In this paper, we propose a novel joint radio resource allocation and successive interference cancellation (SIC) ordering algorithm for the downlink scenario of a power-domain sparse code multiple access (PSMA) based wireless network. To this end, we formulate a novel joint radio and SIC ordering optimization problem. Our aim is to maximize sum rate over codebook assignment, transmit power, and SIC ordering variables. Since the proposed optimization problem is NP-hard and mathematically intractable, we exploit alternate search method (ASM). Based on this algorithm, the proposed optimization problem is decomposed into three sub-problems, namely, codebook assignment, power allocation, and SIC ordering. To solve the codebook assignment sub-problem, we exploit matching theory and submodularity and compared them from the performance and complexity perspectives. Due to the fact that PD-NOMA-based networks adopt SIC at the receiver side, the proposed SIC ordering algorithm is also studied for this type of networks. Moreover, the proposed algorithms are investigated from the performance, convergence, and computational complexity perspectives. Numerical results show that the proposed SIC ordering method outperforms the conventional one by approximately 48% in the studied NOMA-based networks.