Retrieving Reed-Solomon coded data under interpolation-based list decoding
نویسندگان
چکیده
A transform that enables generator-matrix-based Reed-Solomon (RS) coded data to be recovered under interpolation-based list decoding is presented. The transform matrix needs to be computed only once and the transformation of an element from the output list to the desired RS coded data block incurs k field multiplications, given a code of dimension k. Index Terms Galois Field Fourier Transform, list decoding, Reed-Solomon codes
منابع مشابه
The Re-Encoding Transformation in Algebraic List-Decoding of Reed-Solomon Codes
The main computational steps in algebraic softdecoding, as well as Sudan-type list-decoding, of Reed-Solomon codes are bivariate polynomial interpolation and factorization. We introduce a computational technique, based upon re-encoding and coordinate transformation, that significantly reduces the complexity of the bivariate interpolation procedure. This re-encoding and coordinate transformation...
متن کاملAlgebraic List Decoding of Reed-Solomon product codes
The product code of two Reed-Solomon codes can be regarded as an evaluation codes of bivariate polynomials, whose degrees in each variable are bounded. We propose to decode these codes with a generalization of the Guruswami-Sudan interpolation-based list decoding algorithm. A relative decoding radius of 1 − 6 √4R is found, where is the rate of the product code. We also discuss a generalization ...
متن کاملEfficient Interpolation and Factorization in Algebraic Soft-Decision Decoding of Reed-Solomon Codes
Algebraic soft-decision decoding of Reed-Solomon codes delivers promising coding gains over conventional hard-decision decoding. The main computational steps in algebraic soft-decoding (as well as Sudan-type list-decoding) are bivariate interpolation and factorization. We discuss a new computational technique, based upon re-encoding and coordinate transformation, that significantly reduces the ...
متن کاملInterpolation in list decoding of Reed-Solomon codes
The problem of efficient implementation of two-dimensional interpolation in the Guruswami-Sudan list decoding algorithm for Reed-Solomon codes is considered. It is shown that it can be implemented by computing the product of the ideals of interpolation polynomials constructed for subsets of interpolation points. A method for fast multiplication of zero-dimensional co-prime ideals product is pro...
متن کاملAn Interpolation Algorithm for List Decoding of Reed-Solomon Codes
The interpolation step of Sudan’s list decoding of Reed-Solomon codes sets forth the problem of finding the minimal polynomial of the ideal of interpolating polynomials with respect to a certain monomial order. An efficient algorithm that solves the problem is presented based on the theory of Gröbner bases of modules. In a special case, this algorithm is shown to be equivalent with the Berlekam...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- CoRR
دوره abs/cs/0612067 شماره
صفحات -
تاریخ انتشار 2006