  Communication and computation are traditionally treated as separate entities,
allowing for individual optimizations. However, many applications focus on
local information's functionality rather than the information itself. For such
cases, harnessing interference for computation in a multiple access channel
through digital over-the-air computation can notably increase the computation,
as established by the ChannelComp method. However, the coding scheme originally
proposed in ChannelComp may suffer from high computational complexity because
it is general and is not optimized for specific modulation categories.
Therefore, this study considers a specific category of digital modulations for
over-the-air computations, QAM and PAM, for which we introduce a novel coding
scheme called SumComp. Furthermore, we derive an MSE analysis for SumComp
coding in the computation of the arithmetic mean function and establish an
upper bound on the MAE for a set of nomographic functions. Simulation results
affirm the superior performance of SumComp coding compared to traditional
analog over-the-air computation and the original coding in ChannelComp
approaches regarding both MSE and MAE over a noisy multiple access channel.
Specifically, SumComp coding shows approximately $10$ dB improvements for
computing arithmetic and geometric mean on the normalized MSE for low noise
scenarios.
