  The thesis is dedicated to studying methods to improve the efficiency of
random access schemes and to facilitate their deployment in machine-type
communications (MTC). First, a joint user activity identification and channel
estimation scheme is designed for grant-free random access systems. We propose
a decentralized transmission control and design a compressed sensing (CS)-based
user identification and channel estimation scheme. We analyze the packet delay
and throughput of the proposed scheme. We also optimize the transmission
control scheme to maximize the system throughput. Second, a random access
scheme, i.e., the coded slotted ALOHA (CSA) scheme, is designed for erasure
channels to improve the system throughput. By deriving the extrinsic
information transfer (EXIT) functions and optimizing their convergence
behavior, we design the code probability distributions for CSA schemes with
repetition codes and maximum distance separable (MDS) codes to maximize the
expected traffic load, under packet erasure and slot erasure channels. We
derive the asymptotic throughput of CSA schemes over the erasure channels for
an infinite frame length, which is verified to well approximate the throughput
for a practical frame length. Third, an efficient data decoding algorithm for
the CSA scheme is proposed to further improve the system efficiency. We present
a low-complexity physical-layer network coding (PNC) method to obtain linear
combinations of collided packets and design an enhanced message-level
successive interference cancellation (SIC) algorithm to exploit the linear
combinations of collided packets. We propose an analytical framework and derive
the system throughput for the proposed scheme. The CSA scheme is further
optimized to maximize the system throughput and energy efficiency.
