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Detecting Cycles of Length 10 in the Tanner Graph of a QC-LDPC Code Based on Protograph Analysis

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Abstract

We complete the description of the procedure of topological expansion of a bipartite graph without parallel branches on the plane of changing the structure of cycles of length up to 10 inclusive. Based on previous papers, we have extended a set of theorems specifying transformation rules for cycles and paths when passing from a protograph to the Tanner graph. We propose a procedure for detecting the existence of a cycle of length 10 in the expanded graph by analyzing the protograph.

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References

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Acknowledgements

The authors are especially grateful to A.N. Voropaev for his assistance in elaborating Theorem 1 and to a reviewer for careful reading of the manuscript and valuable remarks, which helped the authors to improve the final paper.

Funding

The research was carried out at the expense of the Russian Science Foundation, project no. 17-79-20302.

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Authors and Affiliations

  1. Department of Theoretical Foundations of Electrical Engineering, Faculty of Radio Engineering and Telecommunications, Utkin Ryazan State Radio Engineering University, Ryazan, Russia

    A. V. Kharin, K. N. Zavertkin & A. A. Ovinnikov

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  1. A. V. Kharin
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  2. K. N. Zavertkin
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  3. A. A. Ovinnikov
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Kharin, A., Zavertkin, K. & Ovinnikov, A. Detecting Cycles of Length 10 in the Tanner Graph of a QC-LDPC Code Based on Protograph Analysis. Probl Inf Transm 56, 317–331 (2020). https://doi.org/10.1134/S0032946020040031

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  • DOI: https://doi.org/10.1134/S0032946020040031

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