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caused by a long burst), one alternative is to declare an erasure in the whole row, which will be communicated<br />

to the outer code C 1. The other event is a miscorrection, that cannot be detected. In this case,<br />

we expect that the errors will be corrected by the error-erasure decoder of the outer code.<br />

Product codes are important in practical applications. For instance, the code used in the DVD (digital<br />

video disk) is a product code where C 1 is a [208,192,17] RS code and C 2 is a [182,172,11] RS code. Both<br />

RS codes are defined over GF(256), where GF(256) is generated by the primitive polynomial 1 + x 2 + x 3 +<br />

x 4 + x 8 .<br />

References<br />

1. R. E. Blahut, Theory and Practice of Error Control Codes, Addison-Wesley, Reading, MA, 1983.<br />

2. C. Heegard and S. B. Wicker, Turbo Coding, Kluwer Academic Publishers, Dordrecht, the Netherlands,<br />

1999.<br />

3. S. Lin and D. J. Costello, Error Control Coding: Fundamentals and Applications, Prentice-Hall, Englewood<br />

Cliffs, NJ, 1983.<br />

4. F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, North-Holland Publishing<br />

Company, 1978.<br />

5. R. J. McEliece, The Theory of Information and Coding, Addison-Wesley, Reading, MA, 1977.<br />

6. C. E. Shannon, “A mathematical theory of communication,” Bell Syst. Tech. Journal, vol. 27, pp. 379–423<br />

and 623–656, 1948.<br />

7. W. Wesley Peterson and E. J. Weldon, Error-Correcting Codes, MIT Press, Cambridge, MA, second<br />

edition, 1984.<br />

8. S. Wicker, Error Control Systems for Digital Communications and Storage, Prentice-Hall, Englewood<br />

Cliffs, NJ, 1995.<br />

© 2002 by CRC Press LLC

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