The NOAA GOES-R Hyperspectral Environmental Suite (HES) represents a significant technical advancement in terms of data quality and quantity for environmental and meteorological applications. Given the large volume of data that will be generated by the HES sounder, the use of effective data compression techniques will be beneficial for data transfer and storage. To support the NOAA GOES-R HES data compression studies, we systematically study various lossless compression techniques on the grating-type AIRS data and the interferometer-type NAST-I data. These lossless compression techniques include (i) transform-based (e.g. 3D JPEG2000, 3D SPIHT, PLT), (ii) prediction-based (e.g. 2D JPEG-LS, 2D CALIC), (iii) projection-based (e.g. Lossless PCA, OOMP), and (iv) clustering-based (e.g. PPVQ, FPVQ, AVQLP) methods. To take satellite noisy transmittance into account, we also develop 3DWT-RVLC, which has more superior error resilience than JPEG2000 Part 2. The ultraspectral sounder data features strong correlations in disjoint spectral regions due to the same type of absorbing gases. Robust data preprocessing schemes (e.g. BAR, MST reordering) are also demonstrated to improve compression gains of existing state-of-the-art compression methods such as 3D JPEG2000, 3D SPIHT, 2D JPEG-LS, and 2D CALIC. Furthermore, error-correcting channel codes, including turbo product codes and low-density parity-check codes, are investigated for transmission of compressed ultraspectral sounder data bit streams.