This repository includes two algorithms:

1. The enumerator of minimum weight codewords of polar codes: The algorithm to find the error coefficient (or the number of minimum weight codewords) of Polar Codes is in files err_coeff.m and err_coeff_full.m The MATLAB function err_coeff(I,N) that returns [d_min,A_dmin] where d_min is the minimum Hamming distance (or minimum weight of non-zero codewords) of the polar code with information ste I (constructed with an specific design SNR) and length N, and A_dmin is the number of minimum wieght codewords.

The difference between the two files is that the file err_coeff_full.m construct polar codes using density evolution with GA method and proviles set I to the enumerator function err_coeff(I,N) while err_coeff.m includes only the enumerator and you need to provide set I to the function.

2. The algorithm to reduce the number of minimum weight of polar codes: The set of Python functions to modify a polar code with index set I a.k.a $\mathcal{A}$, code length N and n=log2(N).

Note that the main function is modify_profile. As these functions are taken from a user-defined Python class with modifications, if you find any minor error in it, please let me know.

The details of this procedure can be found on https://arxiv.org/abs/2111.08843

This implementation was added to rate_profile.py in the following repository titled list decoder for polar and PAC codes. https://github.com/mohammad-rowshan/List-Decoder-for-Polar-and-PAC-Codes

Please report any bugs to mrowshan at ieee dot org