Application of Residue Arithmetic in Communication and Signal Processing

Abstract

Residue Number System (RNS) is a non-weighted number system. In RNS, the arithmetic operations are split into smaller parallel operations which are independent of each other. There is no carry propagation between these operations. Hence devices operating in this principle inherit property of high speed and low power consumption. But this property makes overflow detection is very difficult. Hence the moduli set is chosen such that there is no carry generated. In this thesis, the use of residue number system (RNS) is portrayed in designing solution to various applications of Communication and Signal Processing. RNS finds its application where integer arithmetic is authoritative process, since residue arithmetic operates efficiently on integers. New moduli set selection process, magnitude comparison routine and sign detection methods were limed on the onset of this dissertation.
A good example of integer arithmetic is digital image. The pixels are represented by 8 bit unsigned number. Thus the operations are primarily unsigned and restricted to a small range. Hereby, in this thesis, a novel image encryption
technique is depicted. The results show the robustness and timeliness of this technique. This technique is further compared to some of industry standard encryption algorithms for analysis based on robustness, encryption time and various other paradigms.
Filters are signal conditioners. Each filter functions by accepting an input signal, blocking pre-specified frequency components, and passing the original signal minus those components to the output. A lowpass filter allows only low
frequency signals (below some specified cutoff) through to its output, so it can be used to eliminate high frequencies. A novel design approach for a low pass filter based on residue arithmetic was also proposed. Some trite techniques
as well as novel approaches were adopted to solve the design challenges. A technique for mapping the data in another space providing the liberty to work with floating numbers with a precision was adopted.
PN sequence generator based on residue arithmetic is also formulated. This algorithm generates a pseudo-noise sequence which further was used to evince a spread spectrum multiuser communication system. The results are compared with trite techniques like Gold and Kasami sequence generators.