A residue number system based parallel communication scheme using orthogonal signaling .I. System outline

1 * Acknowledgement: The valued comments and critique of the anonymous Reviewers is gratefully acknowledged. The kind assistance of Kai Yen in finding the distribution of the ratio statistic test is gratefully acknowledged. 2 This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version will be superseded. Abstract A novel signaling scheme is presented, where a set of orthogonal signals is transmitted in parallel, which 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 performance can be substantially improved by exploiting a number of advantageous properties of the RNS arithmetic. In part I of the paper, we focus on the system description, the background of the RNS arithmetic, as well as on the performance evaluation of the residue number system arithmetic, using both non-redundant and redundant moduli based orthogonal signaling schemes, over an AWGN channel. Redundant Residue Number System (RRNS) codes are introduced in order to protect the transmitted information. A novel decision algorithm, referred to as a ratio statistic test (RST) 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 erasured symbols (or bits) should be computed and filled during decoding. It is argued that the demodulated/decoded information can be obtained by decoding the retained or un-discarded symbols upon exploiting the properties of the residue number system arithmetic. Numerical results show that the proposed scheme constitutes a high efficiency parallel transmission method for high-bit-rate communication, achieving a coding gain of 2dB at a BER of 10 −6 over AWGN channels.