The wireless landscape is shifting to include more networks with massive numbers of unattended devices, seeking to distribute their information sporadically. This paradigm shift has spawned a lot of interest in the adaptation of multiple access schemes to accommodate such systems. In particular, slotted ALOHA based systems have been largely considered. Researchers have noted the analogous relationship between erasure coding theory and slotted ALOHA based multiple access schemes. This connection has allowed researchers to leverage erasure coding theory research, and use this research to improve slotted ALOHA based multiple access schemes using successive interference cancellation. In this thesis, we carry on with this line of research, and extend the work to consider slotted ALOHA based schemes with the constraint that the number of users in the system is not known. This constraint is not only novel, but also widely applicable to the modern wireless landscape. In particular, systems that are part of the Internet of Things (IoT) may necessitate systems that perform well even when the number of users in the system is unknown. We propose a transmission strategy for active devices based on Markov chains. In addition, we derive necessary and sufficient conditions for probability distributions to be shaped by such Markov chains. Numerical results show that, even with this constraint, a significant improvement to the performance of slotted ALOHA is attainable. In addition, we seek to explore other novel formulations of the uncoordinated slotted multiple access problem that also do not have knowledge of the number of users in the system, but include multiple access points with overlapping users. For this problem formulation, we show that a shared decoding process between the access points provides substantial performance improvements.