A new algorithm for single error correction In RRNS

In this paper, we propose a novel algorithm for single error correction in a redundant residue number system (RRNS). First, the pseudo syndromes are introduced to represent the extention of received residues by implementing the parallelism property of the Chinese remainder theory (CRT). And then for each pseudo syndrome, we modify it by canceling a list of specific values parallelly. For each specific value, we define the corresponding result as the assuming syndrome. Under specific conditions there exists one and only one assuming syndrome equal to the actual sydrome. At last, the assuming syndromes is used to locate a unique error through a mapping we will build in advance. The hardware complexity of this new algorithm is O(k) and the latency is O(log₂k).