List-GRAND: A practical way to achieve Maximum Likelihood Decoding

TL;DR

List-GRAND (LGRAND) enhances ORBGRAND's decoding performance to match ML decoding, offering high throughput and minimal hardware overhead, thus providing a practical solution for reliable, high-speed decoding of linear block codes.

Contribution

The paper introduces List-GRAND (LGRAND), a novel technique that improves ORBGRAND's decoding performance to match SGRAND's ML performance while maintaining hardware efficiency.

Findings

LGRAND improves ORBGRAND's decoding performance by 0.5-0.75 dB.

LGRAND achieves 47.27-51.36 Gbps throughput in VLSI implementations.

Hardware overhead of LGRAND is only 4.84% compared to ORBGRAND.

Abstract

Guessing Random Additive Noise Decoding (GRAND) is a recently proposed universal Maximum Likelihood (ML) decoder for short-length and high-rate linear block-codes. Soft-GRAND (SGRAND) is a prominent soft-input GRAND variant, outperforming the other GRAND variants in decoding performance; nevertheless, SGRAND is not suitable for parallel hardware implementation. Ordered Reliability Bits-GRAND (ORBGRAND) is another soft-input GRAND variant that is suitable for parallel hardware implementation, however it has lower decoding performance than SGRAND. In this paper, we propose List-GRAND (LGRAND), a technique for enhancing the decoding performance of ORBGRAND to match the ML decoding performance of SGRAND. Numerical simulation results show that LGRAND enhances ORBGRAND's decoding performance by $0.5-0.75$ dB for channel-codes of various classes at a target FER of $10^{-7}$. For linear block codes of length $127/128$ and different code-rates, LGRAND's VLSI implementation can achieve an average information throughput of $47.27-51.36$ Gbps. In comparison to ORBGRAND's VLSI implementation, the proposed LGRAND hardware has a $4.84\%$ area overhead.