An Improvement of the Weight Distribution of Polar Codes

Abstract

In this letter, we optimize the weight distribution of the polar codes by exchanging elements in the information set and the frozen set. Based on the work of M. Rowshan et al., we propose two improvements. First, the rows with the twice weight of the minimum weight row are usually selected by the original scheme for the added rows. By our improvement, we select rows with the largest weights such as 4 or 8 times of the minimum weight row. This modification optimizes the weight distribution of polar codes. Furthermore, if there is a case where the selected row weights are the same, the row with higher reliability is selected. Second, we consider the influence of balancing rows for the removed rows. In the original scheme, one core row is removed and then an added row is selected at each step. Our strategy is to fix the position of several added rows, and then remove the core rows or balancing rows globally. This modification can not only reduce the number of Min-Weight codewords but also optimize the channel reliability of the removed rows. Simulation results show that the decoding performance of modified codes has been greatly improved at the practical block error rate of 10^-2 - 10^-3 without changing the code rate of the polar codes.