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

arXiv:2503.19033 · IEEE International Symposium on Information Theory (ISIT)

A Balanced Tree Transformation to Reduce GRAND Queries

Lukas Rapp, Jiewei Feng, Muriel Médard, Ken R. Duffy

Published Jun 22, 2025• 4 citations
arXivHTMLPDF

Abstract

Guessing Random Additive Noise Decoding (GRAND) and its variants, known for their near-maximum likelihood performance, have been introduced in recent years. One such variant, Segmented GRAND, reduces decoding complexity by generating only noise patterns that meet specific constraints imposed by the linear code. In this paper, we introduce a new method to efficiently derive multiple constraints from the parity check matrix. By applying a random invertible linear transformation and reorganizing the matrix into a tree structure, we extract up to$\log _{2} n$constraints, reducing the number of decoding queries while maintaining the structure of the original code for a code length of$n$. We validate the method through theoretical analysis and experimental simulations.

DOI
10.1109/isit63088.2025.11195277

Related papers

Generalized Segmented GRAND for Guesswork Reduction in Turbo Product Decoding

Lukas Rapp, Jiewei Feng, Muriel Médard +1 more

Guessing random additive noise decoding (GRAND) can efficiently decode any moderately redundant code with near maximum likelihood (ML) performance via noise effect guessing. For binary linear codes, Rowshan and Yuan's Segmented GRAND was the first to show that constrained guessing can reduce guesswork. Although powerful, their approach requires a specific parity-check matrix structure that limits the number of constraints that can be exploited as well as the class of applicable codes. Here we introduce GSegGRAND, a generalization of Segmented GRAND that circumvents its limitations. Built on a novel parity check structure and a transformation that maps codes into this structure, GSegGRAND efficiently incorporates up to log2(n) constraints for a wide range of codes, reducing guesswork by an additional 75% over Segmented GRAND. To leverage that advantage for soft-output decoding, we derive an accurate soft-output (SO) equation for GSegGRAND by extending soft-output GRAND (SOGRAND) to incorporate constrained guessing. Applying this SO to turbo product decoding, GSegGRAND achieves up to 88% guesswork reduction, making it a promising candidate for low-latency decoding in future communication systems.

arXiv:2607.12147•Jul 13, 2026•0 citations

Constrained Error Pattern Generation for GRAND

Mohammad Rowshan, Jinhong Yuan

Maximum-likelihood (ML) decoding can be used to obtain the optimal performance of error correction codes. However, the size of the search space and consequently the decoding complexity grows exponentially, making it impractical to be employed for long codes. In this paper, we propose an approach to constrain the search space for error patterns under a recently introduced near ML decoding scheme called guessing random additive noise decoding (GRAND). In this approach, the syndrome-based constraints which divide the search space into disjoint sets are progressively evaluated. By employing p constraints extracted from the parity check matrix, the average number of queries reduces by a factor of 2pwhile the error correction performance remains intact.

arXiv:2205.11773•IEEE International Symposium on Information Theory (ISIT)•Jun 26, 2022•22 citations

Partially Constrained GRAND of Linear Block Codes

Yixin Wang, Jifan Liang, Xiao Ma

This paper is concerned with a search-number-reduced guessing random additive noise decoding (GRAND) algorithm for linear block codes, called partially constrained GRAND (PC-GRAND). In contrast to the original GRAND, which guesses error patterns without constraints, the PC-GRAND guesses only those error patterns satisfying partial constraints of the codes. In particular, the PC-GRAND takes partial rows of the parity-check matrix as constraints for generating candidate error patterns and the remaining rows as checks for validating the candidates. The number of searches can be reduced when the serial list Viterbi algorithm (SLVA) is implemented for searching over a trellis specified by the partial parity-check matrix. This is confirmed by numerical results. Numerical simulations are also provided for comparison with other decoding algorithms. The parallel implementation of PC-GRAND is also presented in this paper.

arXiv:2308.14259•International Conference on Computer and Communication Systems (ICCCS)•Apr 19, 2024•8 citations

Using a Single Parity-Check to Reduce the Guesswork of Guessing Codeword Decoding

Joseph Griffin, Peihong Yuan, Ken R. Duffy +1 more

Guessing Codeword Decoding (GCD) is a recently proposed soft-input forward error correction decoder for arbitrary binary linear codes. Inspired by recent proposals that leverage binary linear codebook structure to reduce the number of queries made by Guessing Random Additive Noise Decoding (GRAND), for binary linear codes that include a full-message single parity-check (SPC) bit, we show that it is possible to reduce the number of queries made by GCD by a factor of up to 2 with the greatest guesswork reduction realized at lower SNRs, without impacting decoding precision. Codes without a full-message SPC can be modified to include one by changing a column of the generator matrix to obtain a decoding complexity advantage, and we demonstrate that this can often be done without losing decoding precision. To practically avail of the complexity advantage, a noise effect pattern generator capable of producing sequences for given Hamming weights, such as the landslide algorithm developed for ORBGRAND, is necessary.

