Eigensequences for Multiuser Communication over the Real Adder Channel

Shape-invariant signals under the Discrete Fourier Transform are investigated, leading to a class of eigenfunctions for the unitary discrete Fourier operator. Such invariant sequences (eigensequences) are suggested as user signatures over the real adder channel (t-RAC) and a multiuser communication system over the t-RAC is presented.Comment: 6 pages, 1 figure, 1 table. VI International Telecommunications Symposium (ITS2006

Orthogonal Multilevel Spreading Sequence Design

Finite field transforms are offered as a new tool of spreading sequence design. This approach exploits orthogonality properties of synchronous non-binary sequences defined over a complex finite field. It is promising for channels supporting a high signal-to-noise ratio. New digital multiplex schemes based on such sequences have also been introduced, which are multilevel Code Division Multiplex. These schemes termed Galois-field Division Multiplex (GDM) are based on transforms for which there exists fast algorithms. They are also convenient from the hardware viewpoint since they can be implemented by a Digital Signal Processor. A new Efficient-bandwidth code-division-multiple-access (CDMA) is introduced, which is based on multilevel spread spectrum sequences over a Galois field. The primary advantage of such schemes regarding classical multiple access digital schemes is their better spectral efficiency. Galois-Fourier transforms contain some redundancy and only cyclotomic coefficients are needed to be transmitted yielding compact spectrum requirements.Comment: 9 pages, 5 figures. In: Coding, Communication and Broadcasting.1 ed.Hertfordshire: Reseach Studies Press (RSP), 2000. ISBN 0-86380-259-

Introducing an Analysis in Finite Fields

Looking forward to introducing an analysis in Galois Fields, discrete functions are considered (such as transcendental ones) and MacLaurin series are derived by Lagrange's Interpolation. A new derivative over finite fields is defined which is based on the Hasse Derivative and is referred to as negacyclic Hasse derivative. Finite field Taylor series and alpha-adic expansions over GF(p), p prime, are then considered. Applications to exponential and trigonometric functions are presented. Theses tools can be useful in areas such as coding theory and digital signal processing.Comment: 6 pages, 1 figure. Conference: XVII Simposio Brasileiro de Telecomunicacoes, 1999, Vila Velha, ES, Brazil. (pp.472-477

Wavelet Analysis as an Information Processing Technique

A new interpretation for the wavelet analysis is reported, which can is viewed as an information processing technique. It was recently proposed that every basic wavelet could be associated with a proper probability density, allowing defining the entropy of a wavelet. Introducing now the concept of wavelet mutual information between a signal and an analysing wavelet fulfils the foundations of a wavelet information theory (WIT). Both continuous and discrete time signals are considered. Finally, we showed how to compute the information provided by a multiresolution analysis by means of the inhomogeneous wavelet expansion. Highlighting ideas behind the WIT are presented.Comment: 6 pages, 6 tables, VI International Telecommunications Symposium (ITS2006), September 3-6, Fortaleza, Brazi

A Low-throughput Wavelet-based Steganography Audio Scheme

This paper presents the preliminary of a novel scheme of steganography, and introduces the idea of combining two secret keys in the operation. The first secret key encrypts the text using a standard cryptographic scheme (e.g. IDEA, SAFER+, etc.) prior to the wavelet audio decomposition. The way in which the cipher text is embedded in the file requires another key, namely a stego-key, which is associated with features of the audio wavelet analysis.Comment: 2 pages, 1 figure, conference: 8th Brazilian Symposium on Information and Computer System Security, 2008, Gramado, RS, Brazi

Efficient Multiplex for Band-Limited Channels: Galois-Field Division Multiple Access

