A Low Complexity Encoding Algorithm for Systematic Polar Codes
  Arikan has shown that systematic polar codes (SPC) outperform nonsystematic polar codes (NSPC). However, the performance gain comes at the price of elevated encoding complexity, i.e., compared to NSPC, the available encoding methods for SPC require higher memory and computation. In this letter, we propose an efficient encoding algorithm requiring only $N$ bits of memory and having $\frac{N}{2}\log_2N$ XOR operations. Moreover, the auxiliary variables in the algorithm can share the memory to reduce extra memory requirement. Furthermore, a parallel 2-bit encoding algorithm is also presented to improve the encoding throughput. Remarkably, we show that parallel encoding can be implemented with the same number of XOR operations and memory bits. Finally, the proposed encoding algorithm can be directly used for NSPC with the same complexity. 
Guo Tai Chen, Zhaoyang Zhang, Caijun Zhong, and Liang Zhang
cs.IT math.IT