Automorphism Set Construction for Automorphism Ensemble Decoding With Reduced Delay

The anticipated demands of 6G ultra-reliable low-latency communications (URLLC) call for near-instantaneous data transfers and error-correction efficiency rivaling maximum-likelihood (ML) decoding. Achieving an effective compromise between latency, power consumption, and decoding accuracy is a pivot...

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Published in:	IEEE open journal of the Communications Society Vol. 6; pp. 8625 - 8635
Main Authors:	Fominykh, Anna, Shabunov, Kirill
Format:	Journal Article
Language:	English
Published:	New York IEEE 2025 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:	Algorithms Automorphism ensemble decoding Automorphisms Codes Complexity theory Decoding Delays Error correction Harnesses low-delay decoding Maximum likelihood decoding Measurement monomial codes Network latency Permutations Polar codes Reed-Muller codes Symmetric matrices Ultra reliable low latency communication Vectors
ISSN:	2644-125X, 2644-125X
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Abstract	The anticipated demands of 6G ultra-reliable low-latency communications (URLLC) call for near-instantaneous data transfers and error-correction efficiency rivaling maximum-likelihood (ML) decoding. Achieving an effective compromise between latency, power consumption, and decoding accuracy is a pivotal challenge in contemporary coding theory. Polar codes have distinguished themselves by achieving capacity on symmetric memoryless channels. To narrow the gap to ML performance, refined techniques like successive-cancellation list (SCL) decoding have been developed, albeit with a rise in computational burden. More recently, automorphism ensemble (AE) decoding has unlocked parallelization benefits for codes with rich automorphism groups, such as Reed-Muller codes. This paper discusses the reduced-delay AE (RD-AE) decoder, which harnesses a carefully chosen subset of automorphisms to drastically cut decoding latency while allowing a flexible trade-off between speed and error-correction performance. This article is an extended version of research previously introduced at a conference. We discuss key aspects and nuances of the algorithm and its implementation, including: (1) algorithms for selecting automorphism sets to meet specific performance targets, (2) a detailed procedure for combining bits from different permutations, (3) code construction methodologies for RD-AE decoding, and (4) implementation considerations. Furthermore, we explore various scenarios and applications of the proposed algorithm and present simulation results demonstrating significant latency reductions while maintaining error-correction performance.
AbstractList	The anticipated demands of 6G ultra-reliable low-latency communications (URLLC) call for near-instantaneous data transfers and error-correction efficiency rivaling maximum-likelihood (ML) decoding. Achieving an effective compromise between latency, power consumption, and decoding accuracy is a pivotal challenge in contemporary coding theory. Polar codes have distinguished themselves by achieving capacity on symmetric memoryless channels. To narrow the gap to ML performance, refined techniques like successive-cancellation list (SCL) decoding have been developed, albeit with a rise in computational burden. More recently, automorphism ensemble (AE) decoding has unlocked parallelization benefits for codes with rich automorphism groups, such as Reed-Muller codes. This paper discusses the reduced-delay AE (RD-AE) decoder, which harnesses a carefully chosen subset of automorphisms to drastically cut decoding latency while allowing a flexible trade-off between speed and error-correction performance. This article is an extended version of research previously introduced at a conference. We discuss key aspects and nuances of the algorithm and its implementation, including: (1) algorithms for selecting automorphism sets to meet specific performance targets, (2) a detailed procedure for combining bits from different permutations, (3) code construction methodologies for RD-AE decoding, and (4) implementation considerations. Furthermore, we explore various scenarios and applications of the proposed algorithm and present simulation results demonstrating significant latency reductions while maintaining error-correction performance.
Author	Fominykh, Anna Shabunov, Kirill
Author_xml	– sequence: 1 givenname: Anna orcidid: 0000-0002-1412-5766 surname: Fominykh fullname: Fominykh, Anna email: anna.fominykh@skoltech.ru organization: Center for Next Generation Wireless and IoT, Skolkovo Institute of Science and Technology, Moscow, Russia – sequence: 2 givenname: Kirill orcidid: 0000-0003-1968-1582 surname: Shabunov fullname: Shabunov, Kirill organization: 6G Research, Moscow Radio Transmission Technology and Computing Laboratory, Moscow, Russia
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SubjectTerms	Algorithms Automorphism ensemble decoding Automorphisms Codes Complexity theory Decoding Delays Error correction Harnesses low-delay decoding Maximum likelihood decoding Measurement monomial codes Network latency Permutations Polar codes Reed-Muller codes Symmetric matrices Ultra reliable low latency communication Vectors
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Title	Automorphism Set Construction for Automorphism Ensemble Decoding With Reduced Delay
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