Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

International Conference on Communication, Image and Signal Processing (CCISP)

Improved ORB-GRAND for PAC Codes

Yueh Wang, Zhiping Shi, Ziyu Han, Zu'en Wei, Kunyang Li

Published Nov 17, 2023• 1 citation
Publisher

Abstract

Polarization-adjusted convolutional (PAC) codes have been proposed to significantly improve error correction ability compared to polar codes by incorporating rate-1 convolutional precoding. However, the development of computationally efficient decoders for PAC codes is still an ongoing research area. Ordered Reliability Bit Guessing Random Additive Noise Decoding (ORB-GRAND), a universal near Maximum Likelihood (near-ML) decoder, has been introduced for decoding moderately redundant block codes by querying a list of putative test error patterns (TEP) in a fixed order, i.e. logistic weight order (LWO) and improved logistic weight order (iLWO). In this study, we undertake a comprehensive investigation into the performance of ORB-GRAND concerning high-rate PAC codes of short-to-medium length. Firstly, we conduct a comparative analysis between ORB-GRAND and successive cancellation list (SCL) decoding for PAC codes and integrate the Cyclic Redundancy Check (CRC) mechanism into ORB-GRAND. Distance properties of PAC and CRC-Aided PAC (CA-PAC) codes are explored to demonstrate the performance results. Secondly, we propose a novel TEP scheduling scheme in response to the distinctive reduction in BLER revealed by scheduling TEP in iLWO, particularly for short PAC codes under low Signal-to-Noise Ratio (SNR) conditions. This remarkable scheme demonstrates its efficacy by effectively mitigating the aforementioned BLER degradation while maintaining the exceptional performance of iLWO in high SNR conditions.

DOI
10.1109/ccisp59915.2023.10355824

Related papers

ORB-Enhanced Belief Propagation Decoding of Polar Codes

Xintao Jin, Zhenyuan Chen, Yuejun Wei +3 more

Guessing random additive noise decoding (GRAND) is a recently proposed decoding approach, and ordered reliability bits GRAND (ORBGRAND) is one of its variants, exploiting channel soft information by sorting error patterns based upon the rank statistics of reliability values of received samples. In this paper, the ORB heuristic is employed to improve belief propagation (BP) decoding of polar codes. Specifically, the improved logistic weight ordering (iLWO) rule of ORB is employed to locate unreliable received samples, and these unreliable samples are flipped and scaled, followed by standard BP decoding. The performance gain of such ORB-enhanced BP decoding can be as high as 1.7dB at block error rate of 10–4with an average number of queries of 1.5.

International Conference on Wireless Communications and Signal Processing (WCSP)•Nov 1, 2022•0 citations

SCL-GRAND: Lower complexity and better flexibility for CRC-Polar Codes

Xuanyu Li, Kai Niu, Jincheng Dai +2 more

Guessing random additive noise decoding (GRAND) is a recently proposed decoding algorithm which can achieve the error performance of maximum likelihood (ML) decoding. However, GRAND and its variants are only suitable for some short codes with high code rates and have large average query numbers. To mitigate these problems, we propose a successive cancellation list (SCL)-GRAND decoding algorithm for the cyclic redundancy check concatenated polar (CRC-polar) codes. The proposed decoder first divides the received sequence into two subblocks. Then SCL is used to decode the upper subblock and output several candidates into the candidate list. For each candidate, GRAND is used to decode the lower subblock and finally choose the most-likely codeword as the decoded result. Since the SCL is integrated into the SCL-GRAND algorithm, this algorithm can achieve lower complexity and better flexibility than the original GRAND.

