New encoding scheme of polar codes

The ‘polar coding’ proposed by Dr. Arıkan can achieve the symmetric capacity of binary-input discrete memoryless channels (B-DMC). The generator matrix of polar codes is GN = BNF⊗n for N=2n, BN was a permutation matrix. In the article it was realized with an interleaver, so the matrix production of GN was avoided; then the generator matrix was just determined by the matrix F⊗n which was constructed with three sub-matrixes of F⊗n−1 and one 2N−1 order zero matrix, it was deal with fast Hadamard transform (FHT) algorithm. The complexity of the new scheme was reduced sharply, and an iterative algorithm also can be used. The example showed that when N=8, complexity of the encoding scheme was just 16 which is obviously less than that of original encoding scheme 36.