As the demand for wireless mobile communication services is constantly growing, the need for mobile systems and devices that support much higher data rates is increasing. The available bandwidth is limited and expensive, thus we need new technologies that utilise the available spectrum more efficiently. One way to increase the spectral efficiency of multiple-access communication systems is to cancel the interference from other users. This method is known as successive decoding, successive cancellation, interference cancellation or stripping. It is a low-complexity method that allows achieving optimal rates by cancelling the contribution of already decoded users. It can be implemented for channels in which the receiver has perfect knowledge about the channel. For channels with slow fading, the channel state information is provided by sending a training sequence that is already known at the receiver. In rapidly changing environments, it may be difficult to have channel state information at the receiver. For such cases, it is useful to find a procedure that does not require knowledge of the channel. The main theme in this thesis is to study the method of successive decoding for multiple-access fading channels, without channel state information. As an initial step we determine the capacity region and design the successive decoder for a simple class of binary channels. We find that using successive decoding we can achieve any point on the boundary of the capacity region with single-user codes and without rate splitting. Moreover, we observe that for a family of channels, each point in the capacity region is achieved by decoding the users in the same order. Rayleigh fading channels are used to model the link if there is no line-of-sight between the transmitter and the receiver. We determine bounds for the capacity region of a two-user Rayleigh fading channel, when neither transmitters nor the receiver have channel state information. In an effort towards building capacity achieving codes for our systems, we propose and investigate the use of low-density parity-check (LDPC) codes in a successive decoding scheme. Another method of increasing the spectral efficiency is using multiple antennas. We compare the system throughput of multi-cell multi-antenna CDMA and TDMA systems. We show that in the low-SNR regime, CDMA achieves better performance, while in the high SNR regime, a regime in which we hope to target high spectral efficiencies, TDMA is desirable. Finally we derive a closed form expression for the number of faces of any dimension in a multidimensional polytope with the same form as the capacity region.