IEEE Wireless Communications and Networking Conference•Mar 1, 2023•7 citations

Soft Maximum Likelihood Decoding using GRAND

Amit Solomon, Ken R. Duffy, Muriel Médard

Maximum Likelihood (ML) decoding of forward error correction codes is known to be optimally accurate, but is not used in practice as it proves too challenging to efficiently implement. Here we propose a development of a previously described hard detection ML decoder called Guessing Random Additive Noise Decoding (GRAND). We introduce Soft GRAND (SGRAND), a ML decoder that fully avails of soft detection information and is suitable for use with any arbitrary high-rate, short-length block code. We assess SGRAND's performance on Cyclic Redundancy Check (CRC)-aided Polar (CA-Polar) codes, which will be used for all control channel communication in 5G New Radio (NR), comparing its accuracy with CRC-Aided Successive Cancellation List decoding (CA-SCL), a state-of-the-art soft-information decoder specific to CA-Polar codes.

arXiv:2001.03089•International Conference on Communications•Jun 1, 2020•119 citations

Performance Analysis and Optimal Design of ORB-Type GRAND Algorithms

Li Wan, Wenyi Zhang

Guessing Random Additive Noise Decoding (GRAND) performs decoding by sequentially guessing channel error patterns (EPs). Ordered Reliability Bits GRAND (ORBGRAND) is a notable instance suitable for efficient implementation, as it schedules EPs solely according to the ranking of soft channel outputs. In this paper, we generalize this principle to a broader class of GRAND algorithms whose testing order depends only on reliability ranking, referred to as ORB-type GRAND. We develop a unified analytical framework based on a key quantity termed the average guessing posterior (AGP), which captures the effectiveness of each EP and reduces decoding into an ordering problem over the EP space. For random code ensembles, we derive exact expressions for the block error rate (BLER), stopping-time distribution, and average number of tests under a fixed test budget. The analysis separates target-miss and target-preemption errors and shows that ordering EPs by non-increasing AGP is optimal over the EP set under consideration. For fixed linear block codes, we derive the BLER expression that isolates the code-dependent target-preemption term and characterize this term through higher-order weight relationships of codeword tuples, with a computable first-order upper bound as a useful special case. Guided by these insights, we formulate ReShuffled-ORBGRAND (RS-ORBGRAND) as an offline AGP-based reshuffling scheme. Numerical results for the Bose--Chaudhuri--Hocquenghem (BCH)$(127,113)$ code show that RS-ORBGRAND consistently improves existing ORB-type GRAND algorithms and lies within $0.1$~dB of a maximum-likelihood decoding lower-bound benchmark at a BLER of $10^{-6}$.

arXiv:2606.28030•Jun 26, 2026•0 citations

A Novel SCL Bit-Flipping Decoding Of Polarization-Adjusted Convolutional (PAC) Codes

Zhang, Wei

Polar codes have attracted the attention of numerous researchers in the past decade due to their excellent performance. However, their performance at short block lengths under standard successive cancellation decoding is far from desirable. An effective method to improve the performance at short lengths is CRC precoding followed by successive-cancellation list decoding. Later, Arikan presented polarization-adjusted convolutional (PAC) codes, which further improve the performance of polar codes. In fact, bit-flipping is another post-processing method that can improve decoding performance. In this paper, we propose a novel SCL Bit-Flipping of PAC Codes. We show that better performance can be achieved using list decoding when the list size is the same for PAC codes (N=128, K=64). The decoding performance of our newly proposed PAC-SCLF with a list size of 32 is 0.3 dB better than that of the traditional PAC-SCL with a list size of 32. We set the maximum number of bit flips to 5. The performance of the list size (L=32) for PAC-SCLF is almost the same as the performance of the list size (L=128) for PAC-SCL.

arXiv:2307.05871•Jul 12, 2023•1 citation

CRC Aided Dynamic List SCL Decoder for Polar and PAC Codes

Hossein Sharifzadeh Behzadi

Error-correction codes are indispensable to ensure reliable data transmission in various communication systems. Among these, Polar codes and PAC (Polarized Adjustable Convolutional) codes have gained significant attention due to their capacity-achieving properties and low encoding complexity. This thesis presents a novel decoding technique that combines the Targeted Parity Protection (TPP) algorithm and Dynamic Successive Cancellation List (SCL) decoding to achieve substantial performance improvements while maintaining much lower complexity compared to the conventional Fano decoder. The proposed technique focuses on leveraging Cyclic Redundancy Check (CRC) bits to protect critical information bits, leading to enhanced error correction capabilities. By applying TPP, the decoding process is accelerated by effectively reducing latency and saves computational resources by eliminating wrong codeword candidates at an earlier stage before the decoder favors them. The integration of Dynamic SCL introduces adaptability to the decoder, allowing it to adjust the list size based on the decoding requirements for different code rates and lengths. This adaptability enables efficient use of hardware resources by optimizing the utilization of the decoder storage but also tailors the decoder's performance to each specific scenario, yielding substantial error correction performance gains in both Polar and PAC codes. Extensive simulations and performance evaluations demonstrate the effectiveness of the proposed technique. The results indicate a gain of up to 0.4 dB for Polar codes and up to 0.6 dB for PAC codes compared to the standard SCL decoding approach. It is worth mentioning that such gains are considered substantial for fiber optical communications which is one of the target applications of the new technique. Furthermore, the technique showcases a reduction in decoding complexity, outperforming the traditional Fano decoder.

