SOGRAND Assisted Guesswork Reduction

TL;DR

This paper tackles the issue of high guesswork in GRAND decoders by decoupling guesswork reduction from BLER degradation. It introduces SOGRAND-based dynamic termination to allow list decoding without harming BLER, and then proposes SyGRAND, which uses syndrome information to find candidate codewords early. The key contribution is showing that with approximate orderings and adaptive termination, GRAND can match or exceed the BLER of GCD while achieving large reductions in average guesswork (up to 32x). The results on eBCH and CAPolar codes with CRC demonstrate practical improvements for hardware-friendly decoding and for use in systems requiring fast, reliable decoding.

Abstract

Proposals have been made to reduce the guesswork of Guessing Random Additive Noise Decoding (GRAND) for binary linear codes by leveraging codebook structure at the expense of degraded block error rate (BLER). We establish one can preserve guesswork reduction while eliminating BLER degradation through dynamic list decoding terminated based on Soft Output GRAND's error probability estimate. We illustrate the approach with a method inspired by published literature and compare performance with Guessing Codeword Decoding (GCD). We establish that it is possible to provide the same BLER performance as GCD while reducing guesswork by up to a factor of 32.

Figures (4)

• Figure 1: Binary words are visualized in 2D, where the distance captures the Hamming Distance between words. To decode the hard decision received words $y^{n, (A)}$ and $y^{n, (B)}$GRAND subtracts a sequence of noise patterns informed by the reliabilities (green and orange path). Decoding terminates once the path reaches a codeword. SyGRAND leverages the syndrome that GRAND calculates at each guess, allowing the decoder to identify candidate codewords if it reaches any of the $n+1$ words of its Hamming sphere of radius 1 (purple sphere, upper left), which reduces guesswork (decoding of $y^{n, (A)}$). However, the decoding may not be the ML codeword (decoding of $y^{n, (B)}$), leading to a degradation in BLER. To ameliorate performance loss, dynamic list decoding terminates once the SOGRAND estimated list error probability is below a threshold.
• Figure 2: eBCH (256, 239). Top panel: BLER vs $E_\textnormal{b} / N_0$. Middle panel: average guesswork vs. $E_\textnormal{b} / N_0$. Bottom panel: average guesswork divided by average guesswork of the ORBGRAND, plotted in $\log_2$-scale. Parameters: SyGRAND: $\theta= 0.7, \mathcal{L}_\text{max} = 5$, ORDEPT: $t=450, c_\text{max}=5$.
• Figure 3: eBCH (32, 21). Parameters: SyGRAND: $\theta= 0.71, \mathcal{L}_\text{max} = 3$, ORDEPT: $t=50, c_\text{max}=3$.
• Figure 4: CA-Polar (128, 110). Parameters: SyGRAND: $\theta= 0.54, \mathcal{L}_\text{max} = 3$, ORDEPT: $t=3500, c_\text{max}=3$.