Statistical characterization of the chordal product determinant of Grassmannian codes

TL;DR

This paper statistically analyzes the chordal product determinant in Grassmannian codes, providing bounds for optimal subspace collections with maximal pairwise distances, relevant for information theory applications.

Contribution

It offers a novel statistical characterization of the chordal product determinant, leading to bounds on minimal chordal product and energy in Grassmannian code collections.

Findings

Derived bounds for minimal chordal product

Provided statistical insights into Grassmannian code distances

Enhanced understanding of subspace collection optimization

Abstract

We consider the chordal product determinant, a measure of the distance between two subspaces of the same dimension. In information theory, collections of elements in the complex Grassmannian are searched with the property that their pairwise chordal products are as large as possible. We characterize this function from an statistical perspective, which allows us to obtain bounds for the minimal chordal product and related energy of such collections.