List Decoding of Universal Polar Codes

Abstract: A list decoding scheme for universal polar codes is presented. Our scheme applies to the universal polar codes first introduced by Sasoglu and Wang, and generalized to processes with memory by the authors. These codes are based on the concatenation of different polar transforms: a sequence of "slow" transforms and Arikan's original "fast" transform. List decoding of polar codes has been previously presented in the context of the fast transform. However, the slow transform is markedly different and requires new techniques and data structures. We show that list decoding is possible with space complexity $O(\mathcal{L} \cdot N)$ and time complexity $O(\mathcal{L} \cdot N \log N)$, where $N$ is the overall blocklength and $\mathcal{L}$ is the list size.