Decoding RS and BCH Codes (Part 1)

  • Emilio Sanvicente


The first problem addressed in this chapter is how to find the number of errors when the capability of the code is not exceeded. It is shown that there is a polynomial (the error locator polynomial) whose roots point to the positions of the errors. This polynomial can be computed solving a set of linear equations and its roots are obtained by a method known as the Chien search. The error values are then found solving another set of linear equations. Appendix E presents a fast way to compute the determinants needed. Several examples illustrate how, when the number of errors surpasses the capability of the code, the decoding algorithm may fail, thus allowing the detection of errors. It is also explained how to decode in the presence of errors and erasures. Finally, the Massey algorithm is presented to find the locator polynomial without having to solve a system of linear equations. The proof of the algorithm is in Appendix F.

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Emilio Sanvicente
    • 1
  1. 1.Former Professor of Electrical Engineering, School of Telecommunication EngineeringPolytechnic University of CataloniaBarcelonaSpain

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