Degeneracy and Its Impact on the Decoding of Sparse Quantum Codes
Degeneracy and Its Impact on the Decoding of Sparse Quantum Codes
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DOI：
10.1109/access.2021.3089829
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发表时间：
2021
期刊：
影响因子：
3.9
通讯作者：
Patricio Fuentes;Josu Etxezarreta Martinez;P. Crespo;J. Garcia-Frías
中科院分区：
文献类型：
--
作者：
Patricio Fuentes;Josu Etxezarreta Martinez;P. Crespo;J. Garcia-Frías
在经典通信领域，稀疏码接近容量的性能已有充分文献记载，这激发了对其量子对应物的探索。稀疏量子码通常是由两种强大的经典码合并构建而成，并通过经典解码算法进行解码。然而，当基于经典方法对稀疏量子码进行解码时，量子范式呈现出一些对其产生有害影响的现象。其中一种现象被称为简并，它是稀疏量子码无法完全唤起其经典对应物那惊人纠错能力的一个主要原因。在本文中，我们采用群论方法来讨论与稀疏量子码相关的简并问题。此外，我们将稀疏量子码的解码过程与稀疏经典码的解码过程进行比较，阐明了在量子领域出现的挑战。最后，我们提供了一个详细的例子来说明简并对稀疏量子码的影响以及为这些方案设计最优解码器的挑战。
The well-documented capacity-approaching performance of sparse codes in the realm of classical communications has inspired the search for their quantum counterparts. Sparse quantum codes are generally built as the amalgamation of two robust classical codes and are decoded via classical decoding algorithms. However, the quantum paradigm presents phenomena that act in a deleterious manner on sparse quantum codes when they are decoded based on classical methodologies. One such phenomenon is known as degeneracy, and it is a major contributor to why sparse quantum codes do not entirely evoke the stupendous error correcting abilities of their classical counterparts. In this paper, we adopt a group theoretical approach to discuss the issue of degeneracy as it relates to sparse quantum codes. Furthermore, we compare the decoding process of sparse quantum codes with that of sparse classical codes, illustrating the challenges that appear in the quantum domain. Finally, we provide a detailed example to illustrate the effects of degeneracy on sparse quantum codes and the challenges of designing an optimum decoder for these schemes.