Polar codes with internal edge permutations

Abstract

In this paper, we propose to add one or more internal edge permutations in the Tanner graph of polar codes, shuffling the columns of one or more sub-matrices of the overall transformation matrix of the code. As a consequence, the code changes as compared to the polar code without such inner edge permutations: properly designed permutations lead to an increase of the minimum distance or at least a decrease of the number of codewords (multiplicity) at the minimum distance. In both cases, the error rate performance is significantly improved, without effecting the polarization effect and hence the bit reliabilities.