Systematic Construction of Golay Complementary Sets of Arbitrary Lengths and Alphabet Sizes
Abhishek Roy, Sudhan Majhi, Subhabrata Paul
TL;DR
The paper tackles the problem of constructing Golay complementary sets with arbitrary lengths and alphabet sizes to enhance PMEPR performance in OFDM. It introduces a direct, function-based method using Extended Boolean Functions (EBFs) to generate a family of $q$-ary sequences; by defining a base function $f: \mathbb{Z}_p^m \to \mathbb{Z}_q$ and a parameterized family $a^{\bm{\gamma}}$, it constructs a $(q, p^{k}, L)$-GCS via the set $\{\psi_L(a^{\bm{\gamma}}) : \bm{\gamma} \in \mathbb{Z}_p^{k}\}$. The approach provides independence between the flock size, length, and alphabet size, achieving PMEPR bounds up to $p^{k}$ under certain conditions, and broadens the design space beyond existing GBF-based methods. The results suggest practical benefits for OFDM spreading and interference reduction, with explicit constructions and comparisons to state-of-the-art. Overall, the work offers a flexible, theory-backed pathway to tailor GCSs to diverse system requirements.
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.