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
Online Access:Get full text
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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
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  fullname: Fominykh, Anna
  email: anna.fominykh@skoltech.ru
  organization: Center for Next Generation Wireless and IoT, Skolkovo Institute of Science and Technology, Moscow, Russia
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  givenname: Kirill
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  surname: Shabunov
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  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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