Error Detection and Correction in Communication Channels Using Inverse Gray RSNS Codes

A novel number theoretic transform called Inverse Gray Robust Symmetrical Number System (IGRSNS) is proposed for error control coding in this paper. IGRSNS is obtained by modifying Robust Symmetrical Number System (RSNS) that was proposed earlier, using Inverse Gray code property. Due to ambiguities present in each residue, RSNS has a short dynamic range (DR) compared to that in other number systems. The short DR of RSNS enables it to be effectively used for error detection without the addition of any redundant modulus as in Redundant Residue Number System. Although RSNS has a large redundant range, its detection ability is not optimal due to the Gray code property associated with it. In an attempt to overcome this limitation, we have proposed Inverse Gray coding to be combined with RSNS in increasing its effectiveness in error detection. The resulting IGRSNS thus inherits properties of both RSNS and Gray code. Analysis and simulations show that IGRSNS has a near-optimal error detection ability. The potential of IGRSNS for error correction is also investigated. Further, a novel error correction algorithm using one redundant modulus is proposed. Simulations show that the proposed algorithm performs well under all cases of single bit errors.