A Mapping Shortening Algorithm for Polar Codes

Shortening is a common way to achieve rate-compatible polar codes. The existing shortening algorithms select shortened bits merely according to the structure of the generator matrix in order to make them known by the receiver. In this paper, we take into account the effect that the shortening has on the capacity of split channels and propose a shortening capacity mapping criterion. Based on the proposed mapping criterion, a mapping shortening (MS) algorithm is proposed. We theoretically prove that the MS algorithm can ensure that the proposed mapping criterion can be adopted reasonably and the shortened bits can be known by the receiver. In addition, the MS algorithm is proved to have the same order of complexity as existing shortening algorithms. What's more, we demonstrate the superiority of the MS algorithm over existing shortened algorithms from the perspective of channel capacity. Finally, the simulation results show that the MS algorithm has a significant advantage over existing shortening algorithms for the bit error rate (BER) and frame error rate (FER) performance under high code rates.