A non-iterative multiple residue digit error detection and correction algorithm in RRNS

Abstract

Error detection and correction code based on Redundant Residue Number System (RRNS) has a unique advantage that arithmetical processing errors can also be corrected. Existing algorithms for multiple residue digit error correction in RRNS require either large modulo operations to decode the magnitude of the residue digits or variable number of iterative computations to identify the locations of erroneous residue digits. This paper presents an efficient syndrome based multiple residue digit error detection and correction algorithm in RRNS. The received residue digits are divided into three groups from which seven error location categories are defined for all combinations of residue digit errors of any legitimate moduli set. Their error magnitudes are abstracted into three syndromes, which are used to identify the exact error location category and retrieve the residue digit errors concurrently from six lookup tables in no more than three cycles. The syndromes can be computed in parallel by small modulo subtractors, and their uniqueness criteria are proved to be easily fulfilled. The redundant residue space due to the uniqueness criteria can also be relaxed by increasing the number of syndrome computations and lookup tables used for the error decoding according to the number of information moduli.