Asymptotically Optimal and Near-optimal Aperiodic Quasi-Complementary Sequence Sets Based on Florentine Rectangles

TL;DR

This paper introduces a systematic method to construct Florentine rectangles and uses them to generate quasi-complementary sequence sets (QCSS) that are asymptotically optimal or near-optimal, supporting more users in multicarrier systems.

Contribution

It proposes a novel systematic construction of Florentine rectangles and uses them to create new asymptotically optimal and near-optimal QCSS over any integer N.

Findings

Constructed CCCs and QCSS over Z_N with bounded cross-correlation

Achieved asymptotically optimal QCSS for any integer N

Solved a long-standing problem in QCSS design

Abstract

Quasi-complementary sequence sets (QCSSs) can be seen as a generalized version of complete complementary codes (CCCs), which enables multicarrier communication systems to support more users. The contribution of this work is two-fold. First, we propose a systematic construction of Florentine rectangles. Secondly, we propose several sets of CCCs and QCSS, using Florentine rectangles. The CCCs and QCSS are constructed over $\mathbb{Z}_N$, where $N\geq2$ is any integer. The cross-correlation magnitude of any two of the constructed CCCs is upper bounded by $N$. By combining the proposed CCCs, we propose asymptotically optimal and near-optimal QCSSs with new parameters. This solves a long-standing problem, of designing asymptotically optimal aperiodic QCSS over $\mathbb{Z}_N$, where $N$ is any integer.