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In this paper, the linear quadratic (LQ) optimal control of continuous-time linear time-invariant (LTI) systems with random input gains is studied. One main novelty of this work is the use of channel/controller co-design framework which bridges and integrates the design of the channels and controller. The co-design is carried out by the twist of channel resource allocation, i.e., the channel capacities can be allocated by the control designer subject to a constraint on the overall channel capacity. With this additional design freedom, under certain conditions, a nice analytic solution is obtained for the LQ optimal control problem with random input gains. The optimal control law is a linear state feedback.