Error-free VLSI architecture for the 2-D Daubechies 4-tap filter using algebraic integers

In this paper, a multi-encoding approach using wavelet based subband coding is proposed to accomplish error free calculations from exact representation of Daubechies 4-tap wavelet filter coefficients using the algebraic integer (AI) representation. By mapping the irrational coefficients to a convenient AI basis, the proposed architecture is designed employing a parallel channel model having two data paths carrying integer sequences. The computations done in the AI architecture are exactly accurate and are done entirely in a multiplier-free circuit. The design is implemented on a Xilinx Virtex-6 device at 172 MHz and hardware co-simulated with an ML605 board at 100 MHz. AI mapping facilitates simplicity and error-free calculations. The proposed architecture has a single final reconstruction step (FRS). Booth encoding has been adopted at the FRS to minimize the error which can be incurred at this point. This paper provides a hardware and power analysis for different bit lengths. An example output image sequence for the mandrill image is also provided.