I have a 612 in the front room of my house that stays inside of a glass front cabinet. And I've recently ran a long HDMI from that room to a new screened porch on the back of my house. Well the picture comes in great to the TV on the porch, but I'm having trouble using my remote from the porch. I have to stand next to the back door for the remote to change the channel. I'm wondering if I can get a short piece of coax (2'-3' long) to run between the antenna and the receiver. So that the antenna will sit on top of the entertainment center. I think that may help with my remote issues. Can this be done?