Hamming and Reed-Solomon codes over certain rings

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Revendo os códigos hamming e CRC para tratar com erros na transmissão de dados

This article has the purpose to review the main codes used to detect and correct errors in data communication specifically in the computer's network. The Hamming's code and the Ciclic Redundancy Code (CRC) are presented as the focus of this article as well as CRC hardware implementation. Each code is reviewed in details in order to fill the gaps in the literature and to make it accessible to the computer science and engineering students as well as to anyone who may be interested in learning the technique to treat error in data communication.

A method for improving the code rate and error correction capability of a cyclic code

Currently, there has been an increasing demand for operational and trustworthy digital data transmission and storage systems. This demand has been augmented by the appearance of large-scale, high-speed data networks for the exchange, processing and storage of digital information in the different spheres. In this paper, we explore a way to achieve this goal. For given positive integers n,r, we establish that corresponding to a binary cyclic code C0[n,n-r], there is a binary cyclic code C[(n+1)3k-1,(n+1)3k-1-3kr], where k is a nonnegative integer, which plays a role in enhancing code rate and error correction capability. In the given scheme, the new code C is in fact responsible to carry data transmitted by C0. Consequently, a codeword of the code C0 can be encoded by the generator matrix of C and therefore this arrangement for transferring data offers a safe and swift mode. © 2013 SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional.

A decoding method of an n length binary BCH code through (n + 1)n length binary cyclic code

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A decoding procedure which improves code rate and error corrections

Corresponding to $C_{0}[n,n-r]$, a binary cyclic code generated by a primitive irreducible polynomial $p(X)\in \mathbb{F}_{2}[X]$ of degree $r=2b$, where $b\in \mathbb{Z}^{+}$, we can constitute a binary cyclic code $C[(n+1)^{3^{k}}-1,(n+1)^{3^{k}}-1-3^{k}r]$, which is generated by primitive irreducible generalized polynomial $p(X^{\frac{1}{3^{k}}})\in \mathbb{F}_{2}[X;\frac{1}{3^{k}}\mathbb{Z}_{0}]$ with degree $3^{k}r$, where $k\in \mathbb{Z}^{+}$. This new code $C$ improves the code rate and has error corrections capability higher than $C_{0}$. The purpose of this study is to establish a decoding procedure for $C_{0}$ by using $C$ in such a way that one can obtain an improved code rate and error-correcting capabilities for $C_{0}$.

The STATFLUX code: a statistical method for calculation of flow and set of parameters, based on the Multiple-Compartment Biokinetical Model

