A real-time FPGA-based cluster finding algorithm for LHCb silicon pixel detector

<!--HTML-->Starting from the next LHC run, the upgraded LHCb High Level Trigger will process events at the full LHC collision rate (averaging 30 MHz). This challenging goal, tackled using a large and heterogeneous computing farm, can be eased addressing lowest-level, more repetitive tasks at the earliest stages of the data acquisition chain. FPGA devices are very well-suited to perform with a high degree of parallelism and efficiency certain computations, that would be significantly demanding if performed on general-purpose architectures. A particularly time-demanding task is the cluster-finding process, due to the 2D pixel geometry of the new LHCb pixel detector. We describe here a custom highly parallel FPGA-based clustering algorithm and its firmware implementation. The algorithm implementation has shown excellent reconstruction quality during qualification tests, while requiring a modest amount of hardware resources. Therefore it can run in the LHCb FPGA readout cards in real time, during data taking at 30 MHz, representing a promising alternative solution to more common CPU-based algorithms.