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arXiv:2308.14259 · International Conference on Computer and Communication Systems (ICCCS)

Partially Constrained GRAND of Linear Block Codes

Yixin Wang, Jifan Liang, Xiao Ma

Published Apr 19, 2024• 8 citations
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Abstract

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.

DOI
10.1109/icccs61882.2024.10602848

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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.
This paper is concerned with a universal guessing codeword decoding (GCD) of linear block codes, referred to as locally constrained GCD (LC-GCD), which does not require the online Gaussian elimination (GE). Distinguished from the GCD algorithm, the proposed LC-GCD queries the partial error patterns using the serial list Viterbi algorithm (SLVA) over a trellis specified by a local parity-check matrix, typically reducing the number of queries. Moreover, we introduce a parallel implementation of the LC-GCD algorithm to reduce decoding latency without compromising performance. Numerical results show that the LC-GCD requires a fewer number of queries than the GCD without performance loss, indicating a lower complexity in general. The comparisons with other decoding algorithms are also provided to demonstrate the potential advantage in complexity of the LC-GCD.
This paper is concerned with the locally constrained ordered statistic decoding (LC-OSD) of binary linear block codes, which is a near maximum-likelihood decoding algorithm. Compared with the conventional OSD, the LC-OSD significantly reduces both the maximum and average number of searches. The former is achieved by performing the serial list Viterbi algorithm (SLVA) over a trellis for local constraints on the test error patterns, while the latter is achieved by incorporating tailored early termination criteria. The main objective of this paper is to explore the relationship between the performance of the LC-OSD and decoding parameters, such as the constraint degree and the maximum list size. To this end, we approximate the local parity-check matrix as a totally random matrix and then estimate the performance of the LC-OSD by analyzing the performance of random codes over the channels associated with the most reliable bits (MRBs). The random coding approach enables us to derive an upper bound on the performance and predict the average rank of the transmitted codeword in the list delivered by the LC-OSD. This allows us to balance the constraint degree and the maximum list size for the average (or maximum) time complexity reduction. Simulation results show that the approximation is numerically effective and the random coding approach is powerful. Simulation results also show that the LC-OSD is comparable to other existing decoding algorithms, including soft guessing random additive noise decoding (SGRAND), verifying the efficiency and universality of the LC-OSD.
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 the locally constrained ordered statistic decoding (LC-OSD) of binary linear block codes, which is a near maximum-likelihood decoding algorithm. Compared with the conventional OSD, the LC-OSD significantly reduces both the maximum and average number of searches. The former is achieved by performing the serial list Viterbi algorithm (SLVA) over a trellis for local constraints on the test error patterns, while the latter is achieved by incorporating tailored early termination criteria. The main objective of this paper is to explore the relationship between the performance of the LC-OSD and decoding parameters, such as the constraint degree and the maximum list size. To this end, we approximate the local parity-check matrix as a totally random matrix and then estimate the performance of the LC-OSD by analyzing the performance of random codes over the channels associated with the most reliable bits (MRBs). The random coding approach enables us to derive an upper bound on the performance and predict the average rank of the transmitted codeword in the list delivered by the LC-OSD. This allows us to balance the constraint degree and the maximum list size for the average (or maximum) time complexity reduction. Simulation results show that the approximation is numerically effective and the random coding approach is powerful. Simulation results also show that the LC-OSD is comparable to other existing decoding algorithms, including soft guessing random additive noise decoding (SGRAND), verifying the efficiency and universality of the LC-OSD.
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.
This letter is concerned with a generalized ordered statistic decoding (OSD) algorithm, called locally constrained OSD (LC-OSD). Instead of order-tttreprocessing on the most reliable independent bits, the LC-OSD searches for test error patterns using the serial list Viterbi algorithm (SLVA) over a trellis specified by a local parity-check matrix. We derive several early stopping criteria that can be used to reduce the number of searches. Numerical results show that the LC-OSD algorithm with the proposed stopping criteria has much lower time complexity than the original OSD but incurs negligible performance loss.