arXiv:2411.09803•Conference on Information Sciences and Systems•Mar 19, 2025•1 citation

A Parallelization Strategy for GRAND With Optimality Guarantee by Exploiting Error Pattern Tree Representation

Li Wan, Huarui Yin, Wenyi Zhang

Parallelism has become a central concern in modern decoding frameworks aiming to meet stringent throughput and latency requirements. Guessing Random Additive Noise Decoding (GRAND) is a recently proposed decoding paradigm that tests candidate Error Patterns (EPs) until a valid codeword is found. Among its variants, Soft GRAND (SGRAND) achieves maximum-likelihood (ML) decoding but relies on real-time generation and likelihood ordering of EPs, making parallel execution nontrivial under the ML optimality constraint. In this work, we introduce a unified binary tree representation of EPs, termed the EP tree, which formalizes the hierarchical structure underlying SGRAND and Ordered Reliability Bits (ORB) GRAND algorithms, enabling structured organization of EPs and algorithmic-level parallel exploration. Building upon this unified framework, we propose a parallel design of SGRAND that preserves ML optimality while significantly reducing decoding complexity through pruning strategies and tree-based computation. Furthermore, we develop an enhanced ORBGRAND algorithm based on the same EP tree representation, improving decoding performance toward ML while retaining parallel efficiency. Numerical experiments show that the proposed parallel SGRAND achieves a 3.96× reduction in decoding latency compared with its serial counterpart, while the enhanced ORBGRAND achieves a 4.21× speedup, demonstrating the effectiveness of the unified tree-based framework and its strong potential for future algorithmic and hardware optimizations.

arXiv:2510.01813•IEEE Transactions on Communications•Jan 1, 2026•1 citation

IGRAND Query Reduction using Even Codes

Arslan Riaz, Jiewei Feng, Kevin Galligan +3 more

Guessing Random Additive Noise Decoding (GRAND) algorithms can decode any moderate redundancy code of any structure, with integrated circuits demonstrating that it is possible to execute GRAND efficiently in hardware. By using GRAND as a component decoder, its remit has been extended to efficiently decode long, high redundancy product codes via the Iterative GRAND (IGRAND) algorithm in the hard detection setting. Here, by leveraging the property of even codebooks to split the noise effect search space into even and odd Hamming weights for the rows and columns in product code decoding, we demonstrate significant reductions in the number of queries IGRAND makes without any degradation in decoding performance. For IGRAND, we establish that the reduction in query numbers can be significantly higher than for the component code alone, resulting in significant efficiency gains. In particular, simulation results show that the average number of guesses reduces by a factor of 4 at a bit flip probability of $10^{-1.5}$ when the CRC $(64,53)^{2}$ codebook is used, without impacting on its decoding accuracy.

