HpGAN: Sequence Search with Generative Adversarial Networks

Sequences play an important role in many engineering applications and systems. Searching sequences with desired properties has long been an interesting but also challenging research topic. This article proposes a novel method, called HpGAN, to search desired sequences algorithmically using generative adversarial networks (GAN). HpGAN is based on the idea of zero-sum game to train a generative model, which can generate sequences with characteristics similar to the training sequences. In HpGAN, we design the Hopfield network as an encoder to avoid the limitations of GAN in generating discrete data. Compared with traditional sequence construction by algebraic tools, HpGAN is particularly suitable for intractable problems with complex objectives which prevent mathematical analysis. We demonstrate the search capabilities of HpGAN in two applications: 1) HpGAN successfully found many different mutually orthogonal complementary code sets (MOCCS) and optimal odd-length Z-complementary pairs (OB-ZCPs) which are not part of the training set. In the literature, both MOCSSs and OB-ZCPs have found wide applications in wireless communications. 2) HpGAN found new sequences which achieve four-times increase of signal-to-interference ratio--benchmarked against the well-known Legendre sequence--of a mismatched filter (MMF) estimator in pulse compression radar systems. These sequences outperform those found by AlphaSeq.Comment: 12 pages, 16 figure

On the ground states of the Bernasconi model

The ground states of the Bernasconi model are binary +1/-1 sequences of length N with low autocorrelations. We introduce the notion of perfect sequences, binary sequences with one-valued off-peak correlations of minimum amount. If they exist, they are ground states. Using results from the mathematical theory of cyclic difference sets, we specify all values of N for which perfect sequences do exist and how to construct them. For other values of N, we investigate almost perfect sequences, i.e. sequences with two-valued off-peak correlations of minimum amount. Numerical and analytical results support the conjecture that almost perfect sequences do exist for all values of N, but that they are not always ground states. We present a construction for low-energy configurations that works if N is the product of two odd primes.Comment: 12 pages, LaTeX2e; extended content, added references; submitted to J.Phys.

TWO GENERALIZATIONS OF SKEW-SYMMETRIC SEQUENCES WITH ODD LENGTHS

The signals, exploited by the radar sensor networks and remote control systems, have to provide simultaneously high range resolution and ability to work stable in a hostile radio electronic environment. An effective approach for satisfying of these requirements is the frequent change of many different signals, which autocorrelation functions have small sidelobes. Accounting this situation in the paper the generalizations of the skew-symmetric sequences with odd lengths, which are phase manipulated signals, possessing high autocorrelation merit factor, are explored. As a result, two methods for synthesis of infinite families of phase manipulated signals with good autocorrelation properties are substantiated

A Stochastic Modeling Approach to Region-and Edge-Based Image Segmentation

The purpose of image segmentation is to isolate objects in a scene from the background. This is a very important step in any computer vision system since various tasks, such as shape analysis and object recognition, require accurate image segmentation. Image segmentation can also produce tremendous data reduction. Edge-based and region-based segmentation have been examined and two new algorithms based on recent results in random field theory have been developed. The edge-based segmentation algorithm uses the pixel gray level intensity information to allocate object boundaries in two stages: edge enhancement, followed by edge linking. Edge enhancement is accomplished by maximum energy filters used in one-dimensional bandlimited signal analysis. The issue of optimum filter spatial support is analyzed for ideal edge models. Edge linking is performed by quantitative sequential search using the Stack algorithm. Two probabilistic search metrics are introduced and their optimality is proven and demonstrated on test as well as real scenes. Compared to other methods, this algorithm is shown to produce more accurate allocation of object boundaries. Region-based segmentation was modeled as a MAP estimation problem in which the actual (unknown) objects were estimated from the observed (known) image by a recursive classification algorithms. The observed image was modeled by an Autoregressive (AR) model whose parameters were estimated locally, and a Gibbs-Markov random field (GMRF) model was used to model the unknown scene. A computational study was conducted on images having various types of texture images. The issues of parameter estimation, neighborhood selection, and model orders were examined. It is concluded that the MAP approach for region segmentation generally works well on images having a large content of microtextures which can be properly modeled by both AR and GMRF models. On these texture images, second order AR and GMRF models were shown to be adequate

Конструиране на булеви функции и цифрови последователности за криптологията и комуникациите

ИМИ-БАН, секция "Математически основи на информатиката", 2023 г., присъждане на образователна и научна степен "доктор" на Мирослав Маринов Димитров в професионално направление информатика и компютърни науки. [Dimitrov Miroslav Marinov; Димитров Мирослав Маринов