Pseudo-Boolean Functions for Optimal Z-Complementary Code Sets with Flexible Lengths

TL;DR

This paper introduces a novel method using pseudo-Boolean functions to construct optimal Z-complementary code sets with flexible, non-power-of-two lengths, enhancing interference-free multicarrier communication systems.

Contribution

It is the first to utilize pseudo-Boolean functions for directly constructing optimal ZCCSs with NPT lengths, surpassing previous sub-optimal methods based on generalized Boolean functions.

Findings

First construction of optimal ZCCSs with NPT lengths using PBFs

Achieves optimal set size with respect to theoretical bounds

Enables interference-free MC-CDMA systems with flexible code lengths

Abstract

This paper aims to construct optimal Z-complementary code set (ZCCS) with non-power-of-two (NPT) lengths to enable interference-free multicarrier code-division multiple access (MC-CDMA) systems. The existing ZCCSs with NPT lengths, which are constructed from generalized Boolean functions (GBFs), are sub-optimal only with respect to the set size upper bound. For the first time in the literature, we advocate the use of pseudo-Boolean functions (PBFs) (each of which transforms a number of binary variables to a real number as a natural generalization of GBF) for direct constructions of optimal ZCCSs with NPT lengths.