That’s the whole point of using a digital connection: The HDMI connection is driven at a very high level by the settop box, and then well-terminated at the TV. (Like a million times stronger than the microvolt levels between a DTV over-the-air antenna and the tuner input.)The bit error rate over that 6 feet of shielded cable is almost unmeasurable with the finest lab equipment, unless you are running some sort of transmitting equipment right next to your TV. Even then, such noise is much more likely to enter through your TV’s power cable than through the HDMI cable. Using thicker conductors, gold-plating the terminals, adding noise filters, etc. will not make any difference.

If you want to spend some money on equipment where it will make a terrific difference, buy a good antenna with an antenna-mounted preamp.