On Polar Code Based Bit-level Probabilistic Shaping

Probabilistic shaping (PS) that assigns different probabilities to the constellation points is regarded as a promising scheme to increase spectral efficiency. A distribution matcher (DM) in PS is utilized to transform the equiprobable binary bits into non-equiprobable symbols. In this paper, we propose an efficient bit-level DM (BL-DM) method via polar codes to only shape the most significant bits (MSB). For minimizing the average transmit power and constrained by a given shaping overhead, the optimal probability distributions (PD) of MSBs are theoretically derived by considering the instance of other unshaped bit levels. Correspondingly, the theoretical PD results are simply determined by an intermediate parameter, which is indeed efficient for the indication between the transmitter and receiver. Furthermore, different from the existing design of polar codes-based PS, MSBs with multiple target PD are proposed to be jointly shaped via single polar code. Finally, by conducting link level simulations, the designed polar code based BLU-DM and BLC-DM show significant shaping gain.