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Fast decoding algorithms for first order Reed-Muller and related codes

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Abstract

Fast decoding algorithms for short codes based on modifications of maximum likelihood decoding algorithms of first order Reed-Muller codes are described. Only additions-subtractions, comparisons and absolute value calculations are used in the algorithms. Soft and hard decisions maximum likelihood decoding algorithms for first order Reed-Muller and the Nordstrom-Robinson codes with low complexity are proposed.

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Authors and Affiliations

  1. Institute for Problems of Information Transmission, Ermolovoy 19, Moscow, Russia

    Alexey E. Ashikhmin

  2. Department of Electrical Engineering-Systems, Tel Aviv University, 69978, Ramat Aviv, Israel

    Simon N. Litsyn

Authors
  1. Alexey E. Ashikhmin
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  2. Simon N. Litsyn
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Additional information

Communicated by: D. Jungnickel

Supported by the Guastallo Foundation and a grant from the Ministry of Science and Technology, Israel

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Ashikhmin, A.E., Litsyn, S.N. Fast decoding algorithms for first order Reed-Muller and related codes. Des Codes Crypt 7, 187–214 (1996). https://doi.org/10.1007/BF00124511

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  • DOI: https://doi.org/10.1007/BF00124511

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