Low-Complexity Decoding Algorithm Utilizing Degeneracy for Quantum LDPC Codes

Quantum low-density parity-check (QLDPC) codes have been considered as a promising solution for the fault-tolerant quantum computing. However, the belief propagation (BP) decoding for QLDPC codes does not take into account the degeneracy, resulting in certain performance degradation. Recently, vario...

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Published in:MILCOM IEEE Military Communications Conference pp. 115 - 120
Main Authors: Kim, Jaemin, Jung, Hyunwoo, Ha, Jeongseok
Format: Conference Proceeding
Language:English
Published: IEEE 30.10.2023
Subjects:
Decoding
decoding algorithm
degeneracy
Fault tolerance
Fault tolerant systems
low-density parity-check codes
Military communication
Performance evaluation
Quantum computing
Quantum error correction codes
Simulation
ISSN:2155-7586
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Abstract Quantum low-density parity-check (QLDPC) codes have been considered as a promising solution for the fault-tolerant quantum computing. However, the belief propagation (BP) decoding for QLDPC codes does not take into account the degeneracy, resulting in certain performance degradation. Recently, various post-processing algorithms have been proposed to address this issue but they in return require excessive additional complexity and/or long decoding latency. Motivated by this, in this paper, we propose an efficient decoding algorithm that takes reduced decoding complexity for the post-processing. In particular, the proposed algorithm performs the post-processing in such a way that it first selects a variable node based on a proposed metric, and the depolarizing channel model for the selected variable node is reinitialized according to the BP decoding results. Then, the BP decoding is performed for the depolarizing channel model in which the selected node follows the reinitialized channel characteristics. The process of selection, reinitialization and BP decoding, say a trial, is iterated until it reaches a predetermined value or all syndromes are met. The main ideas of this work lie in formulating the metric for selection and reinitialization to minimize the number of trials until the degeneracy is resolved. Finally, simulation results show that the proposed decoding algorithms can significantly reduce the decoding complexity with similar decoding performance to that of an existing algorithm.
AbstractList Quantum low-density parity-check (QLDPC) codes have been considered as a promising solution for the fault-tolerant quantum computing. However, the belief propagation (BP) decoding for QLDPC codes does not take into account the degeneracy, resulting in certain performance degradation. Recently, various post-processing algorithms have been proposed to address this issue but they in return require excessive additional complexity and/or long decoding latency. Motivated by this, in this paper, we propose an efficient decoding algorithm that takes reduced decoding complexity for the post-processing. In particular, the proposed algorithm performs the post-processing in such a way that it first selects a variable node based on a proposed metric, and the depolarizing channel model for the selected variable node is reinitialized according to the BP decoding results. Then, the BP decoding is performed for the depolarizing channel model in which the selected node follows the reinitialized channel characteristics. The process of selection, reinitialization and BP decoding, say a trial, is iterated until it reaches a predetermined value or all syndromes are met. The main ideas of this work lie in formulating the metric for selection and reinitialization to minimize the number of trials until the degeneracy is resolved. Finally, simulation results show that the proposed decoding algorithms can significantly reduce the decoding complexity with similar decoding performance to that of an existing algorithm.
Author Kim, Jaemin
Ha, Jeongseok
Jung, Hyunwoo
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  givenname: Jaemin
  surname: Kim
  fullname: Kim, Jaemin
  email: jmkinn@kaist.ac.kr
  organization: Korea Advanced Institute of Science and Technology,School of Electrical Engineering,Daejeon,Republic of Korea
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  givenname: Hyunwoo
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  givenname: Jeongseok
  surname: Ha
  fullname: Ha, Jeongseok
  email: jsha@kaist.edu
  organization: Korea Advanced Institute of Science and Technology,School of Electrical Engineering,Daejeon,Republic of Korea
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Snippet Quantum low-density parity-check (QLDPC) codes have been considered as a promising solution for the fault-tolerant quantum computing. However, the belief...
SourceID ieee
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StartPage 115
SubjectTerms Decoding
decoding algorithm
degeneracy
Fault tolerance
Fault tolerant systems
low-density parity-check codes
Military communication
Performance evaluation
Quantum computing
Quantum error correction codes
Simulation
Title Low-Complexity Decoding Algorithm Utilizing Degeneracy for Quantum LDPC Codes
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