Energy-Efficient Approximate Wallace-Tree Multiplier using Significance-Driven Logic Compression

In this paper, we propose an energy-efficient approximate multiplier design approach. Fundamental to this approach is configurable lossy logic compression, coupled with low-cost error mitigation. The logic compression is aimed at reducing the number of product rows using progressive bit significance, and thereby decreasing the number of reduction stages in Wallace-tree accumulation. This accounts for substantially lower number of logic counts and lengths of the critical paths at the cost of errors in lower significant bits. These errors are minimised through a parallel error detection logic and compensation vector. To validate the effectiveness of our approach, multiple 8-bit multipliers are designed and synthesized using Synopses Design Compiler with different logic compression levels. Post synthesis experiments showed the trade-offs between energy and accuracy for these compression levels, featuring up to 70% reduction in power-delay product (PDP) and 60% lower area in the case of a multiplier with 4-bit logic compression. These gains are achieved at a low loss of accuracy, estimated at less than 0.0554 of mean relative error. To demonstrate the impact of approximation on a real application, a case study of image convolution filter was extensively investigated, which showed up to 62% (without error compensation) and 45% (with error compensation) energy savings when processing image with a multiplier using 4-bit logic compression.