Sparse code multiple access (SCMA) is a new type of non-orthogonal modulation suggested for 5G systems offering lower bit-error rate and higher spectral efficiency. There are many challenges when designing high throughput SCMA message passing decoders to meet the standards expected from 5G networks. Particularly, the message passing algorithm (MPA) needs many exponential computations to calculate conditional probabilities in case of Gaussian noise channels. This paper describes a sub-optimal modeling of noise using polynomial probability distributions rather than a normal distribution to eliminate the exponential calculations for MPA detectors. Simulation results demonstrate that an estimated SCMA MPA reaches the desired bit-error rate performance with much lower computational/hardware complexity.