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1DTIC ADA434253: Coding Theory Information Theory And Radar

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This project provides a theoretical foundation for the development of algorithms to significantly expand radar functionality, given a facility capable of high levels of temporal and spatial diversity of waveforms and polarization, where the mode of operation can be rapidly scheduled. The long term aim is to exploit the diversity and flexibility provided by this advanced functionality through adaptive multidimensional waveform and polarization scheduling based on environment modeling and tracking, as well as multi-dimensional adaptive processing of the returns. In collaboration with Bill Moran (Melbourne) and Stephen Howard (DSTO, Australia) we found that the discrete Heisenberg-Weyl group provides a unifying framework for a number of important sequences significant in the construction of phase coded radar waveforms, in communications as spreading sequences, and in the theory of error correcting codes. Among the sequences which can be associated with the Heisenberg-Weyl group are the Golay or Welti sequences, which are pairs of sequences of unimodular complex numbers such that the sum of their individual auto-correlation functions forms delta spike or thumb tack.

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2DTIC ADA456510: Coding Theory Information Theory And Radar

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The discrete Heisenberg-Weyl group provides a unifying framework for a number of important sequences significant in the construction of phase coded radar waveforms, in communications as spreading sequences, and in the theory of error correcting codes. Among the sequences which can be associated with the Heisenberg-Weyl group are the first and second order Reed-Muller codes, the Golay or Welti sequences, and the Kerdock and Preparata codes , which are non-linear binary error correcting codes containing more codewords for a given minimum distance than any linear code. The Kerdock codes are associated with decomposition of the Heisenberg-Weyl group into disjoint maximally commutative subgroups. It is a surprising fact that a certain general class of Golay sequences exist within the Kerdock codes. This had had previously been noted by Davis and Jedwab. Golay sequences are pairs of sequences of unimodular complex numbers with the property that the sum of their individual auto- correlation functions forms delta spike or thumb tack. These sequences have found application in the construction of radar waveforms and in modulation schemes for communications.

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3ETN 2126 - Information Theory And Error Coding

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Trimester 2 - 2016/2017

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4ERIC ED218084: Aspects Of Coding. Applications Of Linear Algebra To Communication And Information Science. [and] A Double-Error Correcting Code. Applications Of Algebra To Information Theory. Modules And Monographs In Undergraduate Mathematics And Its Applications Project. UMAP Units 336 And 337.

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These two modules cover aspects of the coding process and algebraic coding theory. The first unit defines coding as a branch of information and communication science, which draws extensively upon many diverse mathematical fields, primarily abstract and linear algebra, number theory, probability and statistics, and combinatorial theory. Aspects of the process, including linear codes and error correction, are discussed. The second unit focuses on the construction of a double-error correcting code. Both units contain problems and answers to these exercises. The second unit contains a model exam and concludes with an answer key to this test. (MP)

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“ERIC ED218084: Aspects Of Coding. Applications Of Linear Algebra To Communication And Information Science. [and] A Double-Error Correcting Code. Applications Of Algebra To Information Theory. Modules And Monographs In Undergraduate Mathematics And Its Applications Project. UMAP Units 336 And 337.” Subjects and Themes:

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5DTIC AD0415178: AN INTRODUCTION TO MODULATION, CODING, INFORMATION THEORY, AND DETECTION

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This is an expository essay on information theory for engineers interested in communications, sonar, and radar who have no specialized knowledge of statistical communication theory. The fundamental concepts of information theory, and in particular, quantity of information and channel capacity, are defined and explained in simple terms. These concepts are used to make a quantitative estimate of the performance of several common modulation schemes and to analyze the performance of search and detection systems. The effectiveness of repeated or prolonged observations on detection thresholds and reliability of detection, and the relative performance of coherent and incoherent integration, are explained and illustrated quantitatively.

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6ETM 2126 - Information Theory And Error Control Coding

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Trimester 2 - 2019/2020

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7Bucketing Coding And Information Theory For The Statistical High Dimensional Nearest Neighbor Problem

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Consider the problem of finding high dimensional approximate nearest neighbors, where the data is generated by some known probabilistic model. We will investigate a large natural class of algorithms which we call bucketing codes. We will define bucketing information, prove that it bounds the performance of all bucketing codes, and that the bucketing information bound can be asymptotically attained by randomly constructed bucketing codes. For example suppose we have n Bernoulli(1/2) very long (length d-->infinity) sequences of bits. Let n-2m sequences be completely independent, while the remaining 2m sequences are composed of m independent pairs. The interdependence within each pair is that their bits agree with probability 1/2 0. Moreover if one sequence out of each pair belongs to a a known set of n^{(2p-1)^{2}-\epsilon} sequences, than pairing can be done using order n comparisons!

