A General Reverse Converter Architecture with Low Complexity and High Performance


IEICE TRANSACTIONS on Information and Systems   Vol.E94-D   No.2   pp.264-273
Publication Date: 2011/02/01
Online ISSN: 1745-1361
DOI: 10.1587/transinf.E94.D.264
Print ISSN: 0916-8532
Type of Manuscript: PAPER
Category: Computer System
residue arithmetic,  reverse converter,  residue number system (RNS),  VLSI architecture,  

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This paper presents a general architecture for designing efficient reverse converters based on the moduli set {2α, 22β+1-1, 2β-1}, where β < α ≤ 2β, by using a parallel implementation of mixed-radix conversion (MRC) algorithm. The moduli set {2α, 22β+1-1, 2β-1} is free from modulo (2k+1)-type which can result in an efficient arithmetic unit for residue number system (RNS). The values of α and β can be selected to provide the required dynamic range (DR) and also to adjust the desired equilibrium between moduli bit-width. The simple multiplicative inverses of the proposed moduli set and also using novel techniques to simplify conversion equations lead to a low-complexity and high-performance general reverse converter architecture that can be used to support different DRs. Moreover, due to the current importance of the 5n-bit DR moduli sets, we also introduced the moduli set {22n, 22n+1-1, 2n-1} which is a special case of the general set {2α, 22β+1-1, 2β-1}, where α=2n and β=n. The converter for this special set is derived from the presented general architecture with higher speed than the fastest state-of-the-art reverse converter which has been designed for the 5n-bit DR moduli set {22n, 22n+1-1, 2n-1}. Furthermore, theoretical and FPGA implementation results show that the proposed reverse converter for moduli set {22n, 22n+1-1, 2n-1} results in considerable improvement in conversion delay with less hardware requirements compared to other works with similar DR.