Code Design for Iterative Decoding of Multilevel Codes

The code design problem for multilevel coded modulation with iterative decoding (MLCM-ID) has been left unsolved over a decade. In this paper, we define the code design criterion for MLCM-ID based on a novel concept-parametrically-mapped EXIT (PM-EXIT) function. We derive the EXIT functions for MLCM-ID, and present the mathematical work by which the three area theorems of PM-EXIT function are proved. This gives theoretical support of the curve-fitting techniques used in MLCM-ID, and also provides firm proof that the PM-EXIT function design rule allows in principle capacity-achieving code assignment. The simulation results perfectly match the theoretical analysis, and also confirm that the design rule proposed fully exploits the flexibility of MLCM-ID in the choice of codes. Both in theory and simulations, our code design is verified.