•Aug 15, 2023•0 citations
Polarization-adjusted convolutional (PAC) codes have been proposed to significantly improve error correction ability compared to polar codes by incorporating rate-1 convolutional precoding. However, the development of computationally efficient decoders for PAC codes is still an ongoing research area. Ordered Reliability Bit Guessing Random Additive Noise Decoding (ORB-GRAND), a universal near Maximum Likelihood (near-ML) decoder, has been introduced for decoding moderately redundant block codes by querying a list of putative test error patterns (TEP) in a fixed order, i.e. logistic weight order (LWO) and improved logistic weight order (iLWO). In this study, we undertake a comprehensive investigation into the performance of ORB-GRAND concerning high-rate PAC codes of short-to-medium length. Firstly, we conduct a comparative analysis between ORB-GRAND and successive cancellation list (SCL) decoding for PAC codes and integrate the Cyclic Redundancy Check (CRC) mechanism into ORB-GRAND. Distance properties of PAC and CRC-Aided PAC (CA-PAC) codes are explored to demonstrate the performance results. Secondly, we propose a novel TEP scheduling scheme in response to the distinctive reduction in BLER revealed by scheduling TEP in iLWO, particularly for short PAC codes under low Signal-to-Noise Ratio (SNR) conditions. This remarkable scheme demonstrates its efficacy by effectively mitigating the aforementioned BLER degradation while maintaining the exceptional performance of iLWO in high SNR conditions.
Guessing random additive noise decoding (GRAND) is a recently proposed decoding approach, and ordered reliability bits GRAND (ORBGRAND) is one of its variants, exploiting channel soft information by sorting error patterns based upon the rank statistics of reliability values of received samples. In this paper, the ORB heuristic is employed to improve belief propagation (BP) decoding of polar codes. Specifically, the improved logistic weight ordering (iLWO) rule of ORB is employed to locate unreliable received samples, and these unreliable samples are flipped and scaled, followed by standard BP decoding. The performance gain of such ORB-enhanced BP decoding can be as high as 1.7dB at block error rate of 10–4with an average number of queries of 1.5.
Guessing random additive noise decoding (GRAND) is a recently proposed decoding algorithm which can achieve the error performance of maximum likelihood (ML) decoding. However, GRAND and its variants are only suitable for some short codes with high code rates and have large average query numbers. To mitigate these problems, we propose a successive cancellation list (SCL)-GRAND decoding algorithm for the cyclic redundancy check concatenated polar (CRC-polar) codes. The proposed decoder first divides the received sequence into two subblocks. Then SCL is used to decode the upper subblock and output several candidates into the candidate list. For each candidate, GRAND is used to decode the lower subblock and finally choose the most-likely codeword as the decoded result. Since the SCL is integrated into the SCL-GRAND algorithm, this algorithm can achieve lower complexity and better flexibility than the original GRAND.
Maximum Likelihood (ML) decoding of forward error correction codes is known to be optimally accurate, but is not used in practice as it proves too challenging to efficiently implement. Here we propose a development of a previously described hard detection ML decoder called Guessing Random Additive Noise Decoding (GRAND). We introduce Soft GRAND (SGRAND), a ML decoder that fully avails of soft detection information and is suitable for use with any arbitrary high-rate, short-length block code. We assess SGRAND's performance on Cyclic Redundancy Check (CRC)-aided Polar (CA-Polar) codes, which will be used for all control channel communication in 5G New Radio (NR), comparing its accuracy with CRC-Aided Successive Cancellation List decoding (CA-SCL), a state-of-the-art soft-information decoder specific to CA-Polar codes.
