Systematic Construction of Golay Complementary Sets of Arbitrary Lengths and Alphabet Sizes

TL;DR

This paper introduces a systematic method to construct Golay complementary sets of any length and alphabet size using extended Boolean functions, enhancing their application in modern wireless communication systems.

Contribution

It presents a novel systematic construction approach for GCSs of arbitrary lengths and alphabet sizes based on extended Boolean functions, allowing independent parameter choices.

Findings

Enables construction of GCSs with arbitrary lengths.

Uses extended Boolean functions for systematic code generation.

Supports diverse parameter configurations for GCSs.

Abstract

One of the important applications of Golay complementary sets (GCSs) is the reduction of peak-to-mean envelope power ratio (PMEPR) in orthogonal frequency division multiplexing (OFDM) systems. OFDM has played a major role in modern wireless systems such as long-term-evolution (LTE), 5th generation (5G) wireless standards, etc. This paper searches for systematic constructions of GCSs of arbitrary lengths and alphabet sizes. The proposed constructions are based on extended Boolean functions (EBFs). For the first time, we can generate codes of independent parameter choices.