Pseudo-Boolean Functions for Optimal Z-Complementary Code Sets With Flexible Lengths
Palash Sarkar, Sudhan Majhi, Zilong Liu
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.
Topics & Concepts
Boolean functionGeneralizationMathematicsCode division multiple accessSet (abstract data type)Boolean expressionBinary numberConstruct (python library)Code (set theory)Discrete mathematicsUpper and lower boundsBoolean circuitDivision (mathematics)AlgorithmComputer scienceTheoretical computer scienceArithmeticTelecommunicationsMathematical analysisProgramming languagePAPR reduction in OFDMAdvanced Wireless Communication TechniquesWireless Communication Networks Research