Hybrid-Radix Approximate CORDIC Multiplier for Error-Resilient Applications

CORDIC is a hardware-efficient algorithm that is often used in digital signal processing to generate a wide variety of linear and transcendental functions. It is an iterative algorithm in which the number of iterations can be controlled to meet the application's accuracy requirements. With approximate computing gaining a lot of impetus in signal processing, the algorithm has been widely used to generate trigonometric and hyperbolic functions. Very recently, the algorithm has also been used to emulate certain linear functions, such as multiplication, albeit with some error. While the use of Radix-2 CORDIC for designing approximate multipliers has been reported, it suffers from performance issues due to its slow convergence. In this paper, we propose a hybrid-radix CORDIC multiplier that combines radix-2 and radix-4 CORDIC to approximate multiplication. The proposed multiplier results in a lot of resource savings and has a comparable error performance as a stand-alone multiplier unit. A distinctive feature of the proposed multiplier is that, unlike the radix-2 CORDIC multiplier, the errors are distributed on both the positive and negative axes. Thus, when used in some error-resilient application that uses repeated multiplication or multiply-and-accumulate operation, the error performance is much better. Evidently, our experimentation with various image enhancement applications reveals that although the hybrid CORDIC multiplier has a higher MED, the PSNR of the enhanced images is much higher than that of the radix-2 CORDIC multiplier.