A new Efficient-bandwidth code-division-multiple-access (CDMA) for band-limited channels is introduced which is based on finite field transforms. A multilevel code division multiplex exploits orthogonality properties of nonbinary sequences defined over a complex finite field. Galois-Fourier transforms contain some redundancy and just cyclotomic coefficients are needed to be transmitted yielding compact spectrum requirements. The primary advantage of such schemes regarding classical multiplex is their better spectral efficiency. This paper estimates the \textit{bandwidth compactness factor} relatively to Time Division Multiple Access TDMA showing that it strongly depends on the alphabet extension. These multiplex schemes termed Galois Division Multiplex (GDM) are based on transforms for which there exists fast algorithms. They are also convenient from the implementation viewpoint since they can be implemented by a Digital Signal Processor.Comment: 6 pages, 5 figures, in: Workshop on Coding and Cryptography, INRIA, 1999, Paris. pp.235-241. arXiv admin note: text overlap with arXiv:1502.0588

A Factorization Scheme for Some Discrete Hartley Transform Matrices

Discrete transforms such as the discrete Fourier transform (DFT) and the discrete Hartley transform (DHT) are important tools in numerical analysis. The successful application of transform techniques relies on the existence of efficient fast transforms. In this paper some fast algorithms are derived. The theoretical lower bound on the multiplicative complexity for the DFT/DHT are achieved. The approach is based on the factorization of DHT matrices. Algorithms for short blocklengths such as $N \in \{3, 5, 6, 12, 24 \}$ are presented.Comment: 10 pages, 4 figures, 2 tables, International Conference on System Engineering, Communications and Information Technologies, 2001, Punta Arenas. ICSECIT 2001 Proceedings. Punta Arenas: Universidad de Magallanes, 200

Multilayer Hadamard Decomposition of Discrete Hartley Transforms

Discrete transforms such as the discrete Fourier transform (DFT) or the discrete Hartley transform (DHT) furnish an indispensable tool in signal processing. The successful application of transform techniques relies on the existence of the so-called fast transforms. In this paper some fast algorithms are derived which meet the lower bound on the multiplicative complexity of the DFT/DHT. The approach is based on a decomposition of the DHT into layers of Walsh-Hadamard transforms. In particular, fast algorithms for short block lengths such as $N \in \{4, 8, 12, 24\}$ are presented.Comment: Fixed several typos. 7 pages, 5 figures, XVIII Simp\'osio Brasileiro de Telecomunica\c{c}\~oes, 2000, Gramado, RS, Brazi

Radix-2 Fast Hartley Transform Revisited

A Fast algorithm for the Discrete Hartley Transform (DHT) is presented, which resembles radix-2 fast Fourier Transform (FFT). Although fast DHTs are already known, this new approach bring some light about the deep relationship between fast DHT algorithms and a multiplication-free fast algorithm for the Hadamard Transform.Comment: 5 pages, 4 figures: Anais do I Congresso de Inform\'atica da Amaz\^onia, 2001. v.1.pp.285-29

Thermal entanglement in an orthogonal dimer-plaquette chain with alternating Ising-Heisenberg coupling

In this paper we explore the entanglement in orthogonal dimer-plaquette Ising-Heisenberg chain, assembled between plaquette edges, also known as orthogonal dimer plaquettes. The quantum entanglement properties involving an infinite chain structure are quite important, not only because the mathematical calculation is cumbersome but also because real materials are well represented by infinite chain. Using the local gauge symmetry of this model, we are able to map onto a simple spin-1 like Ising and spin-1/2 Heisenberg dimer model with single effective ion anisotropy. Thereafter this model can be solved using the decoration transformation and transfer matrix approach. First, we discuss the phase diagram at zero temperature of this model, where we find five ground states, one ferromagnetic, one antiferromagnetic, one triplet-triplet disordered and one triplet-singlet disordered phase, beside a dimer ferromagnetic-antiferromagnetic phase. In addition, we discuss the thermodynamic properties such as entropy, where we display the residual entropy. Furthermore, using the nearest site correlation function it is possible also to analyze the pairwise thermal entanglement for both orthogonal dimers, additionally we discuss the threshold temperature of the entangled region as a function of Hamiltonian parameters. We find quite interesting thin reentrance threshold temperature for one of the dimers, and we also discuss the differences and similarities for both dimers.Comment: 7 pages,8 figure