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This paper presents a Long Range (LoRa) physical-layer data aggregation system (LoRaPDA) that aggregates data (e.g., sum, average, min, max) directly in the physical layer. In particular, after coordinating a few nodes to transmit their data simultaneously, the gateway leverages a new multi-packet reception (MPR) approach to compute aggregate data from the phase-asynchronous superimposed signal. Different from the analog approach which requires additional power synchronization and phase synchronization, our MRP-based digital approach is compatible with commercial LoRa nodes and is more reliable. Different from traditional MPR approaches that are designed for the collision decoding scenario, our new MPR approach allows simultaneous transmissions with small packet arrival time offsets, and addresses a new co-located peak problem through the following components: 1) an improved channel and offset estimation algorithm that enables accurate phase tracking in each symbol, 2) a new symbol demodulation algorithm that finds the maximum likelihood sequence of nodes' data, and 3) a soft-decision packet decoding algorithm that utilizes the likelihoods of several sequences to improve decoding performance. Trace-driven simulation results show that the symbol demodulation algorithm outperforms the state-of-the-art MPR decoder by 5.3$\times$ in terms of physical-layer throughput, and the soft decoder is more robust to unavoidable adverse phase misalignment and estimation error in practice. Moreover, LoRaPDA outperforms the state-of-the-art MPR scheme by at least 2.1$\times$ for all SNRs in terms of network throughput, demonstrating quick and reliable data aggregation.