The code STATFLUX, implementing a new and simple statistical procedure for the calculation of transfer coefficients in radionuclide transport to animals and plants, is proposed. The method is based on the general multiple-compartment model, which uses a system of linear equations involving geometrical volume considerations. Flow parameters were estimated by employing two different least-squares procedures: Derivative and Gauss-Marquardt methods, with the available experimental data of radionuclide concentrations as the input functions of time. The solution of the inverse problem, which relates a given set of flow parameter with the time evolution of concentration functions, is achieved via a Monte Carlo Simulation procedure.Program summaryTitle of program: STATFLUXCatalogue identifier: ADYS_v1_0Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADYS_v1_0Program obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandLicensing provisions: noneComputer for which the program is designed and others on which it has been tested: Micro-computer with Intel Pentium III, 3.0 GHzInstallation: Laboratory of Linear Accelerator, Department of Experimental Physics, University of São Paulo, BrazilOperating system: Windows 2000 and Windows XPProgramming language used: Fortran-77 as implemented in Microsoft Fortran 4.0. NOTE: Microsoft Fortran includes non-standard features which are used in this program. Standard Fortran compilers such as, g77, f77, ifort and NAG95, are not able to compile the code and therefore it has not been possible for the CPC Program Library to test the program.Memory, required to execute with typical data: 8 Mbytes of RAM memory and 100 MB of Hard disk memoryNo. of bits in a word: 16No. of lines in distributed program, including test data, etc.: 6912No. of bytes in distributed Program, including test data, etc.: 229 541Distribution format: tar.gzNature of the physical problem: the investigation of transport mechanisms for radioactive substances, through environmental pathways, is very important for radiological protection of populations. One such pathway, associated with the food chain, is the grass-animal-man sequence. The distribution of trace elements in humans and laboratory animals has been intensively studied over the past 60 years [R.C. Pendlenton, C.W. Mays, R.D. Lloyd, A.L. Brooks, Differential accumulation of iodine-131 from local fallout in people and milk, Health Phys. 9 (1963) 1253-1262]. In addition, investigations on the incidence of cancer in humans, and a possible causal relationship to radioactive fallout, have been undertaken [E.S. Weiss, M.L. Rallison, W.T. London, W.T. Carlyle Thompson, Thyroid nodularity in southwestern Utah school children exposed to fallout radiation, Amer. J. Public Health 61 (1971) 241-249; M.L. Rallison, B.M. Dobyns, F.R. Keating, J.E. Rall, F.H. Tyler, Thyroid diseases in children, Amer. J. Med. 56 (1974) 457-463; J.L. Lyon, M.R. Klauber, J.W. Gardner, K.S. Udall, Childhood leukemia associated with fallout from nuclear testing, N. Engl. J. Med. 300 (1979) 397-402]. From the pathways of entry of radionuclides in the human (or animal) body, ingestion is the most important because it is closely related to life-long alimentary (or dietary) habits. Those radionuclides which are able to enter the living cells by either metabolic or other processes give rise to localized doses which can be very high. The evaluation of these internally localized doses is of paramount importance for the assessment of radiobiological risks and radiological protection. The time behavior of trace concentration in organs is the principal input for prediction of internal doses after acute or chronic exposure. The General Multiple-Compartment Model (GMCM) is the powerful and more accepted method for biokinetical studies, which allows the calculation of concentration of trace elements in organs as a function of time, when the flow parameters of the model are known. However, few biokinetics data exist in the literature, and the determination of flow and transfer parameters by statistical fitting for each system is an open problem.Restriction on the complexity of the problem: This version of the code works with the constant volume approximation, which is valid for many situations where the biological half-live of a trace is lower than the volume rise time. Another restriction is related to the central flux model. The model considered in the code assumes that exist one central compartment (e.g., blood), that connect the flow with all compartments, and the flow between other compartments is not included.Typical running time: Depends on the choice for calculations. Using the Derivative Method the time is very short (a few minutes) for any number of compartments considered. When the Gauss-Marquardt iterative method is used the calculation time can be approximately 5-6 hours when similar to 15 compartments are considered. (C) 2006 Elsevier B.V. All rights reserved.

A simple mechanism to deal with sequential code in dataflow architectures

The aim of this work is to propose a simple and efficient mechanism to deal with the problem of executing sequential code in a pure dataflow machine. Our results is obtained with a simulator of Wolf [4] architecture. The implemented mechanism improved the architecture performance when executing sequential code and we expect that this improvement could be better if we use some heuristics to deal with some special groups of instructions such as branch operations. Further research will show us if this is true.

Spectroscopic characterization of SnO2 gels - Code: CP11

Excitation and dynamic emission spectra of Eu3+ ions were simultaneously used with FTIR and Raman spectroscopy to study the structural evolution during SnO2 sol → gel → xerogel conversion. Results make evident an increase of the surroundings symmetry for the Eu3+ ions dissolved in SnO2 matrix and a decrease of the amount of hydroxo groups (Sn-OH) during drying. These phenomena were associated to the pursuit of the condensation reaction after gelation. © 1994 Kluwer Academic Publishers.

Pore size distribution of unsupported SnO2 membranes prepared by sol-gel process - Code: EP21

Unsupported SnO2 membranes were prepared by sol-gel process and characterized by N2 adsorption-desorption isotherms and X-ray diffraction. Results show that the texture of dried samples does not change appreciably with the concentration of electrolyte. All of the pore size range used in ultrafiltration process was screened using sintering temperature between 300 and 700°C. © 1994 Kluwer Academic Publishers.

Lattice constellations and codes from quadratic number fields

We propose new classes of linear codes over integer rings of quadratic extensions of Q, the field of rational numbers. The codes are considered with respect to a Mannheim metric, which is a Manhattan metric modulo a two-dimensional (2-D) grid. In particular, codes over Gaussian integers and Eisenstein-Jacobi integers are extensively studied. Decoding algorithms are proposed for these codes when up to two coordinates of a transmitted code vector are affected by errors of arbitrary Mannheim weight. Moreover, we show that the proposed codes are maximum-distance separable (MDS), with respect to the Hamming distance. The practical interest in such Mannheim-metric codes is their use in coded modulation schemes based on quadrature amplitude modulation (QAM)-type constellations, for which neither the Hamming nor the Lee metric is appropriate.

