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We present a hardware Gaussian noise generator based on the Box-Muller method that provides highly accurate noise samples. The noise generator can be used as a key component in a hardware-based simulation system, such as for exploring channel code behavior at very low bit error rates, as low as 10 ^-12 to 10 ^-13 . The main novelties of this work are accurate analytical error analysis and bit-width optimization for the elementary functions involved in the Box-Muller method. Two 16-bit noise samples are generated every clock cycle and, due to the accurate error analysis, every sample is analytically guaranteed to be accurate to one unit in the last place. An implementation on a Xilinx Virtex-4 XC4VLX100-12 FPGA occupies 1,452 slices, three block RAMs, and 12 DSP slices, and is capable of generating 750 million samples per second at a clock speed of 375 MHz. The performance can be improved by …