Sparse Code Multiple Access (SCMA) is a powerful multiple access technique for future generations of wireless communication where users are allowed to transmit through pre-defined channel resources with a controlled degree of collision. The base-station then recovers all the users' data through some iterative method. The well-known Message-Passing Algorithm (MPA) has excellent performance but has exponential decoding complexity. Alternative decoding algorithms, such as MPA in the log-domain (Log-MPA), have been proposed in the literature aiming to reduce the decoding complexity while not significantly decreasing performance. In recent work, the authors proposed a modification in the conventional Log-MPA by exploring a tree structure associated with the decoding equations. By properly avoiding symbols with low reliability, a pruned tree is obtained, yielding an arbitrary trade-off between performance and complexity in the joint detection. In the present work, we extend this contribution by showing that the advantages of the tree-based decoding algorithm are magnified when SCMA is coupled to an error-correcting code, in particular, a Low-Density-Parity-Check (LDPC) code. Through computer simulations, we show that an improved performance-decoding complexity trade-off is obtained.