Enhanced Message-Passing Decoding of Degenerate Quantum Codes Utilizing Trapping Set Dynamics

In this letter, we propose a novel iterative decoding algorithm that exploits the degenerate nature of three different families of quantum low-density parity-check codes, i.e., surface, toric, and row-degree-4 bicycle codes. Such families of codes share harmful trapping sets that constitute symmetri...

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Bibliographic Details
Published in:IEEE communications letters 2024-03, Vol.28 (3), p.444-448
Main Authors: Chytas, Dimitris, Pacenti, Michele, Raveendran, Nithin, Flanagan, Mark F., Vasic, Bane
Format: Article
Language:English
Subjects:
Algorithms
belief propagation decoding
Bicycles
Codes
Complexity theory
Convergence
Decoding
degeneracy
Error correcting codes
Iterative decoding
Iterative methods
Message passing
Oscillators
QLDPC codes
Qubit
symmetric stabilizers
topological codes
Trapping
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Summary:In this letter, we propose a novel iterative decoding algorithm that exploits the degenerate nature of three different families of quantum low-density parity-check codes, i.e., surface, toric, and row-degree-4 bicycle codes. Such families of codes share harmful trapping sets that constitute symmetric stabilizers, making it impossible for any parallel-scheduled iterative message-passing decoder to converge even for error patterns of weight as low as two. By biasing subsets of nodes in the symmetric stabilizers, the decoder is able to converge to a valid error pattern. Furthermore, the proposed decoder has low decoding complexity - linear in the code's blocklength - and a fully parallel schedule, making it suitable for low-latency efficient implementation.
ISSN:1089-7798
1558-2558
DOI:10.1109/LCOMM.2024.3356312