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arXiv:2104.13663 · International Conference on Communications

CRC Codes as Error Correction Codes

Wei An, Muriel Médard, Ken R. Duffy

Published Jun 1, 2021• 55 citations
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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.

DOI
10.1109/icc42927.2021.9500279

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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.
Error correction techniques traditionally focus on the co-design of restricted code-structures in tandem with code-specific decoders that are computationally efficient when decoding long codes in hardware. Modern applications are, however, driving demand for ultra-reliable low-latency communications (URLLC), rekindling interest in the performance of shorter, higher-rate error correcting codes, and raising the possibility of revisiting universal, code-agnostic decoders. To that end, here we introduce a soft-detection variant of Guessing Random Additive Noise Decoding (GRAND) called Ordered Reliability Bits GRAND that can accurately decode any moderate redundancy block-code. It is designed with efficient circuit implementation in mind, and determines accurate decodings while retaining the original hard detection GRAND algorithm's suitability for a highly parallelized implementation in hardware. ORBGRAND is shown to provide excellent soft decision block error performance for codes of distinct classes (BCH, CA-Polar and RLC) with modest complexity, while providing better block error rate performance than CA-SCL, a state of the art soft detection CA-Polar decoder. ORBGRAND offers the possibility of an accurate, energy efficient soft detection decoder suitable for delivering URLLC in a single hardware realization.
Modern applications are driving demand for ultra-reliable low-latency communications, rekindling interest in the performance of short, high-rate error correcting codes. To that end, here we introduce a soft-detection variant of Guessing Random Additive Noise Decoding (GRAND) called Ordered Reliability Bits GRAND that can decode any moderate redundancy block-code. For a code of n bits, it avails of no more than ⎾log2(n)⏋ bits of code-book-independent quantized soft detection information per received bit to determine an accurate decoding while retaining the original algorithm’s suitability for a highly parallelized implementation in hardware. ORBGRAND is shown to provide similar block error performance for codes of distinct classes (BCH, CA-Polar and RLC) with low complexity, while providing better block error rate performance than CA-SCL, a state of the art soft detection CA-Polar decoder.
The ultra-reliable low-latency communication (URLLC), one of the three main scenarios in the fifth-generation (5G) mobile communication system, is promising to be used in various emerging applications with stringent latency and performance requirements. Recently, the guessing random additive noise decoding (GRAND) is proposed, which can perform well for the URLLC due to its excellent error-correction performance with short code length. Compared to other variants of the GRAND, the ordered reliability bits GRAND (ORBGRAND) can provide a good trade-off between error-correction performance and hardware overhead. In this work, the ORBGRAND with a reduced schedule for polar codes is implemented for the first time, which utilizes the special structure of the parity-check matrix of polar codes to reduce the decoding latency while keeping the error-correction performance unaltered. Besides, the sorter employed in the ORBGRAND decoder is well optimized to reduce the area occupation. At a target frame error rate of 10−5when using a (128, 105) 5G polar code, the average decoding latency of the proposed decoder is only 2.46 ns. Moreover, compared to the state-of-the-art ORBGRAND decoder, the proposed decoder can achieve 15% higher decoding throughput and 71% higher area efficiency without any error-correction performance loss.
Maximum Likelihood (ML) decoding of forward error correction codes is known to be optimally accurate, but is not used in practice as it proves too challenging to efficiently implement. Here we propose a development of a previously described hard detection ML decoder called Guessing Random Additive Noise Decoding (GRAND). We introduce Soft GRAND (SGRAND), a ML decoder that fully avails of soft detection information and is suitable for use with any arbitrary high-rate, short-length block code. We assess SGRAND's performance on Cyclic Redundancy Check (CRC)-aided Polar (CA-Polar) codes, which will be used for all control channel communication in 5G New Radio (NR), comparing its accuracy with CRC-Aided Successive Cancellation List decoding (CA-SCL), a state-of-the-art soft-information decoder specific to CA-Polar codes.
Guessing random additive noise decoding (GRAND) is a recently proposed decoding algorithm which can achieve the error performance of maximum likelihood (ML) decoding. However, GRAND and its variants are only suitable for some short codes with high code rates and have large average query numbers. To mitigate these problems, we propose a successive cancellation list (SCL)-GRAND decoding algorithm for the cyclic redundancy check concatenated polar (CRC-polar) codes. The proposed decoder first divides the received sequence into two subblocks. Then SCL is used to decode the upper subblock and output several candidates into the candidate list. For each candidate, GRAND is used to decode the lower subblock and finally choose the most-likely codeword as the decoded result. Since the SCL is integrated into the SCL-GRAND algorithm, this algorithm can achieve lower complexity and better flexibility than the original GRAND.
Guessing Random Additive Noise Decoding (GRAND) is a universal decoding algorithm that has been recently proposed as a practical way to perform maximum likelihood decoding. It generates a sequence of possible error patterns and applies them to the received vector, checking if the result is a valid codeword. Ordered reliability bits GRAND (ORBGRAND) improves on GRAND by considering soft information received from the channel. Both GRAND and ORBGRAND have been implemented in hardware, focusing on average performance, sacrificing worst case throughput and latency. In this work, an improved pattern schedule for ORBGRAND is proposed. It provides>0.5> 0.5>0.5dB gain over the standard schedule at a block error rate≤10−5\le 10^{-5}≤10−5, and outperforms more complex GRAND flavors with a fraction of the complexity. The proposed schedule is used within a novel code-agnositic decoder architecture: the decoder guarantees fixed high throughput and low latency, making it attractive for latency-constrained applications. It outperforms the worst-case performance of decoders by orders of magnitude, and outperforms many best-case figures. Decoding a code of length 128, it achieves a throughput of 79.21 Gb/s with 58.49 ns latency, yielding better energy efficiency and comparable area efficiency with respect to the state of the art.