Efficient decoding up to a constant fraction of the code length for asymptotically good quantum codes
Abstract
We introduce and analyse an efficient decoder for quantum Tanner codes that can correct adversarial errors of linear weight. Previous decoders for quantum lowdensity parity-check codes could only handle adversarial errors of weight O(√ n log n). We also work on the link between quantum Tanner codes and the Lifted Product codes of Panteleev and Kalachev, and show that our decoder can be adapted to the latter. The decoding algorithm alternates between sequential and parallel procedures and converges in linear time.
Domains
Information Theory [cs.IT] Atmospheric and Oceanic Physics [physics.ao-ph] Fluid Dynamics [physics.flu-dyn] General Physics [physics.gen-ph] Geophysics [physics.geo-ph] History of Physics [physics.hist-ph] Instrumentation and Detectors [physics.ins-det] Medical Physics [physics.med-ph] Optics [physics.optics] Plasma Physics [physics.plasm-ph] Popular Physics [physics.pop-ph] Physics and Society [physics.soc-ph] Atomic and Molecular Clusters [physics.atm-clus] Space Physics [physics.space-ph] Quantum Physics [quant-ph] Atomic Physics [physics.atom-ph] Biological Physics [physics.bio-ph] Chemical Physics [physics.chem-ph] Classical Physics [physics.class-ph] Computational Physics [physics.comp-ph] Data Analysis, Statistics and Probability [physics.data-an] Physics Education [physics.ed-ph]
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