Cube-Split: Structured Quantizers on the Grassmannian of Lines

TL;DR

This paper presents a new structured quantization method for Grassmannian sources using bent grids, offering low complexity encoding and decoding suitable for real-time MIMO wireless applications.

Contribution

It introduces a novel geometric codebook construction for Grassmannian quantization with efficient algorithms and competitive distortion performance.

Findings

Achieves distortion comparable to the best structured approaches

Low complexity encoding and decoding algorithms

Suitable for high-resolution, real-time applications like MIMO feedback

Abstract

This paper introduces a new quantization scheme for real and complex Grassmannian sources. The proposed approach relies on a structured codebook based on a geometric construction of a collection of bent grids defined from an initial mesh on the unit-norm sphere. The associated encoding and decoding algorithms have very low complexity (equivalent to a scalar quantizer), while their efficiency (in terms of the achieved distortion) is on par with the best known structured approaches, and compares well with the theoretical bounds. These properties make this codebook suitable for high-resolutions, real-time applications such as channel state feedback in massive multiple-input multiple-output (MIMO) wireless communication systems.