A Systematic Framework for the Construction of Optimal Complete Complementary Codes

TL;DR

This paper introduces a systematic framework for constructing optimal complete complementary codes (CCCs) using N-shift cross-orthogonal sequence families, providing theoretical bounds and algorithms for their generation with flexible sequence lengths.

Contribution

It presents a novel, systematic method for constructing optimal CCCs based on N-CO-SFs, achieving theoretical bounds and allowing variable sequence lengths.

Findings

Algorithms achieve optimal sequence family sizes.

Constructed CCCs have flexible, almost arbitrary lengths.

Theoretical bounds on N-CO-SFs and CCCs are established.

Abstract

The complete complementary code (CCC) is a sequence family with ideal correlation sums which was proposed by Suehiro and Hatori. Numerous literatures show its applications to direct-spread code-division multiple access (DS-CDMA) systems for inter-channel interference (ICI)-free communication with improved spectral efficiency. In this paper, we propose a systematic framework for the construction of CCCs based on $N$-shift cross-orthogonal sequence families ($N$-CO-SFs). We show theoretical bounds on the size of $N$-CO-SFs and CCCs, and give a set of four algorithms for their generation and extension. The algorithms are optimal in the sense that the size of resulted sequence families achieves theoretical bounds and, with the algorithms, we can construct an optimal CCC consisting of sequences whose lengths are not only almost arbitrary but even variable between sequence families. We also discuss the family size, alphabet size, and lengths of constructible CCCs based on the proposed algorithms.