A novel channel polarization on binary discrete memoryless channels
Ying Guo, Moon Ho Lee, Jun Li · 2010
Polar code was proposed by Erdal Arikan as an incentive idea splitting input channels to increase its transition performance. The proposed code that is related to the recursive construction of Reed-Muller codes on the basis of 2-order square matrix G2, can achieve the symmetric capacity of arbitrary binary-input discrete memoryless channels. It has already been mentioned that in principle larger matrices can be employed to construct polar codes with better performances. Motivated by this statement, this paper analyzes a novel polar channel coding and decoding approach by using the 4 × 4 matrix G4= G2⊗2as a core on binary discrete memoryless channels (B-DMC). Based on this polar codes, we characterize its parameters for a given core square matrix G4and derive upper and lower bounds on achievable exponents of derived polar codes based on G(4n) = G4⊗nwith block-length 4n, through which the performance can be improved. Moreover, we give a general family of polar codes based on Reed-Mull codes.