Future space missions will require increased on-board computing power to process and compress massive amounts of data. Consequently, embedded multi-core and GPU platforms are considered, which have been shown beneficial for data processing. However, the acceleration of data compression - an inherently sequential task - has not been explored. In this on-going research paper, we parallelize two space compression standards on both CPUs and GPUs using two candidate embedded GPU platforms for space showing that despite the challenging nature of CCSDS algorithms, their parallelization is possible and can provide significant performance benefits.