CRC selection for decoding of CRC-polar concatenated codes

TL;DR

This paper investigates the optimal CRC codes for concatenation with polar codes, identifying those with the best error control performance for certain lengths to enhance decoding efficiency.

Contribution

It systematically analyzes CRC codes of 11 to 19 parity bits to find those with maximum minimum distance, improving polar code concatenation performance.

Findings

CRC codes of degrees 11, 16, and 24 outperform 3GPP standards

Identified CRC codes with maximum minimum distance for various lengths

Presented best results for CRC codes of 24 parity bits

Abstract

An efficient scheme to increase the performance of polar codes at short and moderate block lengths is a concatenation of CRC code and a polar code. In order to obtain better result of the concatenation, a CRC code with best error control performance among all CRC codes with a fixed number of check bits has to be used. In this work we investigate CRC codes of 11 to 19 parity bits and determine those of them which have maximum minimum distance at any length it can be used. For CRC codes of 24 parity bits we were not able to perform complete search and we present the best obtained results. The investigation shows that there are better CRC polynomials of degrees 11, 16 and 24 than those suggested by the 3rd Generation Partnership Project (3GPP).