Achieving PAC Code Performance with SCL Decoding without Extra Computational Complexity

For finite blocklength polar codes, the minimum distance and the number of low weight codewords are essential to obtain good performance under successive cancellation list decoding with moderate and high list sizes. In this paper, we propose a code design method to decrease the number of low weight codewords for some information lengths with a very low computational complexity. In the proposed method, some information bits are encoded by several rows of the polar encoding matrix, i.e., each of the dynamic frozen bits is chosen the same as one of the preceding information bits. The dynamic frozen bit index set is determined by using the connection between the binary representation of the row indices and the number of common 1-bit positions of any given rows. The resulting design is shown to perform as well as polarization-adjusted-convolutional codes [9] under successive cancellation list decoding but with significant computational complexity savings. These findings pave the way for the use of polar codes in applications with stringent complexity and with low energy consumption constraints.