Adding a Rate-1 Third Dimension to Parallel Concatenated Systematic Polar Code: 3D Polar Code

Abstract

In this paper, a three-dimensional polar code (3D-PC) scheme is proposed to improve the error floor performance of parallel concatenated systematic polar code (PCSPC). The proposed 3D-PC is constructed by serially concatenating the PCSPC with a rate-1 third dimension, where only a fraction λ of parity bits of PCSPC are extracted to participate in the subsequent encoding. It takes full advantage of the characteristics of parallel concatenation and serial concatenation. In addition, the convergence behavior of 3D-PC is analyzed by the extrinsic information transfer (EXIT) chart. The convergence loss between PCSPC λ=0 and different λ provides the reference for choosing the value of λ for 3D-PC. Finally, the simulation results confirm that the proposed 3D-PC scheme lowers the error floor.