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Abstract Non-orthogonal multiple access (NOMA) and multiple-input multiple-output (MIMO) are considered promising techniques to satisfy the demands for high spectrum efficiency and massive connectivity in future wireless communication. In this paper, a novel framework to realize transmission in cell-free massive MIMO-NOMA system with deep integration between MIMO and NOMA is proposed. A new method is developed to divide users into different groups according to their equivalent path loss, and then “group-level successive interference cancellation” (GSIC) is used to cancel the inter-group interference when demodulating the users. Based on the new framework, a rigorous closed-form expression of the achievable sum rate in uplink cell-free massive MIMO-NOMA system is derived. In addition, a parallel iterative method is used to obtain the best power control scheme. Simulations show that the proposed scheme can effectively reduce the total power consumption and outperforms the orthogonal multiple access (OMA) transmission and traditional SIC-NOMA schemes based on user clustering.