Aspects of list-of-two decoding by Jonas Eriksson. PDF

By Jonas Eriksson.

ISBN-10: 9185497495

ISBN-13: 9789185497492

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X2s ) = 0, for j = 1, . . , t + s, all yield a well behaved error locator polynomial. He also noted that each such error locator polynomial corresponds to an error pattern of weight t + s belonging to the coset indicated by the known syndromes. This fact—that we allow more than one solution—is typical of a list decoder. The result is in a way equivalent with a list decoding were the list decoding radius is precisely equal to the distance from the received polynomial and the closest codeword polynomial.

The polynomials defining the code are sometimes referred to as message polynomials. The set {αi : i = 0, 1, . . , n − 1} of n distinct points used in the evaluation map is sometimes referred to as the location set of the code. The evaluation map view of Reed-Solomon codes provides an intuitive understanding of the redundancy built into the code. Any polynomial of degree less than k over a field is completely determined by its evaluation in k distinct points. Since a codeword contains n > k such evaluations we can tolerate that some of these evaluations are distorted and still retain enough information to determine which polynomial generated the evaluations.

We adopt the notion of the set of correctable error patterns of that code-decoder combination. We note as a clarification that an error pattern which is not correctable can still be decodable in the sense that the decoder does not declare a decoding failure and produces a faulty codeword as output. A complete characterization of the set of correctable error patterns entails a precise description of exactly which symbol patterns in Fnq it contains. Such a characterization is hard to accomplish and one often has to settle for something more manageable.

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Aspects of list-of-two decoding by Jonas Eriksson.


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