Numerical and analytical bounds on threshold error rates for hypergraph-product codes
Quantum Physics
2018-06-14 v2 Information Theory
math.IT
Abstract
We study analytically and numerically decoding properties of finite rate hypergraph-product quantum LDPC codes obtained from random (3,4)-regular Gallager codes, with a simple model of independent X and Z errors. Several non-trival 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%.
Keywords
Cite
@article{arxiv.1804.01950,
title = {Numerical and analytical bounds on threshold error rates for hypergraph-product codes},
author = {Alexey A. Kovalev and Sanjay Prabhakar and Ilya Dumer and Leonid P. Pryadko},
journal= {arXiv preprint arXiv:1804.01950},
year = {2018}
}
Comments
14 pages, 5 figures