Projected requirements for 6G ultra-reliable low-latency communications (URLLC) scenario require extremely low latency and efficient error correction akin to maximum likelihood (ML) performance. The quest for codes and decoding methods that balance low latency, energy efficiency, and error correction ability is at its height. Polar codes known for their capacity achievement in symmetric memoryless channels have shown promise in 5G applications. Advancing further existing decoding techniques like successive cancellation list (SCL) algorithm offer a path towards ML performance, whilst at the expense of having increased computational complexity. The introduction of automorphism ensemble (AE) decoding provided a novel approach for parallel decoding, particularly beneficial for codes with rich automorphism group like Reed-Muller (RM) codes. This work introduces a novel modification of AE decoding termed reduced-delay AE (RD-AE) decoder. RD-AE leverages a tailored set of automorphisms with the primary aim at diminishing decoding delay but also offering the flexibility to prioritize either delay reduction or error correction performance.
Projected requirements for 6G ultra-reliable low-latency communications (URLLC) scenario require extremely low latency and efficient error correction akin to maximum likelihood (ML) performance. The quest for codes and decoding methods that balance low latency, energy efficiency, and error correction ability is at its height. Polar codes known for their capacity achievement in symmetric memoryless channels have shown promise in 5G applications. Advancing further existing decoding techniques like successive cancellation list (SCL) algorithm offer a path towards ML performance, whilst at the expense of having increased computational complexity. The introduction of automorphism ensemble (AE) decoding provided a novel approach for parallel decoding, particularly beneficial for codes with rich automorphism group like Reed-Muller (RM) codes. This work introduces a novel modification of AE decoding termed reduced-delay AE (RD-AE) decoder. RD-AE leverages a tailored set of automorphisms with the primary aim at diminishing decoding delay but also offering the flexibility to prioritize either delay reduction or error correction performance.
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.
Automorphism ensemble decoding (AED) is a highly parallel approach that enables decoding of polar and Reed-Muller (RM) codes with automorphisms, offering a practical solution with near-maximum likelihood (ML) performance and manageable computational complexity. To meet the growing demands for high throughput and low latency in cloud and virtual random access networks, this paper presents a graphics processing unit (GPU)-based AED architecture for polar and RM codes, utilizing low-complexity successive cancellation (SC) and small list SC (SCL) decoders as the constituent of AED. The proposed architecture exploits the inherent parallelism of AED to optimize decoding tasks on the GPU, significantly enhancing throughput by efficiently harnessing the extensive parallel processing capabilities of the GPU. Additionally, improved thread mapping and data management techniques markedly reduce latency for automorphism ensemble SC (Aut-SC) decoding, while a low-latency sorting mechanism further accelerates automorphism ensemble SCL (Aut-SCL) decoding. Experimental results on an NVIDIA RTX 4090 demonstrate that the proposed Aut-SC decoder, with an ensemble size of 8, achieves a throughput exceeding 17 Gbps. Compared to the state-of-the-art softwarebased SCL decoders, the proposed GPU-based Aut-SC and Aut-SCL architectures outperform existing solutions by factors of up to 28× and 10×, respectively, in normalized throughput while maintaining the same or even superior error correction performance.
Ultra-reliable and low-latency communication (URLLC) in 6G networks is characterized by very high reliability and very low latency to enable mission-critical applications. The ability of a coding scheme to support diverse use cases requires flexibility on the part of the decoder. High reliability and low latency require decoders with improved error rate performance and reduced complexity. This article investigates candidate universal decoding algorithms for 6G communication scenarios. Universal decoders work on a wide range of error-correcting codes, making them scalable for different communication protocols. This article undertakes the comparative analysis and performance evaluation of the code-agnostic decoding schemes, including automorphism ensemble (AED), guessing random additive noise (GRAND), ordered statistics (OSD), belief propagation (BPD), bit flipping (BFD), and their variants. Simulations are carried out in MATLAB (R2024a) for the error rate performance of decoders, and plots are provided for the comparative analysis from the results of inferred data. The key findings in this paper highlight the competitive advantage of universal decoding techniques in comparison to the standardized CA-SCL decoding of polar code. Consequently, this work will help in identifying more efficient decoding algorithms for potential 6G URLLC applications. We aim to provide an insight into the scalability of universal decoding techniques by exploring their key performance metrics and comparing their performances.
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.
In this paper we deal with polar code automorphisms that are beneficial under low-latency automorphism ensemble (AE) decoding, and we propose polar code designs that have such automorphisms. Successive-cancellation (SC) decoding and thus SC-based AE decoding are invariant with respect to the only known polar code automorphisms, namely those of the lower-triangular affine (LTA) group. To overcome this problem, we provide methods to determine whether a given polar code has non-LTA automorphisms and to identify such automorphisms. Building on this, we design specific polar codes that admit automorphisms in the upper-diagonal linear (UTL) group, and thus render SC-based AE decoding effective. Demonstrated by examples, these new polar codes under AE decoding outperform conventional polar codes under SC list decoding in terms of error rate, while keeping the latency comparable to SC decoding. Moreover, state-of-the-art BP-based permutation decoding for polar codes is beaten by BP-based AE thanks to this design.
The discovery of suitable automorphisms of polar codes gained a lot of attention by applying them in Automorphism Ensemble Decoding (AED) to improve the error-correction performance, especially for short block lengths. This paper introduces Successive Cancellation Automorphism List (SCAL) decoding of polar codes as a novel application of automorphisms in advanced Successive Cancellation List (SCL) decoding. Initialized with L permutations selected from the automorphism group, a superposition of different noise realizations and path splitting takes place inside the decoder. In this way, the SCAL decoder automatically adapts to the channel conditions and outperforms the error-correction performance of conventional SCL decoding and AED. For a polar code of length 128, SCAL performs near Maximum Likelihood (ML) decoding with L=8, in contrast to M=16 needed decoder cores in AED. Application-Specific Integrated Circuit (ASIC) implementations in a 12nm technology show that high-throughput, pipelined SCAL decoders outperform AED in terms of energy efficiency and power density, and SCL decoders additionally in area efficiency.