Generalized Segmented GRAND for Guesswork Reduction in Turbo Product Decoding

2026-07-13

AI Summary

This work addresses the limitations of conventional segmented GRAND, which is constrained by specific parity-check matrix structures, lacks generalizability across arbitrary linear codes, and underutilizes available constraints—leading to high guessing complexity. To overcome these issues, the authors propose GSegGRAND, a generalized framework that extends segmented GRAND to arbitrary linear codes through a novel parity-check matrix construction and codeword structure transformation. The method supports up to $\log_2(n)$ constraints, substantially reducing guessing complexity. Furthermore, this study derives, for the first time, a soft-output expression for GSegGRAND, enabling efficient soft-output decoding of Turbo product codes. Experimental results demonstrate a 75% reduction in hard-decision guessing effort compared to the original approach, with gains reaching up to 88% when soft outputs are incorporated.

Abstract

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.

Problem

• guesswork reduction
• turbo product decoding
• constrained guessing
• parity-check matrix
• GRAND

Innovation

• GSegGRAND
• constrained guessing
• soft-output decoding
• turbo product codes
• guesswork reduction