Download Error Correction Codes for Non-Volatile Memories by R. Micheloni, A. Marelli, R. Ravasio PDF

By R. Micheloni, A. Marelli, R. Ravasio

These days it really is demanding to discover an digital equipment which doesn't use codes: for instance, we hearken to tune through seriously encoded audio CD's and we watch videos through encoded DVD's. there's no less than one zone the place using encoding/decoding isn't so constructed, but: Flash non-volatile thoughts. Flash reminiscence high-density, low strength, rate effectiveness, and scalable layout make it a terrific option to gasoline the explosion of multimedia items, like USB keys, MP3 avid gamers, electronic cameras and solid-state disk. In ECC for Non-Volatile Memories the authors reveal the fundamentals of coding idea had to comprehend the appliance to stories, in addition to the appropriate layout subject matters, almost about either NOR and NAND Flash architectures. a suite of software program exercises can also be incorporated for higher figuring out. The authors shape a study workforce (now at Qimonda) that is the common instance of a fruitful collaboration among mathematicians and engineers.

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Extra resources for Error Correction Codes for Non-Volatile Memories

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1 A Boolean function in m variables f(x1, x2,…, xm) is defined as a map from the vector space Vm of binary m-ple (x1, x2,…, xm) toward the set of binary numbers {0, 1}. The Boolean functions are completely described by the truth table containing m+1 rows. The first m rows form a matrix m × 2m which contains all the binary 2m m-ple as columns. The last row represents the binary value assigned to each m-pla by the Boolean function. 1; it is easy to observe that f= v4+v3+v2+v1. 1. 2 A Reed-Muller code R(r,m), of order r with 0 ≤ r ≤ m and with length n=2m, is the set of the images of the Boolean functions with m variables of degree ≤ r.

Rosenthal, “Codes, Systems and Graphical Models”, Springer-Verlag, 2001. Bibliography 33 T. K. , 2005. R. H. , 2002. C. Nill, C. E. W. Sundberg, “List and Soft Symbol Output Viterbi Algorithms: Extensions and Comparisons” in IEEE Transactions on Communications, Vol. 2/3/4, February/ March/April 1995. O. Papini, “Algebre discrete et codes correcteurs”, Springer-Verlag, 1995. W. W. Peterson, E. J. Weldon, “Error-Correcting Codes”, MIT Press, 1998. V. Pless, “Introduction to the Theory of Error-Correcting Codes”, John Wiley and Sons, 1998.

63). S i = E (α i ) = x e1 + x e2 + ... + x ev = X 1i + X 2i + ... 63) l =1 From Eq. 63) we get Eqs. 64) S 2 t −1 = X 12 t −1 + X 22 t −1 + K + X ν2 t −1 Each method for solving these equations is a BCH decoding procedure. The direct method or Peterson method will be now described, since, although not used in applications, it is useful to clarify the theoretical steps of the decoding process. 14 It is defined as error locator polynomial Λ(x) the polynomial whose roots are the inverse of the error positions.

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