Performance Analysis of CRC-Aided Polar Codes with SCL Decoding Algorithm for the Binary Deletion Channel

The performance of the polar coding scheme based on CRC-aided Successive Cancelation List (CA-SCL) decoding algorithm for practical transmission channel applications with deletion properties has been evaluated in this paper. The original information is pre-coded with Cyclic Redundancy Check (CRC) bits which helps to sense the position of deletions with high accuracy. SCL decoding considers these symbols as erasures and retrieves all information bits as well as deleted positions that agree with the CRC. A modification on polar code constructional algorithm is done to apply it in the binary deletion channels (BDC) as conventional polar codes cannot be used directly for channels with memory. The scheme is also applicable to concatenated binary discrete memoryless channels (BDMC) with the d-deletions. Results indicate that the original information can be recovered intact using the proposed scheme and the overall error probability decreases as block size N increases or polar code rate decreases for the variable list sizes. Also, the effect of CRC codelength and generator polynomials on the Block Error Rate (BLER) performance of proposed polar codes in BDC is investigated in this work.