Abstract Sparse Code Multiple Access (SCMA) is a non-orthogonal multiple access (NOMA) scheme which allows multi-user communication with massive connectivity. In this paper, we consider an uplink SCMA network of limited resources (time/frequency/power). We seek to answer the following question: what is the maximum number of users that can be admitted in uplink SCMA subject to user-rate constraints? This is termed “user capacity” in communication network. We first obtain a closed form for the lower bound of user capacity which is the first contribution of this work. We then study the general problem of optimizing the resource allocation in terms of codebook assignment and power allocation to maximize the number of users, as well as the total sum rate subject to power, codebook and user-rate constraints. This optimization problem turns out to be non-convex and NP-hard; therefore, we propose an iterative algorithm that provides sub-optimal codebook assignment and power allocation which can efficiently solve this problem. Specifically, another contribution of this work is showing that using swap matching for codebook assignment and Difference of two Convex functions (DC) programming for power allocation efficiently solve the problem yielding better results compared with, e.g., cooperative co-evolutionary particle swarm optimization (CCPSO) algorithm or simple equal power and conventional codebook allocation. Finally, we verify our analytical bound on the user capacity via Monte Carlo simulations and show that the proposed resource allocation algorithm provides significant gains in the number of scheduled users in the system with higher sum rate compared with other schemes. The proposed algorithm can achieve an increment in the number of scheduled users of 45%, and 80% compared with CCPSO and simple equal power and regular codebook allocation, respectively. We also compare our proposed swap matching criterion based on sum rate maximization with the two-sided exchange stable swap matching and simulation results show the effectiveness of the proposed criterion for our problem.