Error Coding for Arithmetic Processors - 1st Edition - ISBN: 9780125807500, 9780323162289

Error Coding for Arithmetic Processors

1st Edition

Authors: T.R.N. Rao
eBook ISBN: 9780323162289
Imprint: Academic Press
Published Date: 28th January 1974
Page Count: 232
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Description

Error Coding for Arithmetic Processors provides an understanding of arithmetically invariant codes as a primary technique of fault-tolerant computing by discussing the progress in arithmetic coding theory. The book provides an introduction to arithmetic error code, single-error detection, and long-distance codes. It also discusses algebraic structures, linear congruences, and residues. Organized into eight chapters, this volume begins with an overview of the mathematical background in number theory, algebra, and error control techniques. It then explains the basic mathematical models on a register and its number representation system. The reader is also introduced to arithmetic processors, as well as to error control techniques. The text also explores the functional units of a digital computer, including control unit, arithmetic processor, memory unit, program unit, and input/output unit. Students in advanced undergraduate or graduate level courses, researchers, and readers who are interested in applicable knowledge on arithmetic codes will find this book extremely useful.

Table of Contents


Foreword

Preface

Chapter 1 Introduction and Background

1.1 Algebraic Structures

1.2 Theory of Divisibility and Congruences

1.3 Registers and Number Representation Systems

Problems

References

Chapter 2 Arithmetic Processors and Error Control Preliminaries

2.1 Arithmetic Processors and Digital Computers

2.2 Nature and Origin of Errors in AP's

2.3 Error Control Techniques

Problems

References

Chapter 3 Arithmetic Codes, Their Classes and Fundamentals

3.1 Code Classes

3.2 AN Codes and Single-Error Detection

3.3 Checking an Adder by Separate Codes

3.4 Checking Other Elementary Operations

3.5 Residue Generators

Problems

References

Chapter 4 Single-Error Correction

4.1 AN Codes and Preliminaries

4.2 Higher Radix AN Codes

4.3 Cyclic AN Codes

4.4 More on M(A, 3)

Problems

References

Chapter 5 Error Correction Using Separate Codes

5.1 Biresidue Code

5.2 Error Correction Using Biresidue Codes

5.3 Construction of Separate Codes from Nonseparate Codes

Problems

References

Chapter 6 Large-Distance Codes

6.1 Algorithms

6.2 Barrows-Mandelbaum (BM) Codes

6.3 Chien-Hong-Preparata (CHP) Codes

6.4 AN Codes for Composite A = II(2ml - 1)

References

Chapter 7 Other Arithmetic Codes of Interest

7.1 Systematic Nonseparate Codes

7.2 Burst-Error-Correcting Codes

7.3 Iterative Errors

References

Chapter 8 Recent Results on Arithmetic Codes and Their Applications

8.1 Polynomial Cyclic Codes and Cyclic AN Codes

8.2 BCH Codes and BCH Bound

8.3 On Bounds for dmin of Cyclic AN Codes

8.4 Majority Decodable Arithmetic Codes

8.5 Self-Checking Processors

References

Index


Details

No. of pages:
232
Language:
English
Copyright:
© Academic Press 1974
Published:
Imprint:
Academic Press
eBook ISBN:
9780323162289

About the Author

T.R.N. Rao