Positioning systems using families of binary sequences with low correlation

RESUMEN: El objetivo de este trabajo es el estudio de la aplicación de familias de secuencias binarias de baja correlación para su uso en sistemas de posicionamiento en tiempo real en interiores como por ejemplo en entornos industriales o de almacenamiento. Actualmente es un problemas abierto para el que se han propuesto distintas tecnologías como sistemas basados en visión artificial o en redes de sensores entre otros. En este proyecto se ha implementado un sistema de posicionamiento en interiores de bajos recursos por medio de secuencias binarias de baja correlación. La investigación se ha centrado en la revisión de las tecnologías existentes en el mercado, la búsqueda de las secuencias binarias más apropiadas y el estudio de sus propiedades. Siguiendo el modelo GPS como sistema de localización en exteriores, se ha construido un propotipo basado en placas Arduino. Nuestra propuesta codifica la información mediante secuencias Pseudo Noise, códigos Gold y Kasami. Posteriormente estas secuencias son transmitidas utilizando señales de ultrasonido. En el receptor, las señales recibidas se pueden procesar para obtener medidas como la distancia entre dispositivos y el ángulo de llegada entre otras.ABSTRACT: The aim of this project is the study of families of binary sequences of low correlation and its application to real-time indoor positioning systems in industrial or warehousing environments. Many different approaches based on different technologies such as artificial vision or sensor networks have been proposed for indoor localization but it still remains an open problem. In this work, we have implemented a low resources indoor positioning system over over a embedded system, that uses binary sequences of low correlation. The research has focused on existent technologies in the market, on the search of the most appropriate family of sequences and the study of their properties. Taking GPS as a reference model for outdoor localization, we have built a prototype based on Arduino boards. Our approach encodes messages with Pseudo Noise sequences, Gold and Kasami Codes. Afterwards, the sequences are transmitted as ultrasonic signals. Then, the receiver processes the incoming signal to obtain measures such as the distances between devices and the angle of arrival of the signal.Máster en Matemáticas y Computació

All-optical periodic code matching by a single-shot frequency-domain cross-correlation measurement

Optical single-short measurement of the cross-correlation function between periodic sequences is demonstrated. The sequences are encoded into the broadband ultrashort phase-shaped pulses which are mixed in the nonlinear medium with additional amplitude-shaped narrowband pulse. The spectrum of the resulted four wave mixing signal is measured to provide the cross-correlation function. The high contrast between the values of cross-correlation and auto-correlation (the latter includes also the information of the sequence period) has potential to be employed in the optical implementation of CDMA communication protocol

A linear construction for certain Kerdock and Preparata codes

The Nordstrom-Robinson, Kerdock, and (slightly modified) Pre\- parata codes are shown to be linear over \ZZ_4, the integers $\bmod~4$. The Kerdock and Preparata codes are duals over \ZZ_4, and the Nordstrom-Robinson code is self-dual. All these codes are just extended cyclic codes over \ZZ_4. This provides a simple definition for these codes and explains why their Hamming weight distributions are dual to each other. First- and second-order Reed-Muller codes are also linear codes over \ZZ_4, but Hamming codes in general are not, nor is the Golay code.Comment: 5 page

Effective Construction of a Class of Bent Quadratic Boolean Functions

In this paper, we consider the characterization of the bentness of quadratic Boolean functions of the form $f(x)=\sum_{i=1}^{\frac{m}{2}-1} Tr^n_1(c_ix^{1+2^{ei}})+ Tr_1^{n/2}(c_{m/2}x^{1+2^{n/2}}) ,$ where $n=me$, $m$ is even and $c_i\in GF(2^e)$. For a general $m$, it is difficult to determine the bentness of these functions. We present the bentness of quadratic Boolean function for two cases: $m=2^vp^r$ and $m=2^vpq$, where $p$ and $q$ are two distinct primes. Further, we give the enumeration of quadratic bent functions for the case $m=2^vpq$