Study of the Reverse Converters for the Large Dynamic Range Four-Moduli Sets
Amir Sabbagh, Keivan Navi · InTech eBooks · 2011
{2 n -1, 2 n , 2 n +1} (Gallaher et al., 1997;Bhardwaj et al., 1998;Wang et al., 2000;Wang et al., 2002).The main reasons for the popularity of this set are its well-form and balanced moduli.However, the modulo 2 n +1 has lower performance than the other two moduli.Hence, some efforts have been done to substitute the modulo 2 n +1 with other well-form RNS moduli, and the resulted moduli sets are {2 n -1, 2 n , 2 n-1 -1} (Hiasat & Abdel-Aty-Zohdy, 1998;Wang et al., 2000b), {2 n -1, 2 n , 2 n+1 -1} (Mohan, 2007;Lin et al., 2008).The dynamic ranges provided by these three moduli sets are not adequate for recent applications which require higher performance.Two approaches have been proposed to solve this problem.First, using three-moduli sets to provide large dynamic range with some specific forms like {2 , 2 -1, 2 + 1} where < (Molahosseini et al., 2008) and{2 2n , 2 n -1, 2 n+1 - 1} (Molahosseini et al., 2009).Second, using four and five moduli sets to increase dynamic range and parallelism in RNS arithmetic unit.The 4n-bit dynamic range four-moduli sets are {2 n -1, 2 n , 2 n +1, 2 n+1 +1} (Bhardwaj et al., 1999;Mohan & Premkumar, 2007) and {2 n -1, 2 n , 2 n +1, 2 n+1 -1} (Vinod et al., 2000;Mohan & Premkumar, 2007).Although, these four-moduli sets include relatively balanced moduli, their multiplicative inverses are very complicated, and this results in low-performance reverse converters.Furthermore, some recent applications require even more dynamic range than 4n-bit.This demand results in introducing new class of moduli sets which have been called large dynamic range four-moduli sets.The first one is the 5n-bit dynamic range moduli set {2 n -1, 2 n , 2 n +1, 2 2n +1} that was proposed by (Cao et al., 2003).Next, (Zhang et al., 2008) enhanced the dynamic range to 6n-bit, and introduced the set {2 n -1, 2 n +1, 2 2n -2, 2 2n+1 -3}.Moreover, (Molahosseini et al., 2010) proposed the fourmoduli sets {2 n -1, 2 n , 2 n +1, 2 2n+1 -1} and {2 n -1, 2 n +1, 2 2n , 2 2n +1} in 5n and 6n-bit dynamic range, respectively.In this chapter, after an introduction about RNS and reverse conversion algorithms, the architecture of the state-of-the-art reverse cnverters which have been designed for the efficient large dynamic range four-moduli sets {2 n -1, 2 n , 2 n +1, 2 2n +1}, {2 n -1, 2 n +1, 2 2n , 2 2n +1} and {2 n -1, 2 n , 2 n +1, 2 2n+1 -1} will be investigated.Furthermore, a recent contribution about modified version of the four-moduli set {2 n -1, 2 n , 2 n +1, 2 2n+1 -1} that is {2 n -1, 2 n +1, 2 2n , 2 2n+1 -1} will be studied.Finally, we present performance comparison in terms of hardware requirements and conversion delays, between the investigated reverse converters.