Constructing coset codes with optimal same-symbol weight for detecting narrowband interference in M-FSK systems

  • Authors:

  • Daniel J. J. Versfeld;A. J. H. Vinck;James N. Ridley;Hendrik C. Ferreira

  • Affiliations:

  • School of Electrical and Information Engineering, University of theWitwatersrand, Johannesburg, South Africa;Institute for Experimental Mathematics, University of Duisberg-Essen, Essen, Germany;John Knopfmacher Center, School of Mathematics, University of the Witwatersrand, Johannesburg, South Africa;Department of Electrical and Electronic Engineering, University of Johannesburg, Johannesburg, South Africa

  • Venue:
  • IEEE Transactions on Information Theory
  • Year:
  • 2010

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Abstract

Narrowband interference can cause undetected errors when M-FSK data is encoded with an algebraic code containing the all-e codewords. This is due to the fact that the narrowband interferer will cause the output of the M-FSK demodulator to correspond to one of the all-e codewords. One possible solution is to use a coset code of a code containing the repetition code. The choice of the coset leader should be such that the resulting coset code has minimum same-symbol weight. We give a general construction for generating coset codes with minimum same-symbol weight and present results where an optimal coset code for an (n, k) Reed-Solomon code is applied in an M-FSK environment with narrowband interference. From the results it is evident that the optimal coset codes outperform linear codes when narrowband interference is present.