Ironically there's no redundancy in NTSC. There are layers of information and they degrade downward until you have just a black and white picture with no sound.
In ATSC there is two types of forward error correction on the digital bitstream. The problem it faces is it sits in the same channel allocations as NTSC while having to deliver significantly more information than NTSC. That and the actual digital modulation used is not as ideal for receivers to capture.
You can digitize and lossily compress an NTSC signal significantly without losing much detail; that's why I call it redundant. Compression removes redundancy.
In ATSC the tradeoff between compression and error correction is such that a noisy channel is far more likely to cut out or otherwise be unusable than it would have been in NTSC.
In ATSC there is two types of forward error correction on the digital bitstream. The problem it faces is it sits in the same channel allocations as NTSC while having to deliver significantly more information than NTSC. That and the actual digital modulation used is not as ideal for receivers to capture.