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Quantum low-density parity-check codes are a promising approach to fault-tolerant quantum computation, offering potential advantages in rate and decoding efficiency. Quantum Margulis codes are a new class of QLDPC codes derived from Margulis’ classical LDPC construction via the two-block group algebra framework. We show that quantum Margulis codes, unlike bivariate bicycle codes, which require ordered statistics decoding for effective error correction, can be efficiently decoded using a standard min-sum decoder with linear complexity, when decoded under depolarizing noise. This is attributed to their Tanner graph structure, which does not exhibit group symmetry, thereby mitigating the well-known problem of error degeneracy in QLDPC decoding. To further enhance performance, we propose an algorithm for constructing 2BGA codes with controlled girth, ensuring a minimum girth of 6 or 8, and use it to generate several quantum Margulis codes of length 240 and 642. We validate our approach through numerical simulations, demonstrating that quantum Margulis codes behave significantly better than BB codes in the error floor region, under min-sum decoding.
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This content will become publicly available on June 22, 2026
Enhanced Min-Sum Decoding of Quantum Codes with Iteration Dynamics Memory
In this paper, we propose a novel message-passing decoding approach that leverages the degeneracy of quantum low-density parity-check codes to enhance decoding performance, eliminating the need for serial scheduling or post-processing. Our focus is on two-block Calderbank-Shor-Steane (CSS) codes, which are composed of symmetric stabilizers that hinder the performance of conventional iterative decoders with uniform update rules. Specifically, our analysis shows that, under the isolation assumption, the min-sum decoder fails to converge when constant-weight errors are applied to symmetric stabilizers, as variable-to-check messages oscillate in every iteration. To address this, we introduce a decoding technique that exploits this oscillatory property by applying distinct update rules: variable nodes in one block utilize messages from previous iterations, while those in the other block are updated conventionally. Logical error-rate results demonstrate that the proposed decoder significantly outperforms the normalized min-sum decoder and achieves competitive performance with belief propagation enhanced by order-zero ordered statistics decoding, all while maintaining linear complexity in the code’s block length.
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- Award ID(s):
- 2420424
- PAR ID:
- 10645533
- Publisher / Repository:
- IEEE
- Date Published:
- Page Range / eLocation ID:
- 1 to 6
- Subject(s) / Keyword(s):
- QLDPC codes, min-sum decoding, parallel scheduling, degeneracy, symmetric stabilizers
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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