A Smith-Waterman Algorithm Accelerator Based on Residue Number System

One of the biggest challenges confronting the bioinformatics community is fast and accurate sequence alignment. The Smith-Waterman algorithm (SWA) is one of the several algorithms used in addressing some of these challenges. Though very sensitive in doing sequence alignment, SWA is not used in real life applications due to the computational cost associated with the software implementation. Heuristics methods such as BLAST and FASTA are used, though they do not guarantee accurate sequence alignments. In this paper, we proposed a novel accelerator for addressing the challenge using Residue Number System (RNS). RNS is an integer system with properties that support parallel computation, carry-free addition, borrow-free subtraction, and singlestep multiplication (without partial product). Based on some of these properties, the design of a hardware accelerator for SWA is presented on the assumption that two long strings of DNA can be compared in a divide-andconquer manner. Simulation of a sample design indicates modest hardware consumption and much improved overall speed of the SWA. Introduction The origin of Residue Number System (RNS) can be traced to the puzzle given by Sun Tzu, a Chinese Mathematician and is illustrated as follows: How can we determine a number that has the remainders 2, 3, and 2 when divided by the numbers 7, 5, and 3, respectively? This puzzle, written in the form of a verse in the third century book, Suan -ching by the Chinese scholar Sun Tsu, is perhaps the first documented use of number representation using multiple residues. The answer to this puzzle, 23, is outlined in Sun Tzu’s historic work. The puzzle essentially asked us to 100 Kwame O. Boateng and Edward Y. Baagyere convert the residues ( ) 2 3 2 RNS(7|5|3) into its decimal equivalent. Sun Tsu formulated a method for manipulating these remainders (also known as residues), into integers. This method is regarded today as the Chinese Remainder Theorem (CRT). The CRT, as well as the theory of residue numbers, was set forth in the 19 century by Carl Friedrich Gauss in his celebrated Disquisitiones Arithmetical [1]. This over 1700 – year old number system is making waves in computing recently. Digital systems implemented on residue arithmetic units may play an important role in ultra – speed, dedicated, real – time systems that support pure parallel processing of integer – value data due to its inherent features such as carry free addition, borrow free subtraction, single step multiplication without partial product, parallelisms, and fault tolerant. These interesting properties of RNS have lead to its widespread usage in Digital Signal Processing (DSP) applications such as digital filtering [2], [3], [12], convolution, correlation, Fast Fourier Transform (FFT)[2], [18],[19]. Discrete Cosine Transform (DCT)[4], [5], image processing, cryptography, digital communications[16], [17] and other highly intensive arithmetic applications[8], [18]. However, RNS has not found wide spread usage in general purpose processors due to difficulties associated with magnitude comparison, sign representation, overflow detection, data conversion, moduli selection, division, and other complex arithmetic operations[6], [10], [11], [13]. RNS is defined in terms of a relatively – prime moduli set { }, ..., 3 , 2 , 1 n m m m m that is GCD ( ) 1 , = j m i m for j i≠ , where GCD means greatest common divisor. A binary number X can be represented by the residues ( ) n x x x x ,..., 3 , 2 , 1 , where i x i m X mod = , i m i x < ≤ 0 . Such a representation is unique for any integer [ ] 1 , 0 − ∈ M X , where