Efficient Algorithms for Systematic Polar Encoding

Arıkan has laid the foundations of systematic polar codes and has also indicated that the computational complexity order of the systematic polar encoder (SPE) can be the same of a nonsystematic polar encoder (NSPE) i.e., θ(N log N). In this letter, we propose three efficient encoders along with their full pseudocode implementations, all with θ(N log N) complexity. These encoders work for any arbitrary choice of frozen bit indices, and they allow a tradeoff between the number of XOR computations and the number of bits of memory required by the encoder. We show that our best encoder requires exactly the same number of XORs as that of NSPE.