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CS 681: Computational Number Theory and Algebra Lecture 2: Reed Solomon code
 

Summary: CS 681: Computational Number Theory and Algebra Lecture 2: Reed
Solomon code
Lecturer: Manindra Agrawal Notes by: Anindya De
August 8, 2006.
1 Reed Solomon codes-Encoding
Let b0, b1, . . . , bn be a binary sequence which is to be coded for handling a maximum of t
errors. Fix a k < n and split b0, b1, . . . , bn into n/k blocks of k bits each. Let these be
c0, c1, . . . ck. View each ci as an element in F2k .
Define P(x) =
n/k-1
i=1 cixi.
Let dj = P(ej) for e0, e1, e2, . . . , em-1 F2k .
We will output d0, d1, d2, . . . , dm-1 as the encoded message. The input size is n bits as
compared to the output size which is mk bits. Also we assume that the number of errors is
atmost t i.e. atmost t out of the m di get corrupted.
Note that though theoretically it can correct only upto t errors, the number of errors it
can correct in practice is much larger. This is because we assume that the t bits that get
corrupted are in t different di's but usually errors occur in blocks. Hence it can correct upto
tk errors.
2 Decoding

  

Source: Agrawal, Manindra - Department of Computer Science and Engineering, Indian Institute of Technology Kanpur

 

Collections: Computer Technologies and Information Sciences