## 1 Introduction
An uncoordinated NOMA scheme is proposed in [16], which is an enhancement of the recently proposed slotted-ALOHA-NOMA protocol that provides high throughput and meets the low complexity requirements of devices in the Internet of Things (IoT). In [17], a novel uncoordinated multiple access protocol, called iterative conflict resolution for the slotted-ALOHA with NOMA is employed to serve a massive number of heterogeneous users. The integration of the slotted-ALOHA and NOMA will become another key idea in the study of random-access protocols. In this paper, a novel frameless slotted-ALOHA protocol combining signature codes and SIC is considered to solve the conflict. Furthermore, the performance of the system is verified under the condition that the maximum number of detectable conflicting users takes the best value of three. When different users' packets conflict, the receiver buffers these conflicting packets temporarily and uses signature codes to identify the set of transmitting users immediately. Then, the receiver sends responses to the users according to the feedback mechanism and requests to retransmit the replicas of the conflicting packets. After a replica is received, the receiver employs SIC to recover all the conflicting packets. Through theoretical analysis, the feedback mechanism with four cases and the probability of each case are given. Taking the number of backlogged users \(N\) in each slot as the system state, a discrete-time Markov chain model with \(M+1\) states is established. According to the change of the number of backlogged users after a slot, the state transition diagram and state transition probability are given. Further, the flow balance equations are deduced. After this, the expressions of throughput, expected number of backlogged users, expected successful transmission probability and average memory size are presented. Finally, the performance of the protocol is simulated. It is found that the theoretical analysis is consistent with the simulation results, which illustrates the effectiveness of the proposed protocol. The main contributions of this work are summarized as follows:  
* A novel frameless slotted-ALOHA protocol is proposed based on the maximum number of detectable conflicting users and takes the best value of three. * To study the proposed protocol, we set up a frameless slotted-ALOHA system based on its fundamental principle. By analyzing the proposed receiver for the slotted-ALOHA system, the feedback mechanism is established. * To analyze the protocol performance, a discrete-time Markov chain model is established with the number of backlogged users in each slot as the state. Moreover, the state transition diagram and flow conservation equations are demonstrated based on the state transition probability. * Based on theoretical analysis, the throughput, average number of backlogged users, average memory size and average successful transmission probability of the proposed protocol is simulated. The rest of this paper is organized as follows. In Section 2, we describe how the protocol works and set the main parameter. In Section 3, a frameless slotted-ALOHA system is established based on the fundamental principle of the proposed protocol. To analyze the system performance, a discrete-time Markov model is shown. We show the expression of the various performance indicators under the steady state in Section 4. The performance of the proposed protocol is simulated on the basis of the theoretical analysis in Section 5.