List Decoding of Universal Polar Codes
2020 IEEE International Symposium on Information Theory (ISIT)(2020)
Abstract
A list decoding scheme for universal polar codes is presented. Our scheme applies to the universal polar codes first introduced by ŗaşoğlu 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 Arıkan'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(L·N) and time complexity O(L·Nlog N), where N is the overall blocklength and L is the list size.
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Key words
universal polar codes,polar transforms,list decoding scheme,concatenation codes,slow transform sequence,data structures,space complexity O(L·N),time complexity O(L·Nlog N)
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