Iterative Decoding of Spatially-Coupled Product Codes using Guessing Random Additive Noise Decoding Algorithms

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.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 SystemsNov 1, 20253 citations

Iterative Decoding of Product Codes Based on Syndrome Decoding of Sub-Codes

Zongwang Li, Youyun Xu, Wentao Song

IEICE Transactions on CommunicationsOct 1, 20021 citation

SOGRAND decoding of LDPC codes

Ken R. Duffy, Jiewei Feng, Lukas Rapp +1 more

Long forward error correction codes are typically constructed by concatenating shorter component codes that are then decoded through iterative Soft-Input Soft-Output (SISO) of their components. The recently introduced Soft Output Guessing Random Additive Noise Decoding (SOGRAND) has been shown to enable accurate SISO component decoding for a broad range of component codes. Here we establish that by specializing its SISO computation to Single Parity Check codes, SOGRAND offers an alternative existing Check Node (CN) update for decoding Low Density Parity Check codes. Simulation results demonstrate similar or better decoding performance than Gallager's sum-product algorithm and norm-min-sum, while offering two distinct low complexity, hardware friendly CN update algorithms.Long forward error correction codes are typically constructed by concatenating shorter component codes that are then decoded through iterative Soft-Input Soft-Output (SISO) of their components. The recently introduced Soft Output Guessing Random Additive Noise Decoding (SOGRAND) has been shown to enable accurate SISO component decoding for a broad range of component codes. Here we establish that by specializing its SISO computation to Single Parity Check codes, SOGRAND offers an alternative existing Check Node (CN) update for decoding Low Density Parity Check codes. Simulation results demonstrate similar or better decoding performance than Gallager's sum-product algorithm and norm-min-sum, while offering two distinct low complexity, hardware friendly CN update algorithms.

arXiv:2607.04045Jul 4, 20260 citations

Ordered Reliability Direct Error Pattern Testing (ORDEPT) Algorithm

Reza Hadavian, Dmitri V. Truhachev, Kamal El‐Sankary +2 more

In this work we introduce a novel soft-decision decoding algorithm for high-rate short error-correction codes. Our results demonstrate that the proposed algorithm improves over the state-of-the-art algorithms, including recently proposed Ordered Reliability Bits Guessing Random Additive Noise Decoding (ORBGRAND), in terms of latency and decoding complexity. Specifically, we demonstrate that the ability of the proposed algorithm to find multiple candidate codewords with a reduced number of low-complexity queries makes it an efficient component decoder for iterative decoding of product-like codes.In this work we introduce a novel soft-decision decoding algorithm for high-rate short error-correction codes. Our results demonstrate that the proposed algorithm improves over the state-of-the-art algorithms, including recently proposed Ordered Reliability Bits Guessing Random Additive Noise Decoding (ORBGRAND), in terms of latency and decoding complexity. Specifically, we demonstrate that the ability of the proposed algorithm to find multiple candidate codewords with a reduced number of low-complexity queries makes it an efficient component decoder for iterative decoding of product-like codes.

GlobecomDec 4, 20235 citations

10^{-1.5}

when the CRC

(64,53)^{2}

codebook is used, without impacting on its decoding accuracy.