Research On Key Problem Of Residue Nunmber System—Residue To Binary And Its Application

Residue Number System(RNS) has distinct advantage in Digital Signal Processing(DSP) system design with its deepening study and application. However, the development of RNS is still restricted by several key problems based on Chinese Remainder Theorem(CRT), such as Residue to Binary, Base Extension, Scaling. In this dissertation, the key issues based on CRT in RNS are discussed, and Extension Chinese Remainder Theorem(ECRT) is proposed. Then new algorithms including Residue to Binary, Base Extension, Scaling and chaotic sequence generation based on ECRT are profounded.Chinese Remainder Theorem is the foundation of Residue Number System. In the first part of this dissertation, CRT is introduced and ECRT is deduced. Any number could be the weight factor as long as it satisfies the two conditions in ECRT, which has increased the range of choice of the weight factor in CRT. And because of the above-mentioned contribution, CRT has been a special case of ECRT. ECRT has a smaller calculation width and better parallelism in comparison with CRT and mixed radix conversion.In fixed point calculation DSP, The dynamic range of values has to expand with the calculation. But the expansion is more difficult in RNS because of its non-weight. Base Extension has been used to solve the problem. In the second part, two traditional Base Extension algorithms based on Residue to Binary are analysed. Then a new Base Extension algorithm is proposed. The new algorithm would not change the form of moduli set, and just modular addition operation instead of Look Up Table(LUT) is required for its hardware circuit.Besides, DSP often has large successive cascade multiplication and addition or feedback iteration structure, and the full-precision operations usually require a large dynamic range, which not only ask for extremely high consumption of the hardware, but also could not be achieved, while the scaling operation could solve the problem. In the third part, The unsigned value scaling algorithm is introduced at first, and then two different new scaling algorithms are proposed. One defines a new redundancy radix different from traditional redundancy radix, and on this basis four different scaling formula circumstances are derived, establishing a complete numerical scaling algorithm. The other is based on the non-full precision, reducing the hardware complexity of achieving numerical scaling, and lastly a test is conducted on the accuracies that the different implementations could reach.In the last part, several chaotic mappings are presented. A method of generating chaotic sequence based on RNS and way to function-realization in a chaotic system are proposed, and the concept of perfect remainder functions is constructed in this dissertation. Finally, a method of generating chaotic sequence in RNS based on these above concepts is constructed. According to the standards suggested by the US National Institute of Standards and Technology, a random test is given on the sequence generated based on RNS, while the correlation test is performed as well. The results of the tests show that the sequence has good randomness and correlation.