On the Non-Approximate Successive Cancellation Decoding of Binary Polar Codes With Medium Kernels
Zhiliang Huang, Zongsheng Jiang, Shuihong Zhou, Xiaoyan Zhang · IEEE Access · 2023
Polar codes constructed by large kernels can attain better finite length performance than those originating from Arıkan’s 2 × 2 kernel. However, the successive cancellation (SC) decoding for these polar codes is impractical even for relatively small kernel size ofmbecause complexity of thekernel computationgrows exponentially withm. This research shows whenm> 2, there exists a large amount oflike termsin the kernel computation which yields a ground for facilitating the decoding. By transferring the kernel computation from the probability domain to the likelihood ratio domain (l-domain), the so-calledl-formula method provides an efficient way to combine the like terms in the kernel computation for kernels up to size 11. However, thel-formula method becomes intractable for kernel size beyond 11. To further reduce the computational complexity, this paper proposes aW-formula method which transforms the kernel computation into the probability pair domain (W-domain). Advanced from thel-domain, the numerator and denominator of the likelihood ratio are considered separately, which eases the restrictions of combining like terms. TheW-formula method can combine much more like terms resulting in a significant reduction on the number of sub-formulas for medium kernels (m≤ 16). Furthermore, in theW-domain, sub-formulas become regular and there exist many common sub-formulas whose computations can be shared. Being able to handle kernels of size up to 16, we show that theW-formula based SC decoding achieves a significant complexity reduction over the existing non-approximate SC decoding (thel-formula based SC decoding).