Sparse Code Multiple Access (SCMA) has been proposed for the newest generation of communication systems, considering overloaded non-orthogonal multiple access. To deal with the overload, SCMA exploits the sparsity feature with the aid of receivers based on the messsage-passing algorithm (MPA). In this paper, we review a low-complexity MPA receiver based on edge selection and gaussian approximation (ESGA). We improve this receiver by proposing a threshold-based criterion for the edge selection (TB-ESGA). With the threshold, the number of interfering neighbors considered in the calculation of each message of the MPA becomes a random variable. We derive the probability of selecting a given number of edges in our strategy and also an expression for the average complexity order, as a function of the threshold. We also show that the proposed threshold results in a better trade-off between complexity and error-rate performance.