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We present BurstZ, a bandwidth-efficient accelerator platform for scientific computing. While accelerators such as GPUs and FPGAs provide enormous computing capabilities, their effectiveness quickly deteriorates once the working set becomes larger than the on-board memory capacity, causing the performance to become bottlenecked either by the communication bandwidth between the host and the accelerator. Compression has not been very useful in solving this issue due to the difficulty of efficiently compressing floating point numbers, which scientific data often consists of. Most compression algorithms are either ineffective with floating point numbers, or has a high performance overhead. BurstZ is an FPGA-based accelerator platform which addresses the bandwidth issue via a novel hardware-optimized floating point compression algorithm, which we call sZFP. We demonstrate that BurstZ can completely remove the communication bottleneck for accelerators, using a 3D stencil-code accelerator implemented on a prototype BurstZ implementation. Evaluated against hand-optimized implementations of stencil code accelerators of the same architecture, our BurstZ prototype outperformed an accelerator without compression by almost 4X, and even an accelerator with enough memory for the entire dataset by over 2X. BurstZ improved communication efficiency so much, our prototype was even able to outperform the upper limit projected performance of an optimized stencil core with ideal memory access characteristics, by over 2X.