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The novel class of nonbinary maximum minimum distance redundant residue number system (RRNS) codes is invoked in the context of adaptively RRNS coded, symbol-by-symbol adaptive multicarrier modulation, in order to combat the effects of frequency-selective fading inflicted by dispersive wide-band channels. The system's performance can be adjusted in order to maintain a given target bit error rate (BER) and bit per symbol (BPS) performance. The proposed adaptive RRNS scheme outperforms the convolutional constituent code based turbo coded benchmarker system for channel signal-to-noise ratios (SNR) in excess of about 15 dB at a target BER of 10 4 .

Soft-decision based redundant residue number system (RRNS) assisted error control coding is proposed and its performance is evaluated. An RRNS(n,IC) code is a maximum-minimum distance block code, exhibiting identical distance properties to Reed-Solomon (RS) codes. Hence their-error correction capability is given by t = ( n -lc)/2. Different bit mapping methods are proposed, which result in systematic and nonsystematic RRNS encoders. We show that the classic Chase algorithm can be invoked, in order to contrive soft-decision detection for RRNS codes and to exploit the soft channel outputs, which provide the relative reliability of each of the received binary digits. We found that soft decision based RRNS decoding is at least 1.5dB better as compared to hard decision assisted RRNS decoding.

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