The LHCb experiment at CERN has decided to optimise its physics reach by removing the first level hardware trigger for 2020 and beyond. In addition to requiring fully redesigned front-end electronics this design creates interesting challenges for the data-acquisition and the rest of the online computing system. Such a system can only be realized within realistic cost using as much off-the-shelf hardware as possible. Relevant technologies evolve very quickly and thus the system design is architecture-centred and tries to avoid to depend too much on specific technologies. In this paper we describe the design, the motivations for various choices and the current favoured options for the implementation, and the status of the R&D. We will cover the back-end readout, which contains the only custom-made component, the event-building, the event-filter infrastructure, and storage.