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.

翻译：本文提出一种适用于任意量子LDPC码的新型擦除译码器。该译码器被称为簇译码器，其推广了Connelly等人于2022年提出的垂直-水平（VH）译码的分解思想。与VH译码器类似，该方案首先运行剥离译码器，然后对生成的停止集进行后处理。簇译码器将停止集分解为簇的树形结构，这些簇可通过高斯消元法（GE）顺序求解。通过允许无约束大小的簇，该译码器在降低复杂度的同时实现了最大似然（ML）性能。当仅对尺寸小于常数的簇应用高斯消元时，性能会有所下降，但复杂度将随码长呈线性增长。仿真结果表明，对于超图乘积码，采用恒定簇大小的簇译码器在低擦除率区域能达到接近VH译码的近似最大似然性能。对于所研究的一般量子LDPC码，簇译码器可用于在较宽擦除率范围内以较低复杂度估计最大似然性能曲线。