The Algorithm-Based Fault Tolerance (ABFT) approach transforms a system that does not tolerate a specific type of faults, called the fault-intolerant system, to a system that provides a specific level of fault tolerance, namely recovery. The ABFT philosophy leads directly to a model from which error correction can be developed. By employing an ABFT scheme with effective convolutional code, the design allows high throughput as well as high fault coverage. The ABFT techniques that detect errors rely on the comparison of parity values computed in two ways. The parallel processing of input parity values produce output parity values comparable with parity values regenerated from the original processed outputs and can apply convolutional codes for the redundancy. This method is a new approach to concurrent error correction in fault-tolerant computing systems. This chapter proposes a novel computing paradigm to provide fault tolerance for numerical algorithms. The authors also present, implement, and evaluate early detection in ABFT.
