Performance Analysis of Perturbation-enhanced SC decoders
Zhicheng Liu, Liuquan Yao, Shuai Yuan, Guiying Yan, Zhiming Ma, Yuting Liu
TL;DR
This work analyzes how perturbation-enhanced SC decoding affects the delay of the first error position in polar codes. It introduces a $u$-side perturbation model and leverages Gaussian-approximation for LLRs to derive asymptotic results showing that the first error position is either preserved or delayed with probability $\tfrac{1}{2}$ as the code length grows, providing a theoretical justification for observed gains. Simulations on BI-AWGN validate that $y$-side and $u$-side perturbations exhibit similar BLER performance, and that the delay probability converges to $\tfrac{1}{2}$ with increasing $N$. The findings offer insight into why perturbation-enhanced SC decoders maintain or improve performance at long code lengths and point to perturbation-power tuning as a practical direction for finite-length optimization.
Abstract
In this paper, we analyze the delay probability of the first error position in perturbation-enhanced Successive cancellation (SC) decoding for polar codes. Our findings reveal that, asymptotically, an SC decoder's performance does not degrade after one perturbation, and it improves with a probability of $\frac{1}{2}$. This analysis explains the sustained performance gains of perturbation-enhanced SC decoding as code length increases.