List-GRAND: A Practical Way to Achieve Maximum Likelihood Decoding

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 article, 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 frame error rate (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 Gb/s. In comparison to ORBGRAND's VLSI implementation, the proposed LGRAND hardware has a 4.84% area overhead.