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Algebraic Methods for Signal Processing and Communications Coding

Algorithms for computation are a central part of both digital signal pro­ cessing and decoders for error-control codes and the central algorithms of the two subjects share many similarities. Each subject makes extensive use of the discrete Fourier transform, of convolutions, and of algorithms for th...

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Bibliographic Details
Main Author: Blahut, Richard E.
Format: eBook
Language:English
Published: New York, NY Springer New York 1992, 1992
Edition:1st ed. 1992
Series:Signal Processing and Digital Filtering
Subjects:
Telecommunication
Communications Engineering, Networks
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • 1 Introduction
  • 1.1 Digital Signal Processing
  • 1.2 Digital Communications
  • 2 Mathematical Fundamentals
  • 2.1 Algebraic Fields
  • 2.2 Elementary Number Theory
  • 2.3 Extension Fields
  • 2.4 Rings and Groups
  • 2.5 Algebraic Integers
  • 3 Sequences and Spectra
  • 3.1 Weight and Complexity
  • 3.2 The Fourier Transform
  • 3.3 Examples of Fourier Transforms
  • 3.4 Properties of the Fourier Transform
  • 3.5 Decimation of Shift Register Sequences
  • 3.6 A Universal Eigenvector
  • 3.7 Bounds on the Weight of Sequences
  • 3.8 The Gleason-Prange Theorem
  • 4 Cyclic Codes and Related Codes
  • 4.1 Theory of Reed-Solomon Codes
  • 4.2 Reed-Solomon Codes in Infinite Fields
  • 4.3 Reed-Solomon Codes in Finite Fields
  • 4.4 Radix-2 Reed-Solomon Codes
  • 4.5 Conjugaey Constraints and BCH Codes
  • 5 Fast Algorithms for Convolution
  • 5.1 Convolution by Blocks
  • 5.2 Fast Algorithms for Cyclic Convolution
  • 5.3 Convolution of Integer Sequences
  • 5.4 Convolutions Using Residue Number Systems
  • 5.5 Convolution of Polynomial Sequences
  • 6 Solving Toeplitz Systems
  • 6.1 The Sugiyama Algorithm
  • 6.2 The Berlekamp-Massey Algorithm
  • 6.3 Relationships Between Algorithms
  • 6.4 The Levinson and Durbin Algorithms
  • 7 Fast Algorithms for the Fourier Transform
  • 7.1 The Cooley-Tukey FFT
  • 7.2 Radix-2 Transforms
  • 7.3 The Good-Thomas FFT
  • 7.4 FFT Algorithms for Subblocks
  • 7.5 FFT Algorithms Using Algebraic Integers
  • 7.6 The Winograd FFT
  • 8 Decoding of Cyclic Codes
  • 8.1 Decoding of Reed-Solomon Codes
  • 8.2 Erasures and Errors Decoding
  • 8.3 Time Domain Decoder Algorithms
  • 8.4 A Universal Decoder Architecture
  • References

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