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8ETM 2126 - Information Theory And Error Control Coding

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9The Mathematics Of Coding Theory : Information, Compression, Error Correction, And Finite Fields

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Trimester 2 - 2016/2017

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10Coding Theory Projection: Entropy And Mutual Information

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Projection from a course on Coding Theory (2005 - 6) by KIT

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11ETN 2126 - Information Theory And Error Coding

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Trimester 2 - 2018/2019

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12Concentration Of Measure Inequalities In Information Theory, Communications And Coding

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This monograph is focused on some of the key modern mathematical tools that are used for the derivation of concentration inequalities, on their links to information theory, and on their various applications to communications and coding. Although it is a survey, it also includes various new recent results derived by the authors. The first part of this article introduces some classical concentration inequalities for martingales, and it also derives some recent refinements of these inequalities. The power and versatility of the martingale approach is exemplified in the context of codes defined on graphs and iterative decoding algorithms, and some other aspects that are related to wireless communications and coding. The second part of this article introduces the entropy method for deriving concentration inequalities for functions of many independent random variables, and it also exhibits its multiple connections to information theory. The basic ingredients of the entropy method are discussed first in conjunction with the closely related topic of logarithmic Sobolev inequalities. This discussion is complemented by a related viewpoint based on probability in metric spaces. This viewpoint centers around the so-called transportation-cost inequalities, whose roots are in information theory. Some representative results on concentration for dependent random variables are briefly summarized, with emphasis on their connections to the entropy method. Finally, the tutorial addresses several applications of the entropy method and related information-theoretic tools to problems in communications and coding. These include strong converses for several source and channel coding problems, empirical distributions of good channel codes with non-vanishing error probability, and an information-theoretic converse for concentration of measure.

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13Information Theory And Coding. --

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This monograph is focused on some of the key modern mathematical tools that are used for the derivation of concentration inequalities, on their links to information theory, and on their various applications to communications and coding. Although it is a survey, it also includes various new recent results derived by the authors. The first part of this article introduces some classical concentration inequalities for martingales, and it also derives some recent refinements of these inequalities. The power and versatility of the martingale approach is exemplified in the context of codes defined on graphs and iterative decoding algorithms, and some other aspects that are related to wireless communications and coding. The second part of this article introduces the entropy method for deriving concentration inequalities for functions of many independent random variables, and it also exhibits its multiple connections to information theory. The basic ingredients of the entropy method are discussed first in conjunction with the closely related topic of logarithmic Sobolev inequalities. This discussion is complemented by a related viewpoint based on probability in metric spaces. This viewpoint centers around the so-called transportation-cost inequalities, whose roots are in information theory. Some representative results on concentration for dependent random variables are briefly summarized, with emphasis on their connections to the entropy method. Finally, the tutorial addresses several applications of the entropy method and related information-theoretic tools to problems in communications and coding. These include strong converses for several source and channel coding problems, empirical distributions of good channel codes with non-vanishing error probability, and an information-theoretic converse for concentration of measure.

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14Polynomial Method In Coding And Information Theory

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Polynomial, or Delsarte's, method in coding theory accounts for a variety of structural results on, and bounds on the size of, extremal configurations (codes and designs) in various metric spaces. In recent works of the authors the applicability of the method was extended to cover a wider range of problems in coding and information theory. In this paper we present a general framework for the method which includes previous results as particular cases. We explain how this generalization leads to new asymptotic bounds on the performance of codes in binary-input memoryless channels and the Gaussian channel, which improve the results of Shannon et al. of 1959-67, and to a number of other results in combinatorial coding theory.

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15Coding Theory Projection: Entropy And Mutual Information

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Projection from a course on Coding Theory (2005 - 6) by KIT

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16Coding Theory Lecture: Entropy And Mutual Information

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Lecture from a course on Coding Theory (2005 - 6) by KIT

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17Information Theory And Coding

Lecture from a course on Coding Theory (2005 - 6) by KIT

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18URSI National Committee Report: Commission 6. Radio Waves And Circuits. Part 1. Information Theory And Coding

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Journal of Research of the National Bureau of Standards

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19ETN 2126 - Information Theory And Error Coding

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TRIMESTER 2, 2022/2023

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20The Theory Of Information And Coding : A Mathematical Framework For Communication

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TRIMESTER 2, 2022/2023

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21ETM 2126 - Information Theory And Error Control Coding

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Tri 2 2022/2023

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22Information And Coding Theory

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23Information And Coding Theory

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24ETN 2126 - Information Theory And Error Coding

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Trimester 2 - 2017/2018

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25ETN 2126 - Information Theory And Error Coding

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Trimester 2 - 2019/2020

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26ETM 2126 - Information Theory And Error Control Coding

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Trimester 2 - 2018/2019

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27ETM 2126 - Information Theory And Error Control Coding

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Trimester 2 - 2019/2020

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28The Theory Of Information And Coding : A Mathematical Framework For Communication

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Trimester 2 - 2019/2020

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29The Theory Of Information And Coding

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Trimester 2 - 2019/2020

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30Coding Theory Lecture: Entropy And Mutual Information

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Lecture from a course on Coding Theory (2005 - 6) by KIT

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31Coding And Information Theory

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Lecture from a course on Coding Theory (2005 - 6) by KIT

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32Fundamentals Of Information Theory And Coding Design

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Lecture from a course on Coding Theory (2005 - 6) by KIT

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33Foundations Of Coding : Theory And Applications Of Error-correcting Codes, With An Introduction To Cryptography And Information Theory

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Lecture from a course on Coding Theory (2005 - 6) by KIT

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1Information and coding theory

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“Information and coding theory” Metadata:

  • Title: Information and coding theory
  • Author:
  • Language: English
  • Number of Pages: Median: 229
  • Publisher: Intext Educational Publishers
  • Publish Date:
  • Publish Location: Scranton

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Access and General Info:

  • First Year Published: 1971
  • Is Full Text Available: Yes
  • Is The Book Public: No
  • Access Status: Borrowable

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