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Problems of Information Transmission

, Volume 55, Issue 2, pp 145–151 | Cite as

On Application of the Modulus Metric to Solving the Minimum Euclidean Distance Decoding Problem

  • V. A. DavydovEmail author
Coding Theory

Abstract

We prove equivalence of using the modulus metric and Euclidean metric in solving the soft decoding problem for a memoryless discrete channel with binary input and Q-ary output. For such a channel, we give an example of a construction of binary codes correcting t binary errors in the Hamming metric. The constructed codes correct errors at the output of a demodulator with Q quantization errors as (t + 1)(Q − 1) − 1 errors in the modulus metric. The obtained codes are shown to have polynomial decoding complexity.

Key words

modulus metric Euclidean metric soft decoding binary-input Q-ary output channel codes in the modulus metric 

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References

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    Davydov, V.A., Codes Correcting Errors in the Modulus Metric, Lee Metric, and Operator Errors, Probl. Peredachi Inf., 1993, vol. 29, no. 3, pp. 10–20 [Probl. Inf. Transm. (Engl. Transl.), 1993, vol. 29, no. 3, pp. 208–216].zbMATHGoogle Scholar
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    Davydov, V.A., Methods for Error Correction in the Modulus Metric and Derived Metrics, Cand. Sci. (Engrg.) Dissertation, St. Petersburg, 1993.Google Scholar

Copyright information

© Pleiades Publishing, Inc. 2019

Authors and Affiliations

  1. 1.Tikhonov Moscow Institute of Electronics and MathematicsNational Research University—Higher School of EconomicsMoscowRussia

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