Analysis of Polarization-adjusted Convolutional Codes (PAC): A Source-Channel Coding Method

Polarization-adjusted convolutional (PAC) code improves the error-correction ability of polar codes by concatenating a convolutional transform with polar transform. In this paper, we establish a source-channel coding framework to develop the theory of the optimal rate assignment for PAC codes. In the source-channel coding model, each column of the convolutional matrix corresponds to a source encoder, in which multiple bits are compressed into one polarized channel. According to the source coding theory, the distortion function of each source encoder is derived. With the Shannon coding theorem, the achievable source coding rates are characterized by the polarized channel capacity and the rate distortion function. With the achievable source coding rates, the rate assignment after convolutional transform is obtained. Simulation results show that the PAC codes achieve better rate assignment than polar codes, leading to a better exploitation of the capacity on the insufficiently polarized channels and an improved error-correction performance.