And your speakers are playing an analog signal. Cable quality matters even more there.
Yes. Which is why the poorly made cable can be said to not work.
> And your speakers are playing an analog signal.
Huh? I've never heard of HDMI cables capable of carrying analog sound.
That's why CDs (and cellphones, modems, and countless other digital devices) use channel encoding.[1] That way you don't have to have a perfectly noise-free signal to reconstruct the original information.
I don't know that many specifics of the DVD or Blu-Ray standards, but I'd put money on them using Reed-Solomon or something similar.
[1] http://en.wikipedia.org/wiki/Reed-Solomon_error_correction#D...
(Edit: forgot footnote)
My guess is that very few digital A/V systems implement this. Proof of this is the weird sound you may hear on a damaged compact disc, it half works.
There are additional protection schemes that can detect and correct bit errors. Those are probably also run during the decoding process. The problem is that you can only detect so many wrong bits in a given word, and beyond that no correction can be made. That is probably why the damaged disc half works.
In my opinion that is just the proof that it's not as simple as "it just works or not" but rather : depending on muptiple factors such as error correction and the way your algorithm works on the receiver it may "half work" no matter what kind of cable you plug in.
Even with an error-detecting code, there comes a point where there's too many errors to know if you received a valid code word or if the errors just "canceled each other". If 000 and 111 are your only valid words, it's still possible that a 111 gets turned into a 000 (3 consecutive errors) and there's no way to know about it...