Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 1 of 1
Full-Text Articles in Physics
Numerical And Analytical Bounds On Threshold Error Rates For Hypergraph-Product Codes, Alexey Kovalev, Sanjay Prabhakar, Ilya Dumer, Leonid P. Pryadko
Numerical And Analytical Bounds On Threshold Error Rates For Hypergraph-Product Codes, Alexey Kovalev, Sanjay Prabhakar, Ilya Dumer, Leonid P. Pryadko
Department of Physics and Astronomy: Faculty Publications
We study analytically and numerically decoding properties of finite-rate hypergraph-product quantum low density parity-check codes obtained from random (3,4)-regular Gallager codes, with a simple model of independent X and Z errors. Several nontrivial lower and upper bounds for the decodable region are constructed analytically by analyzing the properties of the homological difference, equal minus the logarithm of the maximum-likelihood decoding probability for a given syndrome. Numerical results include an upper bound for the decodable region from specific heat calculations in associated Ising models and a minimum-weight decoding threshold of approximately 7%.