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SiPS ... design and implementation - IEEE Workshop on Signal Processing Systems

IGRAND Query Reduction using Even Codes

Arslan Riaz, Jiewei Feng, Kevin Galligan, Muriel Médard, Rabia Tugce Yazicigil, Ken R. Duffy

Published Nov 1, 2025• 3 citations
Publisher

Abstract

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.

DOI
10.1109/sips66314.2025.11261257

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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.
We establish that a large, flexible class of long, high redundancy error correcting codes can be efficiently and accurately decoded with guessing random additive noise decoding (GRAND). Performance evaluation demonstrates that it is possible to construct simple product codes with lengths of approximately 200 to 4000 bits and rates between 0.2 and 0.8 that outperform low-density parity-check (LDPC) codes from the 5G New Radio standard in both AWGN and fading channels. The concatenated structure enables many desirable features, including: low-complexity hardware-friendly encoding and decoding; significant flexibility in length and rate through modularity; and high levels of parallelism in encoding and decoding that enable low latency. Central is the development of a method through which any soft-input (SI) GRAND algorithm can provide soft-output (SO) in the form of an accurate a-posteriori estimate of the likelihood that a decoding is correct or, in the case of list decoding, the likelihood that each element of the list is correct. The distinguishing feature of soft-output GRAND (SOGRAND) is the provision of an estimate that the correct decoding has not been found, even when providing a single decoding. Per-block SO can be converted into accurate per-bit SO by a weighted sum that includes a term for the SI. Implementing SOGRAND adds negligible computation and memory to the existing decoding process, and using it results in a practical, low-latency alternative to LDPC codes.
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.
Error correction techniques traditionally focus on the co-design of restricted code-structures in tandem with code-specific decoders that are computationally efficient when decoding long codes in hardware. Modern applications are, however, driving demand for ultra-reliable low-latency communications (URLLC), rekindling interest in the performance of shorter, higher-rate error correcting codes, and raising the possibility of revisiting universal, code-agnostic decoders. To that end, here we introduce a soft-detection variant of Guessing Random Additive Noise Decoding (GRAND) called Ordered Reliability Bits GRAND that can accurately decode any moderate redundancy block-code. It is designed with efficient circuit implementation in mind, and determines accurate decodings while retaining the original hard detection GRAND algorithm's suitability for a highly parallelized implementation in hardware. ORBGRAND is shown to provide excellent soft decision block error performance for codes of distinct classes (BCH, CA-Polar and RLC) with modest complexity, while providing better block error rate performance than CA-SCL, a state of the art soft detection CA-Polar decoder. ORBGRAND offers the possibility of an accurate, energy efficient soft detection decoder suitable for delivering URLLC in a single hardware realization.
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.
Modern applications are driving demand for ultra-reliable low-latency communications, rekindling interest in the performance of short, high-rate error correcting codes. To that end, here we introduce a soft-detection variant of Guessing Random Additive Noise Decoding (GRAND) called Ordered Reliability Bits GRAND that can decode any moderate redundancy block-code. For a code of n bits, it avails of no more than ⎾log2(n)⏋ bits of code-book-independent quantized soft detection information per received bit to determine an accurate decoding while retaining the original algorithm’s suitability for a highly parallelized implementation in hardware. ORBGRAND is shown to provide similar block error performance for codes of distinct classes (BCH, CA-Polar and RLC) with low complexity, while providing better block error rate performance than CA-SCL, a state of the art soft detection CA-Polar decoder.