Message Passing Algorithms for Upper and Lower Bounding the Coded Modulation Capacity in a Large-Scale Linear System

The coded modulation (CM) capacity represents the maximum achievable data rate for a CM scheme assuming optimal decoding at the receiver. It is an important analytical tool, providing theoretic limits for near-optimum transceiver design. Next generation wireless communications systems with the use of new technologies, such as massive antennas and nonorthogonal waveforms, tend to be large scale. However, the conventional ways developed for evaluating the CM capacity of small-scale systems expose exponential complexity with respect to the system's input dimension. Therefore, they become infeasible when the input dimension increases by one or two orders of magnitude in large-scale systems of interest. This letter resorts to a lower and upper bound of the CM capacity, allowing for a computationally efficient evaluation with polynomial complexity. In particular, two message passing algorithms, namely expectation propagation (EP) and variational message passing (VMP), are applied to evaluate the bounds. Two applications are examined in the end. The presented results bring valuable information about the system design, allowing one to evaluate the impact of suboptimal implementation in the overall system performance.