Concurrent error detection and fault-tolerance in linear digital state variable systems

The problem of error detection and correction (both transient and permanent) in linear digital state variable systems, a very large class of circuits used in digital signal processing and control, is considered. The case of single faulty modules (adders, multipliers, shifters, etc.) is studied, and general circuit data flow graphs (with and without fanout) that realize linear digital state variable systems are analyzed to determine how additional system states might be added to the data flow graph to achieve error detection and correction. It is seen that error detection and correction can be achieved by the addition of a relatively small amount of additional hardware which functions as the checking circuitry. Next, error detection under multiple faulty modules with and without fanout of the module outputs is studied. An analysis tool called the gain matrix is introduced. The problem of fault location and correction of single faults is discussed. Recursive as well as nonrecursive systems can be handled.<>