On Design of CRC Codes for Polar Codes with Successive Cancellation List Decoding

Concatenation of polar codes with cyclic redundancy check (CRC) codes, together with successive cancellation list (SCL) decoding, is known to he an effective approach that can significantly enhance the performance of the original polar codes. Most of the studies on the concatenation of CRC and polar codes, however, pay little attention to the structure of CRC codes themselves, even though the longer CRC may lead to loss in terms of information rate. In this work, we investigate the effect of CRC length on the CRC-concatenated polar code performance by developing an analytical bound for the frame error rate (FER) after the CRC-assisted list decoding. As a result, we reveal that there is a trade-off between the CRC length and FER performance, and for a given target FER, there is the minimum length of CRC that satisfies the FER constraint in high signal-to-noise ratio (SNR). The validity of our analytical framework is confirmed by extensive simulation over an additive white Gaussian noise (AWGN) channel. The results thus offer a useful guideline when designing CRC codes for polar codes with SCL decoding.