# Guessing random additive noise decoding with symbol reliability information (SRGRAND)

## TL;DR

This paper introduces SRGRAND, a universal decoding scheme that uses symbol reliability information to improve decoding performance for various codes, especially in low-latency applications.

## Contribution

It develops a novel universal decoding algorithm incorporating soft symbol reliability, with two decoding methods and analysis of error exponents and complexity.

## Key findings

- SRGRAND outperforms hard detection methods in simulations.
- The algorithms achieve near-ML performance for random codes.
- Error exponents and complexity bounds are established for the proposed methods.

## Abstract

The design and implementation of error correcting codes has long been informed by two fundamental results: Shannon's 1948 capacity theorem, which established that long codes use noisy channels most efficiently; and Berlekamp, McEliece, and Van Tilborg's 1978 theorem on the NP-hardness of decoding linear codes. These results shifted focus away from creating code-independent decoders, but recent low-latency communication applications necessitate relatively short codes, providing motivation to reconsider the development of universal decoders. We introduce a scheme for employing binarized symbol soft information within Guessing Random Additive Noise Decoding, a universal hard detection decoder. We incorporate codebook-independent quantization of soft information to indicate demodulated symbols to be reliable or unreliable. We introduce two decoding algorithms: one identifies a conditional Maximum Likelihood (ML) decoding; the other either reports a conditional ML decoding or an error. For random codebooks, we present error exponents and asymptotic complexity, and show benefits over hard detection. As empirical illustrations, we compare performance with majority logic decoding of Reed-Muller codes, with Berlekamp-Massey decoding of Bose-Chaudhuri-Hocquenghem codes, with CA-SCL decoding of CA-Polar codes, and establish the performance of Random Linear Codes, which require a universal decoder and offer a broader palette of code sizes and rates than traditional codes.