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

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.