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This paper provides a detailed tutorial on the Cyclic Redundancy Check (CRC)-aided logarithmic successive cancellation stack (Log-SCS) algorithm. We apply these algorithms for the ultrareliable decoding of polar codes, which has relevance for the control channels of the ultra-reliable low latency communication version of the third generation partnership project (3GPP) New Radio (NR). During the exploitation of the CRC codes to improve the error correction performance, we propose a noveldoi:10.1109/access.2019.2901596 fatcat:qtdj7sjpfjhntom3otje443cd4