Error Detection Strategies for CRC-Concatenated Polar Codes under Successive Cancellation List Decoding

In this work we introduce a framework to study the trade-off between the undetected error rate (UER) and overall frame error rate (FER) of CRC-concatenated polar codes in the short blocklength regime. Three approaches to improve the tradeoff under successive cancellation list (SCL) decoding are outlined. Two techniques are based on the optimum threshold test introduced by Forney in 1968, whereas a third technique partitions the CRC code parity bits in two sets, where one set is used to prune the SCL decoder list, and the other set is used for error detection. The performance of the three schemes is analyzed via Monte Carlo simulations, and compared with a finite-length achievability bound based on Forney's random coding bound.