A Residue Number System Based Parallel Communication Scheme using Orthogonal Signaling: Part I-System Outline

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Description/Abstract

A novel signaling scheme is presented, where a set of orthogonal signals is transmitted in parallel. The signals are selected according to the so-called residue number system (RNS). Hence the system is essentially a multiple code parallel communication scheme using high modulation alphabets. It is demonstrated that the system’s performance can be substantially improved by exploiting a number of advantageous properties of the RNS arithmetic. In Part I of this paper, we focus our attention on the system’s description and on the associated background of the RNS arithmetic, as well as on the performance evaluation of the residue number system arithmetic, using both nonredundant and redundant moduli based orthogonal signaling schemes, over an additive white Gaussian noise (AWGN) channel. Redundant RNS codes are introduced in order to protect the transmitted information. The detection techniques used in this novel system are different from conventional detectors. Specifically, a novel decision algorithm, referred to as a ratio statistic test, is designed, which implies dropping some of the lowest reliability demodulation outputs before the residue digits are transformed back to binary symbols. This improves the system’s performance. This dropping technique is different from the conventional “errors and erasures” decoding, where the erased symbols (or bits) should be computed and filled during decoding. We argue that the demodulated/decoded information can be obtained by decoding the retained or undiscarded symbols upon exploiting the properties of the RNS arithmetic. Our numerical results show that the proposed scheme constitutes a high-efficiency parallel transmission method for high-bit-rate communication, achieving a coding gain of 2 dB at a bit error rate of $10^{-6}$ over AWGN channels. Index Terms—Code-division multiple access (CDMA), error control, orthogonal signalling, parallel signalling, ratio statistic test, redundant residue number system (RRNS), residue number system (RNS).