Error Control Systems for Digital Communication and Storage

Stephen B. Wicker




For introductory graduate courses in coding for telecommunications engineering, digital communications.

This introductory text on error control coding focuses on key implementation issues and performance analysis with applications valuable to both mathematicians and engineers.


Table of Contents:

 1. Error Control Coding for Digital Communication Systems. 

 2. Galois Fields. 

 3. Polynomials over Galois Fields. 

 4. Linear Block Codes. 

 5. Cyclic Codes. 

 6. Hadamard, Quadratic Residue, and Golay Codes. 

 7. Reed-Muller Codes 

 8. BCH and Reed-Solomon Codes. 

 9. Decoding BCH and Reed-Solomon Codes.

10. The Analysis of the Performance of Block Codes.

11. Convolutional Codes.

12. The Viterbi Decoding Algorithm.

13. The Sequential Decoding Algorithms.

14. Trellis Coded Modulation.

15. Error Control for Channels with Feedback.

16. Applications.


A. Binary Primitive Polynomials.

B. Add-on Tables and Vector Space Representations for GF(8) Through GF(1024).

C. Cyclotronic Cosets Modulo 2m-1.

D. Minimal Polynomials for Elements in GF (2m).

E. Generator Polynomials of Binary BCH Codes of Lengths Through 511.