Polar Subcodes with Improved Weight Spectrum

A method for constructing polar subcodes with a reduced number of low-weight codewords is presented. The proposed approach is based on a method for construction of randomized polar sub codes with optimized error coefficient and explicit generation of all codewords of weight less than twice the minimal non-zero weight of a polar code. Such codewords are enumerated based on the structure of the associated Zhegalkin polynomials. This allows one to construct the dynamic freezing constraints such that almost all of the generated low-weight codewords are excluded from the resulting code. Elimination of low-weight codewords is performed by selection of the coefficients in dynamic freezing constraints, such that the identified low-weight codewords of the parent polar code do not satisfy them. The constructed codes provide similar or better error rate than the polar codes created by methods based on reinforcement learning while being significantly faster to generate. Numerical results, such as the number of low-weight codewords and error rate of codes constructed by the proposed method, are provided.