Distance spectrum and optimized design of concatenated polar codes

Recent simulation results have shown that serial concatenation with outer codes such as cyclic redundancy check (CRC) or parity check (PC) codes can boost the error correcting performance of polar codes. A theoretical analysis for further explaining where the performance gain comes from is in order. In this paper, we try to provide such an analysis for concatenated polar codes from the distance spectrum point of view, and explore their performances with the use of successive cancellation list decoding (SCLD) and ordered statistics decoding (OSD), respectively. Numerical results show that, compared with OSD, SCLD cannot fully take the advantage of optimized weight distribution for short polar codes with CRC polynomials. We also investigate a hybrid serial concatenation scheme using both CRC and PC codes, which seems to outperform the cases when using only CRC or only PC codes as the outer code. Furthermore, we introduce an improved design for CRC-polar coding scheme by optimizing CRC bit positions and the information bits involved in the CRC functions. Simulation results show that our design leads to an improved weight distribution and thus achieves better error correcting performance.