Low Autocorrelation Binary Sequences Research Articles

Finding low autocorrelation binary sequences with memetic algorithms

This paper deals with the construction of binary sequences with low autocorrelation, a very hard problem with many practical applications. The paper analyzes several metaheuristic approaches to tackle this kind of sequences. More specifically, the paper provides an analysis of different local search strategies, used as stand-alone techniques and embedded within memetic algorithms. One of our proposals, namely a memetic algorithm endowed with a Tabu Search local searcher, performs at the state-of-the-art, as it consistently finds optimal sequences in considerably less time than previous approaches reported in the literature. Moreover, this algorithm is also able to provide new best-known solutions for large instances of the problem. In addition, a variant of this algorithm that explores only a promising subset of the whole search space (known as skew-symmetric sequences) is also analyzed. Experimental results show that this new algorithm provides new best-known solutions for very large instances of the problem.

Exploiting relaxation in local search for LABS

Branch-and-bound uses relaxation to prune search trees but sometimes scales poorly to large problems. Conversely, local search often scales well but may be unable to find optimal solutions. Both phenomena occur in the construction of low-autocorrelation binary sequences (LABS), a problem arising in communication engineering. This paper proposes a hybrid approach to optimization: using relaxation to prune local search spaces. An implementation gives very competitive results, showing the feasibility of the approach.

Selective nonlinear optical excitation with pulses shaped by pseudorandom Galois fields

We demonstrate high-resolution high-contrast nonlinear optical spectroscopy based on phase-modulated ultrashort pulses. The problem of causing selective nonlinear optical excitation at one frequency while minimizing background is framed in terms of low autocorrelation binary sequences. We investigate phase functions with up to 608-bit resolution for their ability to induce two-photon excitation or stimulated Raman scattering, and find the highest theoretical and experimental signal-to-noise ratios yet reported. We confirm our findings by measuring experimental two-photon excitation spectra.

Exhaustive search for low-autocorrelation binary sequences

Binary sequences with low autocorrelations are important in communication engineering and in statistical mechanics as groundstates of the Bernasconi-model. Computer searches are the main tool to construct such sequences. Due to the exponential size $O(2^N)$ of the configuration space, exhaustive searches are limited to short sequences. We discuss an exhaustive search algorithm with run time characteristic $O(1.85^N)$ and apply it to compile a table of exact groundstates of the Bernasconi-model up to $N=48$. The data suggests $F>9$ for the optimal merit factor in the limit $N\to\infty$.

Optimization on rugged landscapes: A new general purpose Monte Carlo approach.

A new strategy for finding optimal solutions to complex problems with many competing requirements is proposed. It consists in an alternating optimization of the energy, cost, or fitness function of the system itself, and of subsystems of all sizes with an appropriate weight function. For various spin glasses (the $N\ensuremath{-}k$ model, the low autocorrelation binary sequence model, and the Coulomb glass), and for traveling salesman problems, the corresponding Monte Carlo algorithm is shown to yield results superior to those obtained by previous optimization techniques.

Dynamical behaviour of low autocorrelation models

We have investigated the nature of the dynamical behaviour in low autocorrelation binary sequences. These models do have a glass transition TG of a purely dynamical nature. Above the glass transition the dynamics are not fully ergodic and relaxation times diverge like a power law tau approximately (T-TG)- gamma with gamma close to 2. Approaching the glass transition the relaxation slows down, in agreement with the first-order nature of the dynamical transition. Below the glass transition the system exhibits aging phenomena, as in disordered spin glasses. We propose the aging phenomena as a precise method to determine the glass transition and its first-order nature.

Low autocorrelation binary sequences: exact enumeration and optimization by evolutionary strategies

We investigate skew-symmetric sequences with chain lengths up to N = 71, giving a complete table of all merit factors F≥7 and their associated configurations. We also calculate the exact thermodynami-cal properties of shorter chains (N≤55). We then introduce an evolutionary strategy, describing the properties of our search algorithm and comparing our results to those of other heuristic methods such as simulated annealing. We find the highest merit factors ever reached for chains of length 81≤N≤201.

Low autocorrelation binary sequences : statistical mechanics and configuration space analysis

Binary sequences with low off-peak autocorrelations play an important role in several communication engineering applications. The problem of finding such sequences is equivalent to the problem of determining the low-energy configurations of a specific spin model with long-range 4-spin interactions. Using a simulated annealing procedure, the statistical mechanics of this spin model, which exhibits frustration without disorder, is analysed in detail. Comparison is made with predictions based on a simple «ergodicity assumption» which moreover may be used to derive an estimate for the true ground-state energy. Our results are consistent with the occurrence of an «ergodicity-breaking» phase transition at a finite temperature. For long sequences, the energy minima found with the simulated annealing p Des suites binaires avec faible autocorrelation jouent un role important dans divers problemes de communication. Le probleme de trouver de telles suites est equivalent au probleme de la determination des configurations de faible energie dans un modele particulier de spin avec interactions a 4 spins de longue portee. Utilisant une methode de recuit simule, nous analysons en detail la mecanique statistique de ce modele de spin, qui presente des frustrations mais pas de desordre. Nous comparons nos resultats avec des predictions basees sur une hypothese simple d'ergodicite qui, de plus, conduit a une estimation de l'energie de l'etat fondamental. Nos resultats suggerent l'apparition d'une transition de phase du type «brisure d'ergodicite», a temperature finie. Pour des suites longues, les minima d'energie trouves par la methode de recuit simule different d'un facteur 2 de l'energie du fondamental conjecture, ce qui indique que les configurations d'energie minimale sont extremement isolees dans l'espace de configuration. Enfin les minima trouves par le recuit simule ne semblent pas presenter de structure ultrametrique non triviale

Sieves for low autocorrelation binary sequences

The value 2e^{2} is calculated by approximations as a conjectured asymptotic limit for the best central to sidelobe energy ratio of very long low autocorrelation binary sequences. The same bound is calculated by approximation for skewsymmetric sequences, hence it is concluded that the requirement of skewsymmetry constitutes a powerful and effective sieve for the search for near-optimal sequences. A second sieve based on the use of complementary sequences is discussed and shown to be quite effective for sequence lengths up to 31, and its investigation for longer lengths by means of computers is suggested. A third and a fourth sieve, based on the selection of restricted classes of complementary sequences, are also discussed.