Improved Belief Propagation Decoding Algorithm for Short Polar Codes

Abstract

In this paper, we discuss the belief propagation (BP) decoding of polar codes. The performance of polar codes for short lengths is not satisfactory. Therefore, motivated by this we propose a novel technique to improve the performance of polar codes under BP decoding. In order to enhance the reliability of the variable nodes’ propagated messages in BP decoding, the messages are multiplied by previous messages of variable nodes. It is also shown that the BP decoding can be performed on polar codes if the factor graph is constructed according to the parity check matrix of polar codes. Simulation results in binary-input additive white Gaussian noise channel show that using the proposed method a gain of 1–2 dB can be achieved. We also show that the complexity of proposed decoder is same as the complexity of standard BP decoder. Furthermore, we show that the proposed decoder requires about 10–25 iterations less than the standard BP decoder.