ENCORE: Enhanced code Galileo receiver for land management applications in Brazil

Taking benefit of the new Galileo ranging signals, the ENCORE (Enhanced Code Galileo Receiver) project aims to develop a low-cost Land Management Application to cover needs of the Brazilian market in terms of geo-referencing and rural/urban cadastre, using a low-cost Enhanced Galileo Code Receiver as baseline. Land management applications require precision and accuracy levels from a few to several decimetres that are under-met with current pseudorange-based receiver and over-met with phase observations. This situation leads either to a waste of resources, or to lack of accuracy. In this project, it is proposed to fill this gap using the new possibilities of the Galileo ranging signals, in particular E5 AltBOC and E1 CBOC. This approach reduces the cost of the end-user solution, helping the rapid penetration of Galileo technology outside Europe. ©2010 IEEE.

Automatic code generation for microcontrollers from place-transition Petri net models

This paper describes a program for the automatic generation of code for Intel's 8051 microcontroller. The code is generated from a place-transition Petri net specification. Our goal is to minimize programming time. The code generated by our program has been observed to exactly match the net model. It has also been observed that no change is needed to be made to the generated code for its compilation to the target architecture. © 2011 IFAC.

ENCORE: Enhanced Galileo code receiver for surveying applications

In this paper we describe the development of a low-cost high-accuracy Galileo Code receiver, user application software and positioning algorithms for land management applications, which have been implemented using a dedicated FPGA board and dual frequency Galileo E5/L1 Radio Frequency Front-End. The current situation of rural property surveying in Brazil is described and the use of code measurements from the new Galileo signals E5 AltBOC combined with E1 MBOC for use in land management applications is explored. We explain how such approach is expected to allow delivering an absolute positioning solution which could bridge the gap between receivers of high cost/complexity/accuracy based on carrier phase and receivers of lower cost/accuracy based on pseudorange observables. The system is presented together with a detailed description of main components: the Code Receiver and the Application Software. The work presented is part of an ongoing European-Brazilian consortium effort to explore the use of new Galileo for land management applications in Brazil and sponsored by the GNSS Supervisory Authority (GSA).

Computational tool to support design of DAC Converter model AD7528 with the object code in XML

Based on literature review, electronic systems design employ largely top-down methodology. The top-down methodology is vital for success in the synthesis and implementation of electronic systems. In this context, this paper presents a new computational tool, named BD2XML, to support electronic systems design. From a block diagram system of mixed-signal is generated object code in XML markup language. XML language is interesting because it has great flexibility and readability. The BD2XML was developed with object-oriented paradigm. It was used the AD7528 converter modeled in MATLAB / Simulink as a case study. The MATLAB / Simulink was chosen as a target due to its wide dissemination in academia and industry. From this case study it is possible to demonstrate the functionality of the BD2XML and make it a reflection on the design challenges. Therefore, an automatic tool for electronic systems design reduces the time and costs of the design.

Cold Code: The global initiative to DNA barcode amphibians and nonavian reptiles

DNA barcoding facilitates the identification of species and the estimation of biodiversity by using nucleotide sequences, usually from the mitochondrial genome. Most studies accomplish this task by using the gene encoding cytochrome oxidase subunit I (COI; Entrez COX1). Within this barcoding framework, many taxonomic initiatives exist, such as those specializing in fishes, birds, mammals, and fungi. Other efforts center on regions, such as the Arctic, or on other topics, such as health. DNA barcoding initiatives exist for all groups of vertebrates except for amphibians and nonavian reptiles. We announce the formation of Cold Code, the international initiative to DNA barcode all species of these 'cold-blooded' vertebrates. The project has a Steering Committee, Coordinators, and a home page. To facilitate Cold Code, the Kunming Institute of Zoology, Chinese Academy of Sciences will sequence COI for the first 10 specimens of a species at no cost to the steward of the tissues. © 2012 Blackwell Publishing Ltd.