Computational Complexity Reduced Belief Propagation Algorithm for Polar Code Decoders

The belief propagation algorithm is desirable for a polar code based decoder, because of the potentially low latency and the ability of integration in digital signal processing units or other multi-core processor systems to parallelize the computations. Although belief propagation polar code decoder algorithms have the ability for a highly paralleized implementation, the algorithms require many iterations to achieve a comparable frame error rate and bit error rate with respect to a successive cancellation polar code algorithm. The iterative nature of the belief propagation algorithms also result in a higher computational complexity, i.e. O(I N(2 log(2) N - 1)) compared to the computational complexity O(N log(2) N) of the successive cancellation decoder algorithm. In this paper we propose several simplifications for a simplified belief propagation algorithm for polar code decoders, where the arithmetic complexity of the nodes is reduced. The proposed belief propagation algorithm shows preliminary results of a net reduction of the arithmetic complexity of approximate to 13 %. This reduction is a result of the reduced number of arithmetic operations, i.e., additions, compares, and multiplications, without a lost in error-correcting performance.