Fast polarization construction on binary discrete memoryless channels

An fast channel polarization is proposed to construct code sequences as an idea splitting input channels to increase the cutoff rate. The proposed code sequences related to the recursive construction of Reed-Muller code (RM) on the basis of the matrix G(_2n), can achieve the symmetric capacity of arbitrary binary-input discrete memoryless channels under a low complexity successive cancellation decoding strategy. Based on this polar code sequences, we characterize the exponent of any given square matrix O₂ and derive upper and lower bounds on achievable exponents. The proposed polarization scheme can be decoded with a belief propagation (BP) decoder, which render the scheme analytically tractable and provide powerful low-complexity coding algorithm.