Dual-Step Optimization for Binary Sequences with High Merit Factors

TL;DR

This paper presents a dual-step GPU-accelerated algorithm that efficiently finds long binary sequences with high merit factors, surpassing traditional methods and discovering new best-known sequences for lengths 450 to 527.

Contribution

Introduces a novel dual-step optimization algorithm combining parallel skew-symmetry generation and priority queue refinement for high merit factor binary sequences.

Findings

Successfully identified new best-known sequences for lengths 450 to 527.

Outperformed traditional exhaustive and stochastic search methods.

Matched previous best for length 518 with a different sequence.

Abstract

The problem of finding aperiodic low auto-correlation binary sequences (LABS) presents a significant computational challenge, particularly as the sequence length increases. Such sequences have important applications in communication engineering, physics, chemistry, and cryptography. This paper introduces a novel dual-step algorithm for long binary sequences with high merit factors. The first step employs a parallel algorithm utilizing skew-symmetry and restriction classes to generate sequence candidates with merit factors above a predefined threshold. The second step uses a priority queue algorithm to refine these candidates further, searching the entire search space unrestrictedly. By combining GPU-based parallel computing and dual-step optimization, our approach has successfully identified new best-known binary sequences for all lengths ranging from 450 to 527, with the exception of length 518, where the previous best-known value was matched with a different sequence. This hybrid method significantly outperforms traditional exhaustive and stochastic search methods, offering an efficient solution for finding long sequences with good merit factors.