Non-concurrent error detection and correction in discrete-time LTI dynamic systems

We develop fault-tolerant constructions for discrete-time (DT) linear time-invariant (LTI) dynamic systems that are built out of appropriately interconnected delay, adder and gain elements. More specifically, we extend previously developed techniques, in which error detection and correction was based on concurrent parity checks at the end of each time step, by developing schemes that depend on non-concurrent (e.g., periodic) parity checks. Our approach relies on carefully choosing the redundant dynamics of the fault-tolerant implementation in a way that allows parity checks to capture the evolution of errors in the system and determine the initial value of each error, the time at which it took place and the state variable it originally affected. The resulting (non-concurrent) error detection and identification approach significantly reduces the overhead in terms of error detection, identification and correction operations, thereby relaxing the stringent requirements on the checking mechanism