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Compact and fast implementations of digital Rayleigh and Ricean variate generators are presented. Polynomial curve fitting is utilized along with a combination of logarithmic and uniform domain segmentation to provide accuracy, compactness and fast variate generation. A typical instantiation of the proposed Rayleigh generator occupies 124 (<;1%) of the configurable slices, two dedicated multipliers (<;1%), and one on-chip block memory (<; 1%) of a Xilinx Virtex-5 field-programmable gate array (FPGA) and operates at 317 MHz, generating 317 million Rayleigh variates per second. The Ricean variate generator implementation on the same device utilizes 366 (<; 1%) of the logical slices, three on-chip block memories ( <;1%), and 11 (2.8%) of the dedicated multipliers. The application of the Rayleigh and Ricean variate generators is demonstrated in a FPGA-based bit error rate simulator that measures at hardware speeds the symbol error rate performance of a typical wireless communication system over Rayleigh and Ricean fading channels.