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Abstract

We introduce a new erasure decoder that applies to arbitrary quantum LDPC codes. Dubbed the cluster decoder, it generalizes the decomposition idea of Vertical-Horizontal (VH) decoding introduced by Connelly et al. in 2022. Like the VH decoder, the idea is to first run the peeling decoder and then post-process the resulting stopping set. The cluster decoder breaks the stopping set into a tree of clusters which can be solved sequentially via Gaussian Elimination (GE). By allowing clusters of unconstrained size, this decoder achieves maximum-likelihood (ML) performance with reduced complexity compared with full GE. When GE is applied only to clusters whose sizes are less than a constant, the performance is degraded but the complexity becomes linear in the block length. Our simulation results show that, for hypergraph product codes, the cluster decoder with constant cluster size achieves near-ML performance similar to VH decoding in the low-erasure-rate regime. For the general quantum LDPC codes we studied, the cluster decoder can be used to estimate the ML performance curve with reduced complexity over a wide range of erasure rates.

Details

1009240
Identifier / keyword
Title
Cluster Decomposition for Improved Erasure Decoding of Quantum LDPC Codes
Publication title
arXiv.org; Ithaca
Publication year
2024
Publication date
Dec 11, 2024
Section
Computer Science; Mathematics; Quantum Physics
Publisher
Cornell University Library, arXiv.org
Source
arXiv.org
Place of publication
Ithaca
Country of publication
United States
University/institution
Cornell University Library arXiv.org
e-ISSN
2331-8422
Source type
Working Paper
Language of publication
English
Document type
Working Paper
Publication history
 
 
Online publication date
2024-12-13
Milestone dates
2024-12-11 (Submission v1)
Publication history
 
 
   First posting date
13 Dec 2024
ProQuest document ID
3144196477
Document URL
https://www.proquest.com/working-papers/cluster-decomposition-improved-erasure-decoding/docview/3144196477/se-2?accountid=208611
Full text outside of ProQuest
Copyright
© 2024. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.
Last updated
2024-12-14
Database
ProQuest One Academic