Moduli Set Selection and Cost Estimation for RNS-Based FIR Filter and Filter Bank Design

Abstract

Moduli selection is one of the most important issues in the implementation of systems that make use of residue number systems. In this paper, we describe a software tool that assists system designers in moduli selection for the design of RNS-based FIR filters and filter banks. According to some filter specification parameters, the software tool constructs valid moduli sets and calculates their estimated implementations cost in terms of delay, area and power consumption based on results obtained in logic synthesis. Moduli set that is most suitable for the user requirements is selected, together with the estimated cost, to be the output. Outputs of the software tool also indicate that certain level of trade-off among delay, area and power consumption exists for the RNS-based filter and filter bank implementation by using different moduli sets.

Design of Reverse Converters for a New Flexible RNS Five-Moduli Set $$\{ 2^k, 2^n-1, 2^n+1, 2^{n+1}-1, 2^{n-1}-1 \}$$ { 2 k , 2 n - 1 , 2 n + 1 , 2 n + 1 - 1 , 2 n - 1 - 1 } (n Even)

“…Three low-cost classes of moduli (in their order of appearance) are an even modulus m i = 2 b , an odd modulus m i = 2 b − 1, and m i = 2 b + 1, for which hardware implementations of the basic arithmetic circuits can be found: two-operand adders [8,[11][12][13]17,35], multi-operand modular adders (MOMAs) and residue generators (used to build forward converters) [21,23], multipliers [16,34,35], multiplier-accumulators (MACs) and complete residue datapaths [9,14,24,25].…”

Introduction to Residue Number System: Structure and Teaching Methodology

“…If, for the target application, the rate of internal arithmetic operations to conversions is high, arithmetic-friendly should be selected and vice versa. Some hints and useful points about the method of selection and sample moduli sets can be found in [15][16][17][18][19].…”

Design of RNS Reverse Converters with Constant Shifting to Residue Datapath Channels

“…Amongst them, the most hardware efficient and highspeed converters can be designed using the methods from [12,34,35]. To note also that the reverse converter for this moduli set can be also obtained using recently proposed design methods of the converter for the general 3-moduli set {2 n − 1, 2 k , 2 n + 1} with flexible even modulus k [8,36], applied for the special case of k = n. Some specific applications of the 3-moduli set {2 n − 1, 2 n , 2 n + 1} include Finite Input Response (FIR) filters [10,15,24,28]. However, introducing in 2007 the flexible 3-moduli set {2 n − 1, 2 k , 2 n +1}, accompanied by an efficient reverse converter for k ≤ 2n [8], has superseded the 3-moduli set with only a single parameter n. This is because for the dynamic range of 3n−1 bits offered by the former, the equivalent 3-moduli set {2 n−1 − 1, 2 n+1 , 2 n−1 + 1} results in faster and more areaefficient residue datapaths.…”

“…However, introducing in 2007 the flexible 3-moduli set {2 n − 1, 2 k , 2 n +1}, accompanied by an efficient reverse converter for k ≤ 2n [8], has superseded the 3-moduli set with only a single parameter n. This is because for the dynamic range of 3n−1 bits offered by the former, the equivalent 3-moduli set {2 n−1 − 1, 2 n+1 , 2 n−1 + 1} results in faster and more areaefficient residue datapaths. Although, no specific designs have been explicitly considered in the literature, the overall complexity figures of the latter can be easily obtained from complexity characteristics of the MACs mod 2 n ± 1 and 2 k for all the moduli sets concerned, provided in [10,15,25].…”