Generator Matrix Based Puncturing in Polar Coding

Abstract

Polar coding proposed by Arikan has attracted attention as a channel coding scheme with low complexity and high error correction capability. In polar coding, the codeword length that can be output by the encoder is $N=2^{n}$, where n is an integer. Codeword lengths other than 2n can be realized by puncturing. In general, polar codes have the characteristics that the decoding error rate differs for each input bit position of the encoder due to the effect of the channel polarization. Therefore, a method has been proposed in which bits to be punctured are composed of only frozen bits. However, to achieve this, frozen bits might be allocated to bit positions which are insusceptible to decoding errors. In this paper, we propose a puncturing method based on the generator matrix of the encoder. In the proposed method, bits to be punctured are selected from those composed of a smaller number of input bits, and we allocate frozen bits to the corresponding input bit positions. By using the proposed method, it is possible to suppress the degradation of the error correction capability when puncturing is used in polar coding. Through computer simulation, we show that the polar coding with our puncturing method outperforms the polar coding with the method in which positions of punctured bits and frozen bits are selected based on the erasure probabilities.