Scaling Analysis of Multilevel Polar Coded Modulation

In this paper, we analyze and prove the capacity-achieving property of the equivalent asymmetric channels of multilevel polar-coded modulation in view of the scaling assuming regime, which employ some techniques of symmetric channels. Based on the previous framework of the proof of multilevel coding modulation, we apply the scaling exponent to the equivalent asymmetric channels of multilevel polar-coded modulation under the constraint of the finite code length of component polar codes. Then, we prove that the overall capacity is still achievable under the capacity rule of the design concepts of multilevel coding. In order to accomplish reliable communication of the proposed scheme, we combine Gallager's mapping conception and source-channel coding theorems to generate the component polar codes with the optimal input distribution for each equivalent asymmetric channel. The optimal property refers to asymptotic optimization under a total variation distance measure. Finally, we describe the detailed design process of multilevel polar-coded modulation versus multistage decoding applying polar codes as the component codes analytically.