Guessing Random Additive Noise Decoding (GRAND) performs decoding by sequentially guessing channel error patterns (EPs). Ordered Reliability Bits GRAND (ORBGRAND) is a notable instance suitable for efficient implementation, as it schedules EPs solely according to the ranking of soft channel outputs. In this paper, we generalize this principle to a broader class of GRAND algorithms whose testing order depends only on reliability ranking, referred to as ORB-type GRAND. We develop a unified analytical framework based on a key quantity termed the average guessing posterior (AGP), which captures the effectiveness of each EP and reduces decoding into an ordering problem over the EP space. For random code ensembles, we derive exact expressions for the block error rate (BLER), stopping-time distribution, and average number of tests under a fixed test budget. The analysis separates target-miss and target-preemption errors and shows that ordering EPs by non-increasing AGP is optimal over the EP set under consideration. For fixed linear block codes, we derive the BLER expression that isolates the code-dependent target-preemption term and characterize this term through higher-order weight relationships of codeword tuples, with a computable first-order upper bound as a useful special case. Guided by these insights, we formulate ReShuffled-ORBGRAND (RS-ORBGRAND) as an offline AGP-based reshuffling scheme. Numerical results for the Bose--Chaudhuri--Hocquenghem (BCH)(127,113)(127,113)(127,113) code show that RS-ORBGRAND consistently improves existing ORB-type GRAND algorithms and lies within 0.10.10.1~dB of a maximum-likelihood decoding lower-bound benchmark at a BLER of 10−610^{-6}10−6.
Polar codes have attracted the attention of numerous researchers in the past decade due to their excellent performance. However, their performance at short block lengths under standard successive cancellation decoding is far from desirable. An effective method to improve the performance at short lengths is CRC precoding followed by successive-cancellation list decoding. Later, Arikan presented polarization-adjusted convolutional (PAC) codes, which further improve the performance of polar codes. In fact, bit-flipping is another post-processing method that can improve decoding performance. In this paper, we propose a novel SCL Bit-Flipping of PAC Codes. We show that better performance can be achieved using list decoding when the list size is the same for PAC codes (N=128, K=64). The decoding performance of our newly proposed PAC-SCLF with a list size of 32 is 0.3 dB better than that of the traditional PAC-SCL with a list size of 32. We set the maximum number of bit flips to 5. The performance of the list size (L=32) for PAC-SCLF is almost the same as the performance of the list size (L=128) for PAC-SCL.
Error-correction codes are indispensable to ensure reliable data transmission in various communication systems. Among these, Polar codes and PAC (Polarized Adjustable Convolutional) codes have gained significant attention due to their capacity-achieving properties and low encoding complexity. This thesis presents a novel decoding technique that combines the Targeted Parity Protection (TPP) algorithm and Dynamic Successive Cancellation List (SCL) decoding to achieve substantial performance improvements while maintaining much lower complexity compared to the conventional Fano decoder. The proposed technique focuses on leveraging Cyclic Redundancy Check (CRC) bits to protect critical information bits, leading to enhanced error correction capabilities. By applying TPP, the decoding process is accelerated by effectively reducing latency and saves computational resources by eliminating wrong codeword candidates at an earlier stage before the decoder favors them. The integration of Dynamic SCL introduces adaptability to the decoder, allowing it to adjust the list size based on the decoding requirements for different code rates and lengths. This adaptability enables efficient use of hardware resources by optimizing the utilization of the decoder storage but also tailors the decoder's performance to each specific scenario, yielding substantial error correction performance gains in both Polar and PAC codes. Extensive simulations and performance evaluations demonstrate the effectiveness of the proposed technique. The results indicate a gain of up to 0.4 dB for Polar codes and up to 0.6 dB for PAC codes compared to the standard SCL decoding approach. It is worth mentioning that such gains are considered substantial for fiber optical communications which is one of the target applications of the new technique. Furthermore, the technique showcases a reduction in decoding complexity, outperforming the traditional Fano decoder.