# A Commonsense Approach to the Theory of Error-Correcting Codes

## Praise

### Summary

Teaching the theory of error correcting codes on an introductory level is a difficult task. The theory, which has immediate hardware applications, also concerns highly abstract mathematical concepts. This text explains the basic circuits in a refreshingly practical way that will appeal to undergraduate electrical engineering students as well as to engineers and technicians working in industry. Arazi's truly commonsense approach provides a solid grounding in the subject, explaining principles intuitively from a hardware perspective. He fully covers error correction techniques, from basic parity check and single error correction cyclic codes to burst error correcting codes and convolutional codes. All this he presents before introducing Galois field theory - the basic algebraic treatment and theoretical basis of the subject, which usually appears in the opening chapters of standard textbooks. One entire chapter is devoted to specific practical issues, such as Reed-Solomon codes (used in compact disc equipment), and maximum length sequences (used in various fields of communications). The basic circuits explained throughout the book are redrawn and analyzed from a theoretical point of view for readers who are interested in tackling the mathematics at a more advanced level.

#### Hardcover

\$42.00 X ISBN: 9780262010986 220 pp. | 7.2 in x 9.2 in

### Endorsements

• Arazi gives a good introduction to logic and shift-register circuitry and its relation to modular algebra. He introduces some of the more advanced algebraic ideas which were first applied to error correcting codes and are now seeing application in other fields like cryptography. He deals with burst-correcting and convolutional codes as well as with Hamming codes and does his examples in detail, in engineering-school problem-solving style. Should be accessible to Sophomoe Electrical Engineering or Computer Science students.

Peter Elias

Edwin S. Webster Professor of Electrical Engineering

• An exceptionally clear exposition of basic topics in error correcting codes. The author has linked the physical properties of linear feedback shift registers with the mathematical properties of modular arithmetic in a natural and compelling way. After going through the basic topics by presenting them as properties of encoding and decoding circuits, the author supplies a series of appendixes that review the material in light of algebraic coding theory.

Peter Denning

Director of the Research Institute for Advanced Computer Science, RIACS