Abstract
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.
Highlights
Polar codes, proposed by Arikan [1], are theoretically capacity-achieving codes for symmetric binary-input discrete memoryless channels (B-DMCs)
We theoretically prove that the mapping shortening (MS) algorithm can ensure that the mapping criterion can be adopted reasonably and the S shortened code bits can be known by the receiver
In this paper, we propose a MS algorithm based on a proposed mapping criterion
Summary
Polar codes, proposed by Arikan [1], are theoretically capacity-achieving codes for symmetric binary-input discrete memoryless channels (B-DMCs). A mother polar code is designed for the worst channel and some of the code bits can be punctured or shortened. Later in [9] the authors propose a low-complexity implementation of the US algorithm, which makes the shortened polar codes highly suitable for practical application in future communication systems requiring a large set of polar codes with different lengths and rates. The common characteristic of existing shortening algorithms is that they select shortened bits merely according to the structure of the generator matrix in order to make them known by the receiver. The MS algorithm selects the S most reliable message bits according to the reliability order of the mother polar codes, and sets them all as overcapable bits.
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