Quasi-Optimal Path Convergence-Aided Automorphism Ensemble Decoding of Reed–Muller Codes

By exploiting the rich automorphisms of Reed–Muller (RM) codes, the recently developed automorphism ensemble (AE) successive cancellation (SC) decoder achieves a near-maximum-likelihood (ML) performance for short block lengths. However, the appealing performance of AE-SC decoding arises from the div...

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Veröffentlicht in:Entropy (Basel, Switzerland) Jg. 27; H. 4; S. 424
Hauptverfasser: Tian, Kairui, Sun, He, Liu, Yukai, Liu, Rongke
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Switzerland MDPI AG 14.04.2025
MDPI
Schlagworte:
automorphism ensemble decoding
Automorphisms
Codes
Complexity
Convergence
Decoders
Decoding
early termination
Maximum likelihood decoding
Methods
Reed–Muller codes
successive cancellation decoding
South Carolina
early termination
automorphism ensemble decoding
successive cancellation decoding
Reed–Muller codes
ISSN:1099-4300, 1099-4300
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Zusammenfassung:By exploiting the rich automorphisms of Reed–Muller (RM) codes, the recently developed automorphism ensemble (AE) successive cancellation (SC) decoder achieves a near-maximum-likelihood (ML) performance for short block lengths. However, the appealing performance of AE-SC decoding arises from the diversity gain that requires a list of SC decoding attempts, which results in a high decoding complexity. To address this issue, this paper proposes a novel quasi-optimal path convergence (QOPC)-aided early termination (ET) technique for AE-SC decoding. This technique detects strong convergence between the partial path metrics (PPMs) of SC constituent decoders to reliably identify the optimal decoding path at runtime. When the QOPC-based ET criterion is satisfied during the AE-SC decoding, only the identified path is allowed to proceed for a complete codeword estimate, while the remaining paths are terminated early. The numerical results demonstrated that for medium-to-high-rate RM codes in the short-length regime, the proposed QOPC-aided ET method incurred negligible performance loss when applied to fully parallel AE-SC decoding. Meanwhile, it achieved a complexity reduction that ranged from 35.9% to 47.4% at a target block error rate (BLER) of 10−3, where it consistently outperformed a state-of-the-art path metric threshold (PMT)-aided ET method. Additionally, under a partially parallel framework of AE-SC decoding, the proposed QOPC-aided ET method achieved a greater complexity reduction that ranged from 81.3% to 86.7% at a low BLER that approached 10−5 while maintaining a near-ML decoding performance.
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ISSN:1099-4300
1099-4300
DOI:10.3390/e27040424