Performance Analysis of Perturbation-enhanced SC decoders

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.