λ-Domain VVC Rate Control Based on Nash Equilibrium

Jielian Lin, Aiping Huang, Tiesong Zhao, Xu Wang, Sam Kwong

Abstract: With a significant Rate-Distortion (RD) improvement than H.265/HEVC, Versatile Video Coding (VVC) has set a new milestone in lossy video compression. It also incorporates the emerging <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\lambda $ </tex-math></inline-formula> -domain rate control technique, aiming at a higher visual quality under a fixed bit constraint. However, the challenge remains how to efficiently allocate bits to all frames and Coding Tree Units (CTUs). In this paper, we propose an effective solution by formulating the above task as a Nash equilibrium problem, where all CTUs are treated as players that bargains with each other. By introducing <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\lambda $ </tex-math></inline-formula> -domain RD models, a constrained optimization is derived with no closed-form solution. We then propose a two-step strategy to address this issue: a Newton method to iteratively calculate an intermediate variable, and a final solution of Nash equilibrium to obtain an approximately optimal <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\lambda $ </tex-math></inline-formula> . Finally, we utilize the derived <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\lambda $ </tex-math></inline-formula> to perform an effective CTU-level bit allocation, which is the very first attempt to introduce Nash equilibrium in <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\lambda $ </tex-math></inline-formula> -domain rate control. Experimental results with Common Test Conditions (CTC) demonstrate the effectiveness and superiority of our method, which outperforms the state-of-the-art CTU-level rate allocation algorithms for VVC.