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A simplified procedure for correcting both errors and erasures of a Reed-Solomon code using the Euclidean algorithmIt is well known that the Euclidean algorithm or its equivalent, continued fractions, can be used to find the error locator polynomial and the error evaluator polynomial in Berlekamp's key equation needed to decode a Reed-Solomon (RS) code. A simplified procedure is developed and proved to correct erasures as well as errors by replacing the initial condition of the Euclidean algorithm by the erasure locator polynomial and the Forney syndrome polynomial. By this means, the errata locator polynomial and the errata evaluator polynomial can be obtained, simultaneously and simply, by the Euclidean algorithm only. With this improved technique the complexity of time domain RS decoders for correcting both errors and erasures is reduced substantially from previous approaches. As a consequence, decoders for correcting both errors and erasures of RS codes can be made more modular, regular, simple, and naturally suitable for both VLSI and software implementation. An example illustrating this modified decoding procedure is given for a (15, 9) RS code.
Document ID
19880003316
Acquisition Source
Legacy CDMS
Document Type
Reprint (Version printed in journal)
Authors
Truong, T. K. (Geneva Observatory (Switzerland) United States)
Hsu, I. S. (Geneva Observatory (Switzerland) United States)
Eastman, W. L. (Mitre Corp. Bedford, MA., United States)
Reed, I. S. (University of Southern California Los Angeles., United States)
Date Acquired
September 5, 2013
Publication Date
November 15, 1987
Publication Information
Publication: The Telecommunications and Data Acquisition Report
Subject Category
Numerical Analysis
Accession Number
88N12698
Funding Number(s)
PROJECT: RTOP 310-30-71-87-02
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.

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