SiPS ... design and implementation - IEEE Workshop on Signal Processing Systems•Nov 1, 2025•3 citations
Guessing Random Additive Noise Decoding (GRAND) and its variants, known for their near-maximum likelihood performance, have been introduced in recent years. One such variant, Segmented GRAND, reduces decoding complexity by generating only noise patterns that meet specific constraints imposed by the linear code. In this paper, we introduce a new method to efficiently derive multiple constraints from the parity check matrix. By applying a random invertible linear transformation and reorganizing the matrix into a tree structure, we extract up tolog⁡2n\log _{2} nlog2​nconstraints, reducing the number of decoding queries while maintaining the structure of the original code for a code length ofnnn. We validate the method through theoretical analysis and experimental simulations.
Guessing random additive noise decoding (GRAND) can efficiently decode any moderately redundant code with near maximum likelihood (ML) performance via noise effect guessing. For binary linear codes, Rowshan and Yuan's Segmented GRAND was the first to show that constrained guessing can reduce guesswork. Although powerful, their approach requires a specific parity-check matrix structure that limits the number of constraints that can be exploited as well as the class of applicable codes. Here we introduce GSegGRAND, a generalization of Segmented GRAND that circumvents its limitations. Built on a novel parity check structure and a transformation that maps codes into this structure, GSegGRAND efficiently incorporates up to log2(n) constraints for a wide range of codes, reducing guesswork by an additional 75% over Segmented GRAND. To leverage that advantage for soft-output decoding, we derive an accurate soft-output (SO) equation for GSegGRAND by extending soft-output GRAND (SOGRAND) to incorporate constrained guessing. Applying this SO to turbo product decoding, GSegGRAND achieves up to 88% guesswork reduction, making it a promising candidate for low-latency decoding in future communication systems.
Maximum-likelihood (ML) decoding can be used to obtain the optimal performance of error correction codes. However, the size of the search space and consequently the decoding complexity grows exponentially, making it impractical to be employed for long codes. In this paper, we propose an approach to constrain the search space for error patterns under a recently introduced near ML decoding scheme called guessing random additive noise decoding (GRAND). In this approach, the syndrome-based constraints which divide the search space into disjoint sets are progressively evaluated. By employing p constraints extracted from the parity check matrix, the average number of queries reduces by a factor of 2pwhile the error correction performance remains intact.
This paper is concerned with a search-number-reduced guessing random additive noise decoding (GRAND) algorithm for linear block codes, called partially constrained GRAND (PC-GRAND). In contrast to the original GRAND, which guesses error patterns without constraints, the PC-GRAND guesses only those error patterns satisfying partial constraints of the codes. In particular, the PC-GRAND takes partial rows of the parity-check matrix as constraints for generating candidate error patterns and the remaining rows as checks for validating the candidates. The number of searches can be reduced when the serial list Viterbi algorithm (SLVA) is implemented for searching over a trellis specified by the partial parity-check matrix. This is confirmed by numerical results. Numerical simulations are also provided for comparison with other decoding algorithms. The parallel implementation of PC-GRAND is also presented in this paper.
Guessing Codeword Decoding (GCD) is a recently proposed soft-input forward error correction decoder for arbitrary binary linear codes. Inspired by recent proposals that leverage binary linear codebook structure to reduce the number of queries made by Guessing Random Additive Noise Decoding (GRAND), for binary linear codes that include a full-message single parity-check (SPC) bit, we show that it is possible to reduce the number of queries made by GCD by a factor of up to 2 with the greatest guesswork reduction realized at lower SNRs, without impacting decoding precision. Codes without a full-message SPC can be modified to include one by changing a column of the generator matrix to obtain a decoding complexity advantage, and we demonstrate that this can often be done without losing decoding precision. To practically avail of the complexity advantage, a noise effect pattern generator capable of producing sequences for given Hamming weights, such as the landslide algorithm developed for ORBGRAND, is necessary.
Parallelism has become a central concern in modern decoding frameworks aiming to meet stringent throughput and latency requirements. Guessing Random Additive Noise Decoding (GRAND) is a recently proposed decoding paradigm that tests candidate Error Patterns (EPs) until a valid codeword is found. Among its variants, Soft GRAND (SGRAND) achieves maximum-likelihood (ML) decoding but relies on real-time generation and likelihood ordering of EPs, making parallel execution nontrivial under the ML optimality constraint. In this work, we introduce a unified binary tree representation of EPs, termed the EP tree, which formalizes the hierarchical structure underlying SGRAND and Ordered Reliability Bits (ORB) GRAND algorithms, enabling structured organization of EPs and algorithmic-level parallel exploration. Building upon this unified framework, we propose a parallel design of SGRAND that preserves ML optimality while significantly reducing decoding complexity through pruning strategies and tree-based computation. Furthermore, we develop an enhanced ORBGRAND algorithm based on the same EP tree representation, improving decoding performance toward ML while retaining parallel efficiency. Numerical experiments show that the proposed parallel SGRAND achieves a 3.96× reduction in decoding latency compared with its serial counterpart, while the enhanced ORBGRAND achieves a 4.21× speedup, demonstrating the effectiveness of the unified tree-based framework and its strong potential for future algorithmic and hardware optimizations.
Guessing Random Additive Noise Decoding (GRAND) algorithms can decode any moderate redundancy code of any structure, with integrated circuits demonstrating that it is possible to execute GRAND efficiently in hardware. By using GRAND as a component decoder, its remit has been extended to efficiently decode long, high redundancy product codes via the Iterative GRAND (IGRAND) algorithm in the hard detection setting. Here, by leveraging the property of even codebooks to split the noise effect search space into even and odd Hamming weights for the rows and columns in product code decoding, we demonstrate significant reductions in the number of queries IGRAND makes without any degradation in decoding performance. For IGRAND, we establish that the reduction in query numbers can be significantly higher than for the component code alone, resulting in significant efficiency gains. In particular, simulation results show that the average number of guesses reduces by a factor of 4 at a bit flip probability of 10−1.510^{-1.5}10−1.5 when the CRC (64,53)2(64,53)^{2}(64,53)2 codebook is used, without impacting on its decoding accuracy.