Reconstruction of Multi-user Binary Subspace Chirps

TL;DR

This paper introduces Binary Subspace Chirps (BSSCs), a new class of codewords in complex Grassmannian spaces, and demonstrates their reliable multi-user reconstruction leveraging binary symplectic geometry and stabilizer states.

Contribution

It presents a unified framework for BSSC reconstruction, including on-off pattern and BC identification, based on symplectic geometry and stabilizer states, enabling multi-user decoding.

Findings

Reliable multi-user reconstruction of BSSCs demonstrated

Low-complexity algorithms for BSSC decoding developed

Framework unifies on-off pattern and BC identification

Abstract

We consider codebooks of Complex Grassmannian Lines consisting of Binary Subspace Chirps (BSSCs) in $N = 2^m$ dimensions. BSSCs are generalizations of Binary Chirps (BCs), their entries are either fourth-roots of unity, or zero. BSSCs consist of a BC in a non-zero subspace, described by an on-off pattern. Exploring the underlying binary symplectic geometry, we provide a unified framework for BSSC reconstruction---both on-off pattern and BC identification are related to stabilizer states of the underlying Heisenberg-Weyl algebra. In a multi-user random access scenario we show feasibility of reliable reconstruction of multiple simultaneously transmitted BSSCs with low complexity.