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A branch-cut-and-price algorithm for optimal decoding in digital communication systems

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Abstract

Channel coding aims to minimize the errors that occur during the transmission of digital information from one place to another. Low-density parity-check codes can detect and correct transmission errors if one encodes the original information by adding redundant bits. In practice, heuristic iterative decoding algorithms are used to decode the received vector. However, these algorithms may fail to decode if the received vector contains multiple errors. We consider decoding the received vector with minimum error as an integer programming (IP) problem and propose a branch-and-price method for its solution. We improve the performance of our method by introducing heuristic feasible solutions and adding valid cuts to the mathematical formulation. Our computational experiments reveal that our branch-cut-and-price algorithm significantly improves solvability of the problem compared to a state-of-the-art IP decoder in the literature and has superior error performance than the conventional sum-product algorithm.

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Acknowledgements

This research has been supported by the Turkish Scientific and Technological Research Council with Grant No. 113M499.

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Authors and Affiliations

  1. Department of Industrial Engineering, Istanbul Bilgi University, Istanbul, Turkey

    Banu Kabakulak

  2. Department of Industrial Engineering, Boğaziçi University, Istanbul, Turkey

    Z. Caner Taşkın

  3. Department of Electrical and Electronics Engineering, Boğaziçi University, Istanbul, Turkey

    Ali Emre Pusane

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  1. Banu Kabakulak
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  2. Z. Caner Taşkın
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  3. Ali Emre Pusane
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Correspondence to Banu Kabakulak.

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Kabakulak, B., Taşkın, Z.C. & Pusane, A.E. A branch-cut-and-price algorithm for optimal decoding in digital communication systems. J Glob Optim 81, 805–834 (2021). https://doi.org/10.1007/s10898-021-01073-4

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  • DOI: https://doi.org/10.1007/s10898-021-01073-4

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