Algorithms and Architectures for Decoding Reed-Solomon and Hermitian Codes
Title | Algorithms and Architectures for Decoding Reed-Solomon and Hermitian Codes PDF eBook |
Author | Emanuel M. Popovici |
Publisher | |
Pages | 220 |
Release | 2002 |
Genre | Algorithms |
ISBN |
Algorithms and Architectures for Decoding Reed-Solomon Codes
Title | Algorithms and Architectures for Decoding Reed-Solomon Codes PDF eBook |
Author | Padraig O Mahony |
Publisher | |
Pages | 246 |
Release | 1994 |
Genre | |
ISBN |
Algorithms and Architectures for Soft -Decoding Reed -Solomon Codes
Title | Algorithms and Architectures for Soft -Decoding Reed -Solomon Codes PDF eBook |
Author | Arshad Ahmed |
Publisher | |
Pages | |
Release | 2006 |
Genre | |
ISBN |
Algorithms and Architectures for Reed-Solomon Decoding
Title | Algorithms and Architectures for Reed-Solomon Decoding PDF eBook |
Author | |
Publisher | |
Pages | 334 |
Release | 1994 |
Genre | |
ISBN |
Implementation of a Decoding Algorithm for Codes from Algebraic Curves in the Programming Language Sage
Title | Implementation of a Decoding Algorithm for Codes from Algebraic Curves in the Programming Language Sage PDF eBook |
Author | |
Publisher | |
Pages | 50 |
Release | 2013 |
Genre | Dissertations, Academic |
ISBN |
Creating and implementing efficient decoding algorithms is an important study in Coding Theory. This thesis focuses on the decoding algorithms for Reed-Solomon Codes and Hermitian Codes, specifically the Berlekamp-Massey Algorithm and the Berlekamp-Massey- Sakata Algorithm. The Berlekamp-Massey-Sakata Algorithm alone is not enough to decode up to the minimum distance bound so Feng and Rao's technique of Majority Voting is included to allow decoding up to the minimum distance bound and even beyond for some high rate codes. An implementation for each of these decoding algorithms using the programming language Sage was created with the goal that these could be made available to the community of Sage users.
Efficient Algebraic Soft-decision Decoding of Reed-Solomon Codes
Title | Efficient Algebraic Soft-decision Decoding of Reed-Solomon Codes PDF eBook |
Author | Jun Ma |
Publisher | |
Pages | 216 |
Release | 2007 |
Genre | |
ISBN | 9781109966589 |
A divide-and-conquer approach to perform the bivariate polynomial interpolation procedure is discussed in Chapter 3. This method can potentially reduce the interpolation complexity of algebraic soft-decision decoding of Reed-Solomon code.
List Decoding of Error-Correcting Codes
Title | List Decoding of Error-Correcting Codes PDF eBook |
Author | Venkatesan Guruswami |
Publisher | Springer |
Pages | 354 |
Release | 2004-11-29 |
Genre | Computers |
ISBN | 3540301801 |
How can one exchange information e?ectively when the medium of com- nication introduces errors? This question has been investigated extensively starting with the seminal works of Shannon (1948) and Hamming (1950), and has led to the rich theory of “error-correcting codes”. This theory has traditionally gone hand in hand with the algorithmic theory of “decoding” that tackles the problem of recovering from the errors e?ciently. This thesis presents some spectacular new results in the area of decoding algorithms for error-correctingcodes. Speci?cally,itshowshowthenotionof“list-decoding” can be applied to recover from far more errors, for a wide variety of err- correcting codes, than achievable before. A brief bit of background: error-correcting codes are combinatorial str- tures that show how to represent (or “encode”) information so that it is - silient to a moderate number of errors. Speci?cally, an error-correcting code takes a short binary string, called the message, and shows how to transform it into a longer binary string, called the codeword, so that if a small number of bits of the codewordare ?ipped, the resulting string does not look like any other codeword. The maximum number of errorsthat the code is guaranteed to detect, denoted d, is a central parameter in its design. A basic property of such a code is that if the number of errors that occur is known to be smaller than d/2, the message is determined uniquely. This poses a computational problem,calledthedecodingproblem:computethemessagefromacorrupted codeword, when the number of errors is less than d/2.