  This paper presents the joint reference frame synthesis (RFS) and
post-processing filter enhancement (PFE) for Versatile Video Coding (VVC),
aiming to explore the combination of different neural network-based video
coding (NNVC) tools to better utilize the hierarchical bi-directional coding
structure of VVC. Both RFS and PFE utilize the Space-Time Enhancement Network
(STENet), which receives two input frames with artifacts and produces two
enhanced frames with suppressed artifacts, along with an intermediate
synthesized frame. STENet comprises two pipelines, the synthesis pipeline and
the enhancement pipeline, tailored for different purposes. During RFS, two
reconstructed frames are sent into STENet's synthesis pipeline to synthesize a
virtual reference frame, similar to the current to-be-coded frame. The
synthesized frame serves as an additional reference frame inserted into the
reference picture list (RPL). During PFE, two reconstructed frames are fed into
STENet's enhancement pipeline to alleviate their artifacts and distortions,
resulting in enhanced frames with reduced artifacts and distortions. To reduce
inference complexity, we propose joint inference of RFS and PFE (JISE),
achieved through a single execution of STENet. Integrated into the VVC
reference software VTM-15.0, RFS, PFE, and JISE are coordinated within a novel
Space-Time Enhancement Window (STEW) under Random Access (RA) configuration.
The proposed method could achieve -7.34%/-17.21%/-16.65% PSNR-based BD-rate on
average for three components under RA configuration.
