Author Description
This book concerns state-of-the-art coding and decoding methods. Research reviewed in the book include Berlekamp's algorithm for factoring polynomials (the first significant improvement on a classical mathematical problem in almost two centuries), and Berlekamp's algorithm for decoding Bose- Chaudhuri-Hocquenghem and Reed-Solomon codes. For the past 15 years, this coding algorithm has been used universally in algebraic decoders that correct multiple errors in communications or computer memory systems. Chapters Basic Binary Codes; Arithmetic Operations Modulo an Irreducible Binary Polynomial; The Number of Irreducible q-ary Polynomials of Given Degree; The Factorization of Polynomials Over Finite Fields; The Enumeration of Information Symbols in BCH Codes; appendices and references.
Menrva's Summary
THE THESIS
This text investigates the mathematical foundations and practical implementation of algebraic coding and decoding methods for error correction in digital systems. Elwyn R. Berlekamp, a prominent researcher in information theory, provides a rigorous examination of polynomial factorization and error-correcting codes. The work establishes the theoretical framework for BCH and Reed-Solomon codes, detailing the algorithms necessary for their application in modern communication and memory systems.
THE SCOPE MAP
What You Will Find
- Mathematical analysis of binary codes and arithmetic operations modulo irreducible polynomials
- Detailed derivation of the Berlekamp algorithm for polynomial factorization
- Systematic enumeration of information symbols within BCH codes
- Technical appendices and comprehensive bibliographic references
Scope Limits
- The text does not cover post-1960s advancements in turbo codes or low-density parity-check codes
- It focuses primarily on algebraic methods rather than probabilistic or soft-decision decoding techniques
THE AUTHORITY PERSPECTIVE
Experts recognize this work as a foundational text in the field of algebraic coding theory, particularly for its seminal contribution to decoding algorithms. Readers frequently note the high level of mathematical density, which requires a strong background in abstract algebra to fully comprehend the proofs and derivations presented.
Page Count:
400
Publication Date:
1968-01-01
Publisher:
McGraw-Hill Book Company
ISBN-10:
0070049033
ISBN-13:
9780070049031
Coding Theory
Mathematics
Systems Science
Computer Science
Information Theory
Community Tags
Similar Books
