Prior to reception by the set top tuner box, HDTV over the air signals require a cable of at least UHF grade strung from the antenna through your home. I think the actual requirement is 900 MHz, you will have to double check the frequency assignments for each HDTV channel. HDTV via cable requries the same coax as the cable coming in from the street.
After reception and decoding by the set top box, HDTV requires a 35 MHz bandwidth component video cable set going through the walls to TV sets in your home. (For 1080i so few TV sets can reproduce the finest horizontal details that 25 MHz cable will usually suffice.)