3D object detection using point cloud (PC) data is essential for perception pipelines of autonomous driving, where efficient encoding is key to meeting stringent resource and latency requirements. PointPillars, a widely adopted bird's-eye view (BEV) encoding, aggregates 3D point cloud data into 2D pillars for fast and accurate 3D object detection. However, the state-of-the-art methods employing PointPillars overlook the inherent sparsity of pillar encoding where only a valid pillar is encoded with a vector of channel elements, missing opportunities for significant computational reduction. Meanwhile, current sparse convolution accelerators are designed to handle only element-wise activation sparsity and do not effectively address the vector sparsity imposed by pillar encoding. In this paper, we propose SPADE, an algorithm-hardware co-design strategy to maximize vector sparsity in pillar-based 3D object detection and accelerate vector-sparse convolution commensurate with the improved sparsity. SPADE consists of three components: (1) a dynamic vector pruning algorithm balancing accuracy and computation savings from vector sparsity, (2) a sparse coordinate management hardware transforming 2D systolic array into a vector-sparse convolution accelerator, and (3) sparsity-aware dataflow optimization tailoring sparse convolution schedules for hardware efficiency. Taped-out with a commercial technology, SPADE saves the amount of computation by 36.3--89.2\% for representative 3D object detection networks and benchmarks, leading to 1.3--10.9$\times$ speedup and 1.5--12.6$\times$ energy savings compared to the ideal dense accelerator design. These sparsity-proportional performance gains equate to 4.1--28.8$\times$ speedup and 90.2--372.3$\times$ energy savings compared to the counterpart server and edge platforms.

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