Internal pilot insertion for polar codes

Abstract

Two internal pilot insertion methods are proposed for polar codes to improve their error correction performance. The presented methods are based on a study of the weight distribution of the given polar code. The insertion of pilot bits provided a new way to control the coding rate of the modified polar code on the basis of the Hamming weight properties without sacrificing the code construction and the related channel condition. Rate control is highly demanded by 5G channel coding schemes. Two short-length polar codes were considered in the work with successive cancellation list decoding. The results showed that advantages in the range of 0.1 to 0.75 dB were obtained in the relative tolerance of the modified coded signal to the additive white Gaussian noise and fading channels at a bit error rate of 10⁻⁴. The simulation results also revealed that the performance improvements were possible with a careful insertion of the pilots. The modified polar code with pilot insertion provided performance improvement and offered the control of the coding rate without any added complexity at both the encoder and the decoder.