Some Comments About CRC Selection for the 5G NR Specification

Abstract

In the 5G new radio technical specification, 6 cyclic redundancy-check (CRC) codes of 6, 11, 16, and 24 check bits are proposed to be used for error detection. In this work, we consider all CRC codes with the proposed number of check bits and determine those having the best error detection performance in the whole interval of lengths for which, according to the specification, they are supposed to work. To evaluate the error detection performance of the investigated codes we calculate the cumulative value $S_{d}$ of the number of codewords of minimum weight for the whole interval of lengths they will work. We choose as the best code the one having the smallest $S_{d}$ . The determined best CRC codes of 6, 11, and 16 check bits have better error detection performance than those proposed in the specification. For 24 check bits, 3 CRC codes are presented, but only one the best for the whole interval of lengths code was not found.

Keywords

• 5G NR specification
• binary symmetric channel
• CRC codes
• undetected error probability