  In this paper, we study resource allocation algorithm design for multi-user
orthogonal frequency division multiple access (OFDMA) ultra-reliable low
latency communication (URLLC) in mobile edge computing (MEC) systems. To meet
the stringent end-to-end delay and reliability requirements of URLLC MEC
systems, we propose joint uplink-downlink resource allocation and finite
blocklength transmission. Furthermore, we employ a partial time overlap between
the uplink and downlink frames to minimize the end-to-end delay, which
introduces a new time causality constraint. The proposed resource allocation
algorithm is formulated as an optimization problem for minimization of the
total weighted power consumption of the network under a constraint on the
number of URLLC user bits computed within the maximum allowable computation
time, i.e., the end-to-end delay of a computation task. Despite the
non-convexity of the formulated optimization problem, we develop a globally
optimal solution using a branch-and-bound approach based on discrete monotonic
optimization theory. The branch-and-bound algorithm minimizes an upper bound on
the total power consumption until convergence to the globally optimal value.
Furthermore, to strike a balance between computational complexity and
performance, we propose two efficient suboptimal algorithms based on successive
convex approximation and second-order cone techniques. Our simulation results
reveal that the proposed resource allocation algorithm design facilitates URLLC
in MEC systems, and yields significant power savings compared to three baseline
schemes. Moreover, our simulation results show that the proposed suboptimal
algorithms offer different trade-offs between performance and complexity and
attain a close-to-optimal performance at comparatively low complexity.
