Efficient Method for Frozen Bits Encoding and Decoding of Polar Code

Abstract

An efficient encoding and decoding of the Polar code utilizing algebraic method to find error patterns is presented in this study. The key idea behind the proposed decoding method is theoretically based on the existence of a one-to-one mapping between the frozen bits and correctable error patterns. This method would help reduce the decoding time for finding error patterns when decoding the (N=8, K=4) and (N=16, K=8) Polar Code. Furthermore, it would reduce the encoding by 91% with lookup table for G3 and G4 matrix and the encoding method can be used to the decoding of Polar Code with algebraic method. Ultimately, the proposed decoding algorithm for Polar codes can be made regular, simple, and suitable for software implementations.