[Paper Review] Some comments about CRC selection for the 5G NR specification

Tsonka Baicheva, Peter Kazakov+1 more|arXiv (Cornell University)|Apr 6, 2021

Coding theory and cryptography4 citations

TL;DR

This paper evaluates the undetected error probability of 5G NR CRC codes across fixed length intervals and proposes improved CRC codes with 6, 11, 16, and 24 check bits that outperform the 5G NR specification's choices. Using an optimization criterion based on minimum undetected error probability across specified length ranges, the authors identify superior polynomials, especially for 24-bit CRCs where three new codes outperform the standardized ones in most of the 25–8448 length range.

ABSTRACT

In this work the undetected error probability performance of the proposed in the technical specification of 5G new radio cyclic redundancy-check codes taking into consideration that they have to work for fixed interval of lengths are investigated. Codes of 6, 11 and 16 check bits with better error detection performance than the proposed in the specification ones are suggested. For 24 check bits the 3 best CRC codes are presented, but no only one best for the whole interval of lengths code was found.

Motivation & Objective

• To evaluate the undetected error probability performance of 5G NR's proposed CRC codes across fixed-length intervals.
• To identify CRC codes with better error detection performance than those specified in 5G NR for 6, 11, 16, and 24 check bits.
• To optimize CRC selection based on the actual length ranges used in 5G NR, rather than general-purpose criteria.
• To provide a comparative analysis using both optimization and speed-up methods from prior work.
• To demonstrate that codes optimal for general ranges may underperform when tailored to specific 5G NR length intervals.

Proposed method

• The authors use the undetected error probability as the primary performance metric, computed over a Binary Symmetric Channel (BSC).
• They apply an optimization criterion based on minimizing the sum of undetected error probabilities $ S_d $ across the specified length interval $[L, M]$.
• The method involves evaluating generator polynomials for their ability to detect errors across all possible error patterns within the length range.
• For 24-bit CRCs, the authors identify the three best-performing polynomials based on $ S_d $, acknowledging that no single code is optimal across all lengths.
• The analysis incorporates minimum distance properties and codeword weight distributions to assess error detection capability.
• The authors compare their results with those from prior work and Koopman’s CRC database to validate performance gains.

Experimental results

Research questions

• RQ1 Do the CRC codes specified in the 5G NR technical specification achieve optimal undetected error probability across their intended length intervals?
• RQ2 Can alternative CRC generator polynomials be found that yield lower undetected error probability than the 5G NR-specified codes for the same length ranges?
• RQ3 How does the performance of the best CRC codes vary across different length intervals, particularly for 24-bit CRCs?
• RQ4 Is there a single optimal 24-bit CRC code for the full 25–8448 length range, or are multiple codes needed?
• RQ5 To what extent do performance gains from optimized codes compensate for minor performance losses at longer lengths?

Key findings

• For 6, 11, and 16 check bits, the authors identify new CRC polynomials that outperform the 5G NR-specified codes across their entire intended length intervals.
• For 24-bit CRCs, three new polynomials—118b933, 125ae5d, and 10f6f6d—achieve better $ S_d $ values than the 5G NR-specified CRC24A, CRC24B, and CRC24C across the 25–8448 length range.
• At length 920, the best-performing new 24-bit CRC codes are between 94% and 100% better than the 5G NR-specified codes in terms of undetected error probability.
• While CRC24A has a minimum distance of 4 for lengths 542–8448, the new codes maintain a minimum distance of 4 from 881–8448 and show superior $ S_d $ performance across shorter lengths.
• The 5G NR-specified CRC24C performs better than the new codes only in the narrow interval [25–164], where it achieves $ S_d = 924 $, compared to the best new code’s $ S_d = 802 $.
• The study confirms that codes optimized for specific length intervals significantly outperform general-purpose or standardized codes when used in their designated ranges.