Decoding Five Times Extended Reed Solomon Codes Using Syndromes
نویسندگان
چکیده
منابع مشابه
List Decoding of Reed-Solomon Codes
This master thesis has been written for the completion of the author’s study of mathematics and deals with recent developments in coding theory. In particular, descriptions are given of recent algorithms for generating a list of all words form a Reed–Solomon code that are close to a received word. These algorithms may be adapted so that they can take into account the reliability information of ...
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We present a randomized algorithm which takes as input n distinct points {(xi, yi)}i=1 from F ×F (where F is a field) and integer parameters t and d and returns a list of all univariate polynomials f over F in the variable x of degree at most d which agree with the given set of points in at least t places (i.e., yi = f(xi) for at least t values of i), provided t = Ω( √ nd). The running time is ...
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1 Foreword This text is divided in two parts. The first one, the prerequisites, introduces all the necessary concepts of coding theory. If the reader is familiar with the basics of information and coding theory, he might skip this part and go directly to the second part, which is the core of this thesis. This second part studies an algorithm which improves the decoding of Reed-Solomon codes. Fo...
متن کاملPower Decoding of Reed-Solomon Codes Revisited
Power decoding was originally developed by Schmidt, Sidorenko and Bossert for low-rate Reed–Solomon codes (RS) [1], and is usually capable of decoding almost as many errors as the Sudan decoder [2] though it is a unique decoder. When an answer is found, this is always the closest codeword, but in some cases the method will fail; in particular, this happens if two codewords are equally close to ...
متن کاملEfficient erasure decoding of Reed-Solomon codes
We present a practical algorithm to decode erasures of Reed-Solomon codes over the q elements binary field in O(q log 2 q) time where the constant implied by the O-notation is very small. Asymptotically fast algorithms based on fast polynomial arithmetic were already known, but even if their complexity is similar, they are mostly impractical. By comparison our algorithm uses only a few Walsh tr...
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ژورنال
عنوان ژورنال: Computing and Informatics
سال: 2020
ISSN: 2585-8807
DOI: 10.31577/cai_2020_6_1311