1 A. Hocquenghem, Codes correcteurs d'erreurs, ChifFres, Vol. 2, pp. 147-156, 1959. 2 R.C. Bose and D.K. Ray-Chaudhuri, On a class of error-correcting binary group codes, Information and Control, Vol. 3, pp. 68-79, 1960. 3 I.S. Reed and G. Solomon, Polynomial codes over certain finite fields, J. Soc. Indust. Applied Math. Vol. 8, pp. 300–304, 1960. 4 D.C. Gorenstein and N. Zierler, A class of error-correcting codes in pm symbols, J. Soc. Indust. Applied Math. Vol. 9, pp. 207-214, 1961. 5 R.E. Blahut, Theory and Practice of Error Control Codes, Addison Wesley, 1983. 6 G.C. Clark and J.B. Cain, Error-Correction Coding for Digital Communications, Plenum Press, 1981. 7 A.M. Michelson and A.H. Levesque, Error-Control Techniques for Digital Communication, John Wiley & Sons, 1985. 8 S.B. Wicker, Error Control Systems for Digital Communication and Storage, Prentice Hall, 1994. 9 M. Bossert, Channel Coding for Telecommunications, John Wiley and Sons, 1999. 10 Y. Xu, Implementation of Berlekamp-Massey Algorithm without inversion, IEE Proceedings-I, Vol. 138, No. 3, pp. 138-140, June 1991. 11 H-C. Chang and C-S.B. Shung, Method and apparatus for solving key equation polynomials in decoding error correction codes, US Patent US6119262, September 2000.
1 R.E. Blahut, Theory and Practice of Error Control Codes, Addison Wesley, 1983. 2 S. Lin and D.J. Costello, Error Control Coding: fundamentals and applications, Prentice Hall, 1983. 3 S.T.J. Fenn, M. Benaissa and D. Taylor, GF(2m) multiplication and division over the dual basis, IEEE Trans. Computers. Vol. 45, No. 3, pp. 319-327, 1996. 4 S.T.J. Fenn, M. Benaissa and D. Taylor, Finite field inversion over the dual basis, IEEE Trans. VLSI Systems, Vol. 4, pp. 134–137, 1996. 5 S.T.J. Fenn, M. Benaissa and D. Taylor, Fast normal basis inversion in GF(2m), IEE Electronic Letters, Vol. 32 No. 17, pp. 1566–1567, 1996. 6 B. Sunar and C.K. Kog, An Efficient Optimal Normal Basis Type II Multiplier, IEEE Transactions on Computers, Vol. 50, No. 1, pp. 83–87, January 2001.
|Publisher:||Oxford ; New York : Oxford University Press, 2001.|
|Series:||Textbooks in electrical and electronic engineering, 9.|
|Edition/Format:||Print book : EnglishView all editions and formats|
Provides a foundation in the field of error control codes, leading the student step by step through this complex topic, beginning with single parity code checks and repetition codes. Throughout, Read more...
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In this chapter we have been concerned mainly with general concepts and background. There are several good modern books on digital communications that include a treatment of error control codes [2–4]. These can be consulted for more information about digital modulations implementation issues and applications. They can also be used to provide an alternative view of error control coding issues that will be treated later in this book. Another large subject given very brief treatment here is the general topic of information theory, and other sources [5, 6] are recommended for further reading. The next chapter of this book deals with convolutional codes, which are the most commonly adopted codes in digital communications. Chapter 3 will cover linear block codes and a subset of these codes, cyclic codes, will be treated in Chapter 4. The construction of cyclic codes and the decoding methods for multiple-error correction require a knowledge of finite field arithmetic, and this is covered in Chapter 5. Chapter 6 then deals with BCH codes, a large family of binary and nonbinary codes, but concentrating on the binary examples. The most important nonbinary BCH codes are Reed Solomon codes and these are treated in Chapter 7. Chapter 8 then deals with performance issues relevant to all block codes. Multistage coding is introduced in chapter 9. Codes using soft-in-soft-out algorithms for iterative decoding are covered in Chapter 10. It should not be assumed that the length of the treatment of different codes indicates their relative importance. Block codes have a very strong theoretical
The book begins with an introduction to error control codes, explaining the theory and basic concepts underlying the codes. Building on these concepts, the discussion turns to modulation codes, paying special attention to run-length limited sequences, followed by maximum transition run (MTR) and spectrum shaping codes. It examines the relationship between constrained codes and error control and correction systems from both code-design and architectural perspectives as well as techniques based on convolution codes. With a focus on increasing data density, the book also explores multi-track systems, soft decision decoding, and iteratively decodable codes such as Low-Density Parity-Check (LDPC) Codes, Turbo codes, and Turbo Product Codes.