With Edge Computing and 5G, industrial mobile robots will be able to offload computationally expensive algorithms such as sensor-based localization to the edge. However, multiple robots streaming large volumes of data over the network simultaneously will create network congestion, leading to high latencies and data loss, which can severely impact the robot operation. In this paper, we address this problem from a safety perspective by looking at how much communication can be reduced before risking safety violations due to increased localization uncertainty. We propose a co-design approach that adjusts communication and control jointly according to a requirement on localization uncertainty and show that by satisfying this requirement, safety can also be achieved. The method leverages a data-driven model of how the uncertainty depends on both communication and control. The performance of the optimization problem is evaluated experimentally on an ABB Mobile YuMi® Research Platform robot in both simulations and on hardware, and the results indicate that communication can be reduced without compromising safety.