Fast Linear Equation Solving Algorithm and its Pipelined Hardware Architecture Design for VVC Affine Motion Estimation

The latest video coding standard, versatile video coding (VVC), was developed to achieve higher video compression efficiency and support more media applications than its predecessor, high-efficiency video coding (HEVC). To address nontranslational motion, such as rotation and zooming, affine motion compensation has been employed in VVC during interframe prediction. However, the complexity increases significantly due to a large number of linear equation solving steps during affine motion estimation (AME). To address the problem, this paper proposes a fast linear equation solving algorithm and an accompanying pipelined hardware architecture design. To the best of our knowledge, our work is the first attempt to address the hardware architecture design of the linear equation solving algorithm in affine mode. First, an integer-based division-free algorithm (I-DFA) is proposed to achieve fast equation solving. Then, a novel dynamic scaling algorithm is proposed to compensate for integer computation errors due to overflow problems. Finally, a pipelined and interleaved hardware architecture is proposed to minimize the number of iteration clock cycles and improve the throughput. The proposed algorithm achieves average time savings of 5.3% and 5.7% with only 0.03% and 0.07% increase in the Bjøntegaard delta bit rate (BD-BR) under low-delay P (LDP) and random access (RA) configurations, respectively. The proposed hardware architecture can solve 16.7M six-parameter affine systems of linear equations per second under a working frequency of 100MHz, which represents a 21x improvement compared to the existing methods.