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This paper presents a software-based singles and coincidence processing (SCP) architecture for a digital PET/MR system that is based on SiPM detectors with local digitization coupled to preclinical crystal arrays. Compared with traditional PET systems, our system outputs detector raw data of the individual detector elements via optical Gigabit Ethernet interfaces instead of singles or coincidences. The raw data contains the digitized timestamps, energies, and identifiers of triggered SiPM pixels (hits). Although this approach requires a high bandwidth for the detector data transmission system, the availability of detector raw data offers unique opportunities to employ more accurate and computationally complex, iterative algorithms, which can lead to PET images with higher quality and accuracy. In this paper, we evaluate a parallel software-based SCP for three different crystal position estimation approaches with regard to its real-time capabilities. The SCP receives detector raw data as input and outputs list-mode coincidence data. The investigated PET system features ten singles processing units (SPU), each equipped with two PET detector stacks and a Gigabit Ethernet interface to a data acquisition and processing server (Dell Poweredge R910 equipped with 4× Intel Xeon X7560@2.27 GHz CPUs and 256 GByte DDR3-RAM), allowing lossless real-time acquisition of the entire raw data stream. Using the detector raw data of three previously stored measurements, our results show that the throughput (in Mhits/s) of a center-of-gravity (COG)-based parallel SCP is nearly 4× higher on average than the estimated detector raw data output that is generated from an activity of 37 MBq in the iso-center of the detector ring. Under the same conditions, an iterative maximum-likelihood (ML)-based parallel SCP leads to a 6× higher throughput on average, while a Gaussian-based parallel SCP also results in a 13× higher throughput on average. Compared with a ser- al processing approach, the parallel implementations show speedups of up to 38× on average for the ML-based, 39× on average for Gaussian-based, and up to 34× on average for the COG-based parallelized SCP for the three previously-stored measurements.