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

2024-05-02

Information Theory Workshop

AI Summary

To address the high peak-to-mean envelope power ratio (PMEPR) in OFDM systems, this paper proposes a systematic construction method for Golay complementary sequence (GCS) sets applicable to arbitrary sequence length $N$ and arbitrary alphabet size $q$. Departing from conventional constructions where $N$ and $q$ are tightly coupled, our approach achieves full decoupling between these two parameters, enabling flexible configuration. We establish an algebraic framework based on extended Boolean functions (EBFs), integrating sequence design with discrete Fourier transform (DFT) analysis to rigorously guarantee complementarity. The resulting GCS families satisfy zero autocorrelation and cross-correlation constraints for all $N$ and $q$, thereby substantially reducing PMEPR in OFDM signals. Moreover, the constructed sequences are inherently compatible with modulation schemes and bandwidth requirements of multi-standard wireless systems—including LTE and 5G—thus bridging a critical theoretical and practical gap in the systematic construction of GCSs under general parameter settings.

Technology Category

• Search and Optimization: Combinatorial Optimization
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Security and Privacy: Large-scale security measurements
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

One of the important applications of Golay complementary sets (GCSs) is the reduction of peak-to-mean en-velope 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.

Problem

• Golay complementary sequences
• OFDM peak-to-average power ratio reduction
• 5G communication systems

Innovation

• Extended Boolean Functions
• Golay Complementary Sequences
• OFDM Signal Peak Reduction