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Theoretical and Experimental Upper and Lower Bounds on the Efficiency of Convolutional Codes in a Binary Symmetric Channel

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Abstract

We propose a new approach to the analytical estimation of the error burst probability, the probability of erroneous decoding, and the probability of error per bit for convolutional codes with Viterbi decoding in a binary symmetric channel (BSC). Upper and lower estimates of the probability of error per bit and of the erroneous decoding probability are based on active distances and the distance spectrum of active distances for a convolutional code. The estimates are derived for rate \({1}/{2}\) convolutional codes, but they can also be generalized to any convolutional code with rate \({1}/{n}\). Calculation of the estimates described here has linear time complexity in the error burst minimal length if code distance properties are known. The computational complexity does not depend on the crossover probability of a BSC. Simulation results show that the considered estimates are rather tight, especially for small crossover probabilities.

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Funding

The research was funded under the HSE University Basic Research Program in 2022.

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Authors and Affiliations

  1. Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, Russia

    A. A. Kurmukova, F. I. Ivanov & V. V. Zyablov

  2. Higher School of Economics—National Research University, Moscow, Russia

    A. A. Kurmukova & F. I. Ivanov

  3. Skolkovo Institute of Science and Technology (Skoltech), Moscow, Russia

    A. A. Kurmukova

Authors
  1. A. A. Kurmukova
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  2. F. I. Ivanov
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  3. V. V. Zyablov
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Translated from Problemy Peredachi Informatsii, 2022, Vol. 58, No. 2, pp. 24–40 https://doi.org/10.31857/S055529232202003X.

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Kurmukova, A., Ivanov, F. & Zyablov, V. Theoretical and Experimental Upper and Lower Bounds on the Efficiency of Convolutional Codes in a Binary Symmetric Channel. Probl Inf Transm 58, 122–136 (2022). https://doi.org/10.1134/S003294602202003X

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