Improved error detection and correction capabilities for sequences of basic RNS operations

The residue number system (RNS) has inherent properties that make its use in digital signal processing applications attractive. The data processing of individual RNS residue digits for basic addition, subtraction and multiplication operations can be performed independently in parallel. This parallel processing provides the potential for high-speed computations in applications that are dominated by the use of these basic arithmetic operations. In addition, redundant moduli can be added to a RNS to create an (n,k) redundant residue number system (RRNS) that is capable of providing (n - k) error detection or n-k 2 error correction for the RNS codeword. However, the error detection capability of a traditional RRNS is limited to codeword checking. Extensions to this error detection capability need to be attained in order for the RRNS to be suitable for use in safety-critical applications.; This dissertation describes the Real-Time Concurrent Verification (RECOVER) design methodology that provides the required error detection capability to allow a RRNS based code to be used in safety-critical applications. RECOVER takes advantage of the inherent error tolerance properties of the RRNS and utilizes an independent check process to create a design methodology that provides real-time concurrent verification for a sequence of basic RNS operations using an (n,k) RRNS based code. The error checking provided by RECOVER provides the means to verify that a data processing algorithm is executed correctly, in the correct sequence and that the individual arithmetic operations are actually computed correctly using the correct operands. The (n,k) RRNS based code in RECOVER is capable of performing n error detection and (n - k) error correction.