摘要
The ＇polar coding＇ proposed by Dr. Ankan can achieve channels （B-DMC）. The generator matrix of polar codes is the symmetric capacity of binary-input discrete memoryless Gu = BuF^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 2^N-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.
The ＇polar coding＇ proposed by Dr. Ankan can achieve channels （B-DMC）. The generator matrix of polar codes is the symmetric capacity of binary-input discrete memoryless Gu = BuF^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 2^N-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.
基金
supported by the National Science and Technology Major Project of the Ministry of Science and Technology of China(2012ZX03001025-004)
the National Natural Science Foundation of China (61271276)
the Natural Science Foundation of Shaanxi Education Bureau (09Jk726)
