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The paper "The Discrete Gaussian for Differential Privacy" (https://arxiv.org/pdf/2004.00010.pdf) includes a simple algorithm for sampling from the discrete Gaussian distribution. The suggested algorithm works by first sampling from a discrete Laplace distribution and then using rejection sampling to produce the discrete Gaussian samples.
The rejection sampling step could be easily appended to the existing discrete Laplace sampler for a quick win.
A more thorough review of the discrete Laplace sampler in the paper could suggest improvements that we could incorporate into our exisiting code.
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