Image Processing Reference
In-Depth Information
16
Study of the Reverse Converters for the
Large Dynamic Range Four-Moduli Sets
Amir Sabbagh Molahosseini 1 and Keivan Navi 2
1 Kerman Branch, Islamic Azad University
2 Shahid Beheshti University
Iran
1. Introduction
The Residue Number System (RNS) is an efficient alternative number system which has
been attracted researchers for over three decades. In RNS, arithmetic operations such as
addition and multiplication can be performed on residues without carry-propagation
between them; resulting in parallel arithmetic and high-speed hardware implementations
(Parhami, 2000; Mohan, 2002; Omondi & Premkumar, 2007). Due to this feature, many
Digital Signal Processing architectures based on RNS have been introduced in the literature
(Soderstrand et al., 1986; Diclaudio et al., 1995; Chaves et al., 2004). In particular, RNS is an
efficient method for the implementation of high-speed finite-impulse response (FIR) filters,
where dominant operations are addition and multiplication. Implementation issues of RNS-
based FIR filters show that performance can be considerably increased, in comparison with
traditional two's complement binary number system (Jenkins et al., 1977; Conway et al.,
2004; Cardarilli et al., 2007).
As described in (Navi et al., 2011) a typical RNS system is based on a moduli set which is
included some pair-wise relatively prime integers. The product of the moduli is defined as
the dynamic range, and it denotes the interval of integers which can be distinctively
represented in RNS. The main components of an RNS system are a forward converter,
parallel arithmetic channels and a reverse converter. The forward converter encodes a
weighted binary number into a residue represented number, with regard to the moduli set;
where it can be easily realized using modular adders or look-up tables. Each arithmetic
channel includes modular adder, subtractor and multiplier for each modulo of set. The
reverse converter decodes a residue represented number into its equivalent weighted binary
number. The arithmetic channels are working in a completely parallel architecture without
any dependency, and this results in a considerable speed enhancement. However; the
overhead of forward and reverse converters can counteract this speed gain, if they are not
designed efficiently. The forward converters can be designed using efficient methods. In
contrast, design of reverse converters have many complexities with many important factors
such as conversion algorithm, type and number of moduli.
An efficient moduli set with moduli of the form of powers of two can greatly reduce the
complexity of the reverse converter as well as arithmetic channels. Due to this, many
different moduli sets have been proposed for RNS which can be categorized based on their
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