A paradigm shift from single user to multiuser communications helps improve system capacity for an increasing amount of applications. Such systems such as cellular mobile radio and wireless local area networks are prone to multi-access interference. Although decoding techniques has been developed, the performance of such multi-access systems is severely degraded by increasing the number of users. Network coding increases the performance of such multi-access systems by increasing its diversity over independent or orthogonal channels at least equal to the number of users. A more resource efficient strategy ensures that the number of independent channels are less than the number of users This design also known as Non-Orthogonal Multiple Access (NOMA) provides resource efficiency with the potential of managing interference.

In this thesis, a specific class of Balanced Incomplete Block designs called Steiner designs is analyzed. For this class, the decoding techniques are enhanced by exploiting the structure of these designs. However, decoding criteria for a large number of independent users is prohibitively expensive. Therefore, we provide an optimized way to search through all possible combinations of independent user data. Our work presents decoding users both from a performance oriented and objective oriented viewpoint.

Work in physical layer techniques for non-orthogonal transmission is evolving. The need for finding a structured decoding scheme for large number of designs will pave the way for high data rate transmissions. Also, physical implementation and analysis of decoding techniques for a large number of users will bridge the gap between theory and practice.