Here is what I found looking around for this error message:
Check that the hash of the ISO you downloaded matches the official one. Also try different USB sticks or DVD burners, there may be data corruption on the stick or wear on the drive mechanics you want to rule out.
To rule out hardware issues you can try a different computer, if available. Remember that you can usually install Ubuntu by installing the target harddrive in another computer and complete the installation there, which may be the quickest workaround in such a situation.
Cause analysis and general advice
The cause of the issue seems to be that the USB or SATA device isn't available or detection is too slow at the time the kernel takes over during the boot process, so that it can't find the image of the live OS to load. Similar to the recommendation in the data integrity section above, try burning optical installation media when you are unable to boot from USB and vice versa. If that's not possible because your computer only has USB 3.0 ports and no internal optical drive, try booting from an integrated SD card reader. Also look out for available firmware updates for your computer that may fix the issue. If you are trying to install from an ISO of an older release, then please try the latest ISO.
As a last resort you can try to use the minimal ISO, which doesn't seem to load another filesystem except initrd but requires a working Internet connection for installation. I would recommend this for Intel Macs from Apple that have this issue.
Hardware issues on laptops and desktops
There seem to be issues on laptops from Dell, Lenovo, Toshiba, Sony and may be other manufacturers. Non-custom built desktops may also be affected and as far as I am aware this is specific to modern AMD processors.
Try changing the firmware settings (BIOS/UEFI) for SATA (set to AHCI mode) when using optical media or use another (non 3.0) USB port when using USB, this seems to work in most cases.
Hardware issues on Gigabyte mainboards
There apparently was or still is an issue on some Gigabyte mainboards with the IOMMU on AMD platforms (Intel calls this VT-d).
I found the following post on the forums (1, 2):
Turns out the IOMMU needs to be enabled in the BIOS. This problems seems to be exclusive to Gigabyte boards.
As well as this answer here on AU:
Gigabyte UEFI boot issues - The partition size of the created USB Installer device needs to be under that of 4GB. Others found UEFI/BIOS update solved issue of 4GB FAT limit.