  Rate splitting multiple access (RSMA) provides a flexible transmission
framework that can be applied in mobile edge computing (MEC) systems. However,
the research work on RSMA-assisted MEC systems is still at the infancy and many
design issues remain unsolved, such as the MEC server and channel allocation
problem in general multi-server and multi-channel scenarios as well as the user
fairness issues. In this regard, we study an RSMA-assisted MEC system with
multiple MEC servers, channels and devices, and consider the fairness among
devices. A max-min fairness computation offloading problem to maximize the
minimum computation offloading rate is investigated. Since the problem is
difficult to solve optimally, we develop an efficient algorithm to obtain a
suboptimal solution. Particularly, the time allocation and the computing
frequency allocation are derived as closed-form functions of the transmit power
allocation and the successive interference cancellation (SIC) decoding order,
while the transmit power allocation and the SIC decoding order are jointly
optimized via the alternating optimization method, the bisection search method
and the successive convex approximation method. For the channel and MEC server
allocation problem, we transform it into a hypergraph matching problem and
solve it by matching theory. Simulation results demonstrate that the proposed
RSMA-assisted MEC system outperforms current MEC systems under various system
setups.
