Conditional Entropy-Based Construction of Multilevel Polar-Coded Modulation With Probabilistic Shaping

Code construction is a critical issue for polar-coded systems to ensure competitive performance. In this letter, we propose a conditional entropy-based method to construct multilevel polar-coded modulation (MLC-PCM) with probabilistic shaping. More specifically, we allocate the bit positions in accordance with their conditional entropies induced by channel and source polarization. We show that a surrogate channel can be used to determine the frozen set in each component polar code efficiently. The remaining positions are assigned to the information and shaping bits by the source Bhattacharyya parameter, where the shaping bits are used to achieve non-uniform channel inputs. Approximate bounds are also derived to evaluate the decoding error probability of the probabilistically shaped MLC-PCM.