A Generalised Construction of Multiple Complete Complementary Codes and Asymptotically Optimal Aperiodic Quasi-Complementary Sequence Sets

TL;DR

This paper introduces a novel construction method for multiple complete complementary codes over certain integer sets, enabling the creation of asymptotically optimal quasi-complementary sequence sets with flexible parameters for multi-carrier communication systems.

Contribution

It presents a general construction for multiple complete complementary codes over $\\mathbb{Z}_N$, expanding the design space for sequence sets with optimal correlation properties.

Findings

Maximum inter-set aperiodic cross-correlation magnitude is bounded by N.

Constructed sequence sets are asymptotically optimal for odd N.

Flexible parameters allow for diverse sequence set designs.

Abstract

In recent years, complementary sequence sets have found many important applications in multi-carrier code-division multiple-access (MC-CDMA) systems for their good correlation properties. In this paper, we propose a construction, which can generate multiple sets of complete complementary codes (CCCs) over $\mathbb{Z}_N$, where $N~(N\geq 3)$ is a positive integer of the form $N=p_0^{e^0}p_1^{e^1}\dots p_{n-1}^{e^{n-1}}$, $p_0<p_1<\cdots<p_{n-1}$ are prime factors of $N$ and $e_0,e_1,\cdots,e_{n-1}$ are non-negative integers. Interestingly, the maximum inter-set aperiodic cross-correlation magnitude of the proposed CCCs is upper bounded by $N$. When $N$ is odd, the combination of the proposed CCCs results to a new set of sequences to obtain asymptotically optimal and near-optimal aperiodic quasi-complementary sequence sets (QCSSs) with more flexible parameters.