On the SC decoder for any polar code of length N =ln

Polar codes can achieve symmetric capacity of a channel with a simple encoder and a successive cancellation (SC) decoder, both with complexity of the order of O(N log N). Polar codes of length N = lⁿ may have a faster polarization rate compared to polar codes of length N = 2ⁿ. In this paper, we introduce a simple and explicit method to obtain the recursive formulas of SC decoder for any polar code of length lⁿ, which helps us better understand the essence of SC decoding. Based on this, we give a complete proof that the simplified SC decoding introduced in previous works can also be applicable for polar codes of all kinds of kernels.