The real time coding of high resolution JPEG2000 video requires specialized hardware architectures like Field-Programmable Gate Arrays (FPGAs). Commonly, implementations of JPEG2000 in other architectures such as Graphics Processing Units (GPUs) do not attain sufficient throughput because the algorithms employed in the standard are inherently sequential, which prevents the use of fine-grain parallelism needed to achieve the full GPU performance. This paper presents an architecture for an end-to-end wavelet-based video codec that uses the framework of JPEG2000 but introduces distinct modifications that enable the use of fine-grain parallelism for its acceleration in GPUs. The proposed codec partly employs our previous research on the parallelization of two stages of the JPEG2000 coding process. The proposed solution achieves real-time processing of 4K video in commodity GPUs, with much better power-efficiency ratios compared to server-grade Central Processing Unit (CPU) systems running the standard JPEG2000 codec.