A decoding algorithm and logic implementation is proposed for fast, low-complexity error correction in environments with a high rate of transient faults as well as hard errors. The circuit is able to correct a single error in one clock cycle, making it suitable for mitigating faults in pipelined digital logic systems. The proposed method is also resilient against internal transient gate errors that may occur within the decoder itself. In the presence of a high input error rate (0.001) and high internal gate fault rate (105), the new decoding algorithm is able to reduce the error probability by two orders of magnitude. An asynchronous implementation is also presented for the new algorithm, which performs iterative error-correction with reduced latency compared to synchronous algorithms.