By R. Micheloni, A. Marelli, R. Ravasio
These days it really is challenging to discover an digital gadget which doesn't use codes: for instance, we hearken to track through seriously encoded audio CD's and we watch video clips through encoded DVD's. there's at the very least one region the place using encoding/decoding isn't so built, but: Flash non-volatile thoughts. Flash reminiscence high-density, low strength, expense effectiveness, and scalable layout make it an awesome option to gas the explosion of multimedia items, like USB keys, MP3 gamers, electronic cameras and solid-state disk. In ECC for Non-Volatile Memories the authors divulge the fundamentals of coding concept had to comprehend the applying to stories, in addition to the proper layout subject matters, near to either NOR and NAND Flash architectures. a suite of software program workouts can also be incorporated for higher knowing. The authors shape a examine staff (now at Qimonda) that is the common instance of a fruitful collaboration among mathematicians and engineers.
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Extra info for Error Correction Codes for Non-Volatile Memories
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Every code polynomial c(x) in C can be expressed uniquely as c(x)=m(x)g(x), where g(x) is the generator polynomial of C and m(x) is a polynomial of degree less than n-r in GF(q)[x]. 3. The generator polynomial g(x) of C is a factor of xn–1 in GF(q)[x]. Accordingly, the search of all the divisors of xn–1 allows us to find all the cyclic codes of length n. 4 If the degree of g(x) is n–k, then the code C carries k information bits. 5 If g(x) is a polynomial of degree n–k and it is a factor of xn–1, then g(x) generates a cyclic code [n,k].
The last step of the decoding process consists in searching for the roots of the error locator polynomial. If the roots are separate and they are in the field, then it is enough to calculate their inverse to have the error positions. If they are not separate or they are not in the correct field, it means that the word received has a distance from a codeword greater than t. In this case an incorrigible error pattern occurred and the decoding process fails. The general implementation for a BCH code will be presented in Chap.
Jones, J. M. Jones, “Informations and Coding Theory”, Springer, 2000. A. S. A. G. Khaled, R. J. McEliece, A. M. Odlyzka, H. C. A. von Tilborg, “On the Existence of Optimum Cyclic Burst-Correcting Codes” in IEEE Transactions on Information Theory, Vol. 32, November 1986. S. Lin, D. J. Costello, “Error Control Coding: Fundamentals and Applications”, F. F. Kuo Editor, 1983. F. J. Macwilliams, N. J. A. Sloane, “The Theory of Error-Correcting Codes”, NorthHolland Publishing Company, 1978. H. B. , 1968.