Analysis and Application of Permuted Polar Codes

A special permutation group of polar codes based on $N$/4-cyclic shift is designed and analyzed for practical use. A permutation-transformation equivalence is firstly introduced to transfer the effect of permutation on the codeword side to the uncoded side. Then, we introduce the $N$/4-cyclic shift permutation and analyze the conditions under which it can permute a codeword to another for polar codes that even do not fully respect partial order. We also reveal that the value assignment of frozen bits should follow specific rules related to the permutation pattern. Finally, a novel polar-specific implicit indication method is presented by applying the $N$/4-cyclic shift permutation group to the practical wireless communication scenarios such as Physical Broadcasting Channel (PBCH) of a cellular network, which significantly simplifies the detection algorithm.