CRC Codes as Error Correction Codes

TL;DR

This paper demonstrates that CRC codes, traditionally used for error detection, can be effectively employed for error correction using GRAND decoding, outperforming some existing codes in short, high-rate scenarios.

Contribution

The paper introduces the use of GRAND decoding with CRC codes for error correction, showing it matches or exceeds the performance of established codes like BCH and CA-Polar in certain settings.

Findings

CRC codes with GRAND achieve error correction comparable to BCH codes.

CRC outperforms Polar and CA-Polar codes in short, high-rate scenarios.

GRAND enables low-latency error correction without re-engineering encoders.

Abstract

CRC codes have long since been adopted in a vast range of applications. The established notion that they are suitable primarily for error detection can be set aside through use of the recently proposed Guessing Random Additive Noise Decoding (GRAND). Hard-detection (GRAND-SOS) and soft-detection (ORBGRAND) variants can decode any short, high-rate block code, making them suitable for error correction of CRC-coded data. When decoded with GRAND, short CRC codes have error correction capability that is at least as good as popular codes such as BCH codes, but with no restriction on either code length or rate. The state-of-the-art CA-Polar codes are concatenated CRC and Polar codes. For error correction, we find that the CRC is a better short code than either Polar or CA-Polar codes. Moreover, the standard CA-SCL decoder only uses the CRC for error detection and therefore suffers severe performance degradation in short, high rate settings when compared with the performance GRAND provides, which uses all of the CA-Polar bits for error correction. Using GRAND, existing systems can be upgraded from error detection to low-latency error correction without re-engineering the encoder, and additional applications of CRCs can be found in IoT, Ultra-Reliable Low Latency Communication (URLLC), and beyond. The universality of GRAND, its ready parallelized implementation in hardware, and the good performance of CRC as codes make their combination a viable solution for low-latency applications.