mlsanity.com/paper/2409.17705/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Sep 2024.

## Built on by (most cited first, 1 of 1)

- [Communication-Efficient Distributed Learning with Differential Privacy](https://mlsanity.com/paper/2604.02558/) (2026)

## Abstract (arXiv)

This paper examines the properties of output-redundant systems, that is, systems possessing a larger number of outputs than inputs, through the lenses of the geometric approach of Wonham et al. We begin by formulating a simple output allocation synthesis problem, which involves ``concealing" input information from a malicious eavesdropper having access to the system output, while still allowing for a legitimate user to reconstruct it. It is shown that the solvability of this problem requires the availability of a redundant set of outputs. This very problem is instrumental to unveiling the fundamental geometric properties of output-redundant systems, which form the basis for our subsequent constructions and results. As a direct application, we demonstrate how output allocation can be employed to effectively protect the information of input information from certain output eavesdroppers with guaranteed results.