A method for performing beliefs propagation in a scope of polar code decoding by a decoder , the polar code having a size of N bits and being based on a structure of L sub-polarization stages of N / 2 parallel kernels K i,j , wherein N and L being positive integers such that N = 2 L , wherein i is an index that identifies the sub-polarization stage of the kernel K i,j and j is an index that represents the position of said kernel K i,j among the N / 2 parallel kernels at the sub-polarization stage identified by the index i, the N / 2 parallel kernels at each sub-polarization stage are separated from their neighbour N / 2 parallel kernels at each adjacent sub-polarization stage by a shuffler (Φ i ), characterized in that the decoder performs: - computing (S501) a value of a performance-improvement metric for each kernel K i,j of the structure, wherein the performance-improvement metric is representative of a magnitude in which the input beliefs of the considered kernel K i,j are not in agreement and/or the performance-improvement metric is representative of a magnitude in which the output beliefs of the considered kernel K i,j bring instantaneous information rate to the neighbour kernels of said considered kernel K i,j ; and - sorting (S502) the kernels in a list in decreasing order of the values of the performance-improvement metric ; further in that the decoder performs a beliefs propagation iterative process as follows: - updating (S503) output beliefs for the W top kernels of the list , wherein W is a positive integer, and propagating said output beliefs as input beliefs of neighbour kernel of said W top kernels; - updating (S504) output beliefs for each neighbour kernel of said W top kernels following update of their input beliefs, and re-computing (S505) the performance-improvement metric value for each said neighbour kernel ; - setting (S505) the performance-improvement metric for said W top kernels to a null value; and - re-ordering (S506) the kernels in the list in decreasing order of the values of the performance-improvement metric ; and in that the decoder repeats the beliefs propagation iterative process until a stop condition is met. - computing (S501) a value of a performance-improvement metric for each kernel K i,j of the structure, wherein the performance-improvement metric is representative of a magnitude in which the input beliefs of the considered kernel K i,j are not in agreement and/or the performance-improvement metric is representative of a magnitude in which the output beliefs of the considered kernel K i,j bring instantaneous information rate to the neighbour kernels of said considered kernel K i,j ; and - sorting (S502) the kernels in a list in decreasing order of the values of the performance-improvement metric ; - updating (S503) output beliefs for the W top kernels of the list , wherein W is a positive integer, and propagating said output beliefs as input beliefs of neighbour kernel of said W top kernels; - updating (S504) output beliefs for each neighbour kernel of said W top kernels following update of their input beliefs, and re-computing (S505) the performance-improvement metric value for each said neighbour kernel ; - setting (S505) the performance-improvement metric for said W top kernels to a null value; and - re-ordering (S506) the kernels in the list in decreasing order of the values of the performance-improvement metric ; <EOS>