Distance Verification for Classical and Quantum LDPC Codes
Distance Verification for Classical and Quantum LDPC Codes
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DOI：
10.1109/tit.2017.2690381
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发表时间：
2016-11
影响因子：
2.5
通讯作者：
I. Dumer;A. Kovalev;L. Pryadko
中科院分区：
文献类型：
--
作者：
I. Dumer;A. Kovalev;L. Pryadko
将一般线性码的距离验证技术应用于量子稳定子码。然后，这些技术被认为是经典和量子（稳定）低密度奇偶校验（LDPC）码。新的复杂度范围的距离验证与可证明的性能推导出使用的平均重量谱的集合的LDPC码。这些界限表示在相应的合奏的擦除校正能力。我们还提出了一种新的不可约簇技术，它可以应用于任何LDPC码，并利用奇偶校验的稀疏性的经典和量子LDPC码。该技术降低了为具有小相对距离的通用稳定器码设计的所有现有确定性技术的复杂度指数，所述通用稳定器码还包括所有已知的量子稳定器LDPC码族。
The techniques of distance verification known for general linear codes are first applied to the quantum stabilizer codes. Then, these techniques are considered for classical and quantum (stabilizer) low-density-parity-check (LDPC) codes. New complexity bounds for distance verification with provable performance are derived using the average weight spectra of the ensembles of LDPC codes. These bounds are expressed in terms of the erasure-correcting capacity of the corresponding ensemble. We also present a new irreducible-cluster technique that can be applied to any LDPC code and takes advantage of parity-checks’ sparsity for both the classical and quantum LDPC codes. This technique reduces complexity exponents of all existing deterministic techniques designed for generic stabilizer codes with small relative distances, which also include all known families of the quantum stabilizer LDPC codes.