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Radiation-induced soft errors are the major reliability threat for digital VLSI systems. In particular, field-programmable gate-array (FPGA)-based designs are more susceptible to soft errors compared to application-specific integrated circuit implementations, since soft errors in configuration bits of FPGAs result in permanent errors in the mapped design. In this paper, we present an analytical approach to estimate the soft error rate of designs mapped into FPGAs. Experimental results show that this technique is orders of magnitude faster than the fault injection method while more than 96% accurate. We also present a highly reliable and low-cost soft error mitigation technique which can significantly improve the availability of FPGA-mapped designs. Experimental results show that, using this technique, the availability of an FPGA mapped design can be increased to more than 99.99%.