A FPGA-based architecture for real-time cluster finding in the LHCb silicon pixel detector

The data acquisition system of the LHCb experiment has been substantially upgraded for the LHC Run~3, with the unprecedented capability of reading out and fully reconstructing all proton--proton collisions in real time, occurring with an average rate of 30~MHz, for a total data flow of approximately 32 Tb/s. The high demand of computing power required by this task has motivated a transition to a hybrid heterogeneous computing architecture, where a farm of graphics cores, GPUs, is used in addition to general--purpose processors, CPUs, to speed up the execution of reconstruction algorithms. In a continuing effort to improve real--time processing capabilities of this new DAQ system, also with a view to further luminosity increases in the future, low--level, highly--parallelizable tasks are increasingly being addressed at the earliest stages of the data acquisition chain, using special--purpose computing accelerators. A promising solution is offered by custom--programmable FPGA devices, that are well suited to perform high--volume computations with high throughput and degree of parallelism, limited power consumption and latency. In this context, a two--dimensional FPGA--friendly cluster--finder algorithm has been developed to reconstruct hit positions in the new vertex pixel detector (VELO) of the LHCb Upgrade experiment. The associated firmware architecture, implemented in VHDL language, has been integrated within the VELO readout, without the need for extra cards, as a further enhancement of the DAQ system. This pre--processing allows the first level of the software trigger to accept a 11\% higher rate of events, as the ready--made hit coordinates accelerate the track reconstruction, while leading to a drop in electrical power consumption, as the FPGA implementation requires $\mathcal{O}$(50x) less power than the GPU one. The tracking performance of this novel system, being indistinguishable from a full--fledged software implementation, allows the raw pixel data to be dropped immediately at the readout level, yielding the additional benefit of a 14\% reduction in data flow. The clustering architecture has been commissioned during the start of LHCb Run~3 and it currently runs in real time during physics data taking, reconstructing VELO hit coordinates on--the--fly at the LHC collision rate.