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Paper 1
Noisy-Syndrome Decoding of Hypergraph Product Codes
Venkata Gandikota, Elena Grigorescu, Vatsal Jha, S. Venkitesh
- Year
- 2025
- Journal
- arXiv preprint
- DOI
- arXiv:2510.07602
- arXiv
- 2510.07602
Hypergraph product codes are a prototypical family of quantum codes with state-of-the-art decodability properties. Recently, Golowich and Guruswami (FOCS 2024) showed a reduction from quantum decoding to syndrome decoding for a general class of codes, which includes hypergraph product codes. In this work we consider the "noisy" syndrome decoding problem for hypergraph product codes, and show a similar reduction in the noisy setting, addressing a question posed by Golowich and Guruswami. Our results hold for a general family of codes wherein the code and the dual code are "simultaneously nice"; in particular, for codes admitting good syndrome decodability and whose duals look "similar". These include expander codes, Reed-Solomon codes, and variants.
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