An RNS based Specific Processor for Computing the Minimum Sum-of-Absolute-Differences

The sum of absolute differences (SAD) is a distance metric commonly used to determine the similarity between two data sets. A very recent method for directly comparing the magnitude of two numbers represented in residue number systems (RNS) leads to the possibility of using modular arithmetic to compute the SAD. In this paper we propose an efficient hardware SAD unit that computes this Manhattan distance independently of each RNS channel. Therefore, the processing time can be reduced by simultaneously exploiting the carry-free characteristic of the modular arithmetic and the new method proposed by the authors of this paper to compare the magnitude of numbers in RNS. The proposed architecture is suitable to implement SAD units in application specific integrated circuit (ASIC) and in field programmable gate array (FPGA). In order to evaluate the performance of the proposed structures a hardware processor for computing the minimum SAD was implemented in a FPGA and ASIC. From the experimental results it was possible to obtain operating frequencies above 200 MHz for XILINX FPGAs XC2VP50-7 and XC4VLX80-12, and 300 MHz for the ASIC implementation. These results allow the implementation of real-time motion estimators for high resolution images according to the most recent standards for video coding.