CRC Codes as Error Correction Codes

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 softdetection (ORBGRAND) variants can decode any short, high-rate block code, making them suitable for error correction of CRCcoded 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.

Ordered Reliability Bits Guessing Random Additive Noise Decoding

“…Considered as a single code, a CA-Polar code is itself a linear code, albeit one that has no dedicated decoder. As a result, GRAND algorithms have previously established that there is additional performance left to be squeezed of out of them [46].…”

“…The CA-SCL decoder the list size is set to 16, and apply the CA-SCL decoder from the AFF3CT toolbox [66] as our performance reference. Non-standard codes include BCH codes, which can be well designed for low to moderate redundancy but are not designed for decoding with soft information, and CRCs, which are designed for error detection rather than correction but that are being considered for error correction using GRAND [46], [67]. CRCs present desirable low complexity in encoding and code-book checking.…”

“…CRCs present desirable low complexity in encoding and code-book checking. Finally, we also consider RLCs, whose use with GRAND is also being explored [31], [34], [41], [45], [46].…”

“…A preliminary version of ORBGRAND that provides near-ML performance for arbitrary length, moderateredundancy codes and block error rates (BLER) greater than 10 −3 was presented at IEEE ICASSP in 2021 [41]. Its promise for a highly parallelized hardware realization has already resulted in VLSI architectures being proposed [42]- [44] and it has been used to investigate the suitability of both existing and non-traditionally structured codes for use in URLLC [45], [46]. Here we explain the rationale behind ORBGRAND's design and expand on the preliminary conference version to generate near-ML performance for higher SNR.…”

Quantized Guessing Random Additive Noise Decoding

“…2 shows decoding results for a BCH code. BCH codes traditionally only have a hard detection decoder, Berlekamp-Massey, and previous results have shown that hard detection GRAND provides identical block error rate performance [36]. SGRAND, ORBGRAND and QGRAND enable soft detection decoding of BCH codes.…”