A novel method for error correction using Redundant Residue Number System in digital communication systems

Abstract

Communication channel is highly prone to noise and therefore error correcting codes are required to protect the transmitted data. Residue Number System (RNS) is defined as the representation of an integer in the residue field. Redundant Residue Number System (RRNS) is obtained by adding some redundant residues in the RNS. In RNS, the arithmetic operations are carry free, so errors do not propagate from one residue to other. This enables RRNS to give a promising way to provide a very fast arithmetic in the field of digital computers. The potentiality of the fast RRNS based arithmetic has not yet been explored in communication systems. This paper discusses a single error correction algorithm based on Redundant Residue Number System (RRNS) in communication systems. The practical feasibility of this algorithm is analyzed in terms of Bit Error Rate (BER). The Bit Error Rate (BER) performance of RRNS codes with error correction algorithm for M-ary modulation in an AWGN channel is analyzed and is compared with conventional single bit error correction code, Hamming code. The simulation results show that RRNS codes outperforms Hamming codes in terms of BER.