I wish you'd stop calling HD "1K", that's just being silly. HD is 1920x1080, 4K is 3840x2160 - double the width, not 4x the width.
I don't think compression will be a problem, 4K will use HEVC, which is the next generation after MPEG4/h.264 and requires roughly half the bandwidth for equivalent picture quality. Since 4K has 4x as many pixels, a 4K stream will require roughly double the bandwidth.
The problem for Directv and cable providers is that it actually triples their bandwidth requirements for each 4K channel, since they can't drop the HD version of the channel unless they replaced every HD receiver with one capable of downconverting 4K to HD.
With the new satellite coming, and the obvious eventual dropping of SD feeds for HD only, it's a prime time for DirecTV to do that. I don't know the state of HEVC or of HEVC capable decoding hardware, but as soon as it's to the point that they can put it in boxes, they need to standardize every single customer on an HD/4K/3D capable box and dish. Cable is in a similar situation with most companies beginning to move *all* of their systems to 100% digital and SDV, with IP video being the next logical step.