Systematic redundant residue number system codes: analytical upper bound and iterative decoding performance over AWGN and Rayleigh channels

The novel family of redundant residue number system (RRNS) codes is studied. RRNS codes constitute maximum–minimum distance block codes, exhibiting identical distance properties to Reed–Solomon codes. Binary to RRNS symbol-mapping methods are proposed, in order to implement both systematic and nonsystematic RRNS codes. Furthermore, the upper-bound performance of systematic RRNS codes is investigated, when maximum-likelihood (ML) soft decoding is invoked. The classic Chase algorithm achieving near-ML soft decoding is introduced for the first time for RRNS codes, in order to decrease the complexity of the ML soft decoding. Furthermore, the modified Chase algorithm is employed to accept soft inputs, as well as to provide soft outputs, assisting in the turbo decoding of RRNS codes by using the soft-input/soft-output Chase algorithm. Index Terms—Redundant residue number system (RRNS), residue number system (RNS), turbo detection

Performance Enhancement of MIMO-OFDM using Redundant Residue Number System

Telecommunication industry requires high capacity networks with high data rates which are achieved through utilization of Multiple-Input-Multiple-Output (MIMO) communication along with Orthogonal Frequency Division Multiplexing (OFDM) system. Still, the communication channel suffers from noise, interference or distortion due to hardware design limitations, and channel environment, and to combat these challenges, and achieve enhanced performance; various error control techniques are implemented to enable the receiver to detect any possible received errors and correct it and thus; for a certain transmitted signal power the system would have lower Bit Error Rate (BER). The provided research focuses on Redundant Residue Number System (RRNS) coding as a Forward Error Correction (FEC) scheme that improves the performance of MIMO-OFDM based wireless communications in comparison with current methods as Low-Density Parity Check (LDPC) coders at the transmitter side or equalizers at receiver side. The Bit Error Rate (BER) performance over the system was measured using MATLAB tool for different simulated channel conditions, including the effect of signal amplitude reduction and multipath delay spreading. Simulation results had shown that RRNS coding scheme provides an enhancement in system performance over conventional error detection and correction coding schemes by utilizing the distinct features of Residue Number System (RNS)

Image multiplexing using residue number system coding over MIMO-OFDM communication system

Image transmission over Orthogonal Frequency-Division Multiplexing (OFDM) communication system is prone to distortion and noise due to the encountered High-Peak-to-Average-Power-Ratio (PAPR) generated from the OFDM block. This paper studies the utilization of Residue Number System (RNS) as a coding scheme for digital image transmission over Multiple-Input-Multiple-Output (MIMO) – OFDM transceiver communication system. The use of the independent parallel feature of RNS, as well as the reduced signal amplitude to convert the input signal to parallel smaller residue signals, enable to reduce the signal PAPR, decreasing the signal distortion and the Bit Error Rate (BER). Consequently, improving the received Signal-to-Noise Ratio (SNR) and enhancing the received image quality. The performance analyzed though BER, and PAPR. Moreover, image quality measurement is achieved through evaluating the Mean Squared Error (MSE), Peak Signal to Noise Ratio (PSNR), and the correlation values between the initial and retrieved images. Simulation results had shown the performance of transmission/reception model with and without RNS coding implementation.