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PreprintCC BY 4.0arXiv

Graphical Analysis of Lifted Product Code Constructions

  • Ragnar Freij-Hollanti
  • Kirsten D. Morris
  • Patricija Šapokaitė
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Abstract

Lifted product codes are an important family of quantum low-density parity-check (QLDPC) codes, as they were the first QLDPC code family shown to be asymptotically good. Understanding the structure of their parity-check matrices HX and HZ, as well as the associated Tanner graphs, is essential for analyzing their decoding behavior and error-floor performance. In this work, we show that the Tanner graphs of HX and HZ are indeed isomorphic, and investigate their graph-theoretical structure. We establish conditions ensuring the connectivity of these graphs and provide bounds on their minimal absorbing sets, providing new insight into the combinatorial structures influencing decoding performance.

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Cite

BibTeXRIS
BibTeX
@misc{freijhollanti2026graphical,
  title = {{Graphical Analysis of Lifted Product Code Constructions}},
  author = {Ragnar Freij-Hollanti and Kirsten D. Morris and Patricija Šapokaitė},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2606.11987},
  eprint = {2606.11987},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.11987},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Graphical Analysis of Lifted Product Code Constructions
AU  - Ragnar Freij-Hollanti
AU  - Kirsten D. Morris
AU  - Patricija Šapokaitė
PY  - 2026
DA  - 2026/10/31
PB  - arXiv
DO  - 10.48550/arxiv.2606.11987
UR  - https://arxiv.org/abs/2606.11987
AB  - Lifted product codes are an important family of quantum low-density parity-check (QLDPC) codes, as they were the first QLDPC code family shown to be asymptotically good. Understanding the structure of their parity-check matrices H_X and H_Z, as well as the associated Tanner graphs, is essential for analyzing their decoding behavior and error-floor performance. In this work, we show that the Tanner graphs of H_X and H_Z are indeed isomorphic, and investigate their graph-theoretical structure. We establish conditions ensuring the connectivity of these graphs and provide bounds on their minimal absorbing sets, providing new insight into the combinatorial structures influencing decoding performance.
ER  -