An, Wei and Medard, Muriel and Duffy, Ken R.
(2021)
CRC Codes as Error Correction Codes.
In: IEEE International Conference on Communications : [proceedings] (ICC 2021), Montreal, QC, Canada.
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.
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