> I might be being naive here (it's a long time since I sat my digital
> signals classes) but if some bits are more important than others
> wouldn't that mean that there is some entropy in the signal which can
> be removed to get better compression?

No.

In fact, better compression often leads to _increasing_ disparity in the 
importance of bits. Because to get the most entropy out of each 
decision, you should be coding the current parameter conditioned on 
everything the decoder knows so far. That means using all of the 
previously encoded symbols as context, making those at the beginning 
become far more important than those at the end.

Consider, for example, a single bit that's true for exactly 50% of the 
frames (so the Shannon theorem tells you there's no better way to 
represent it than one bit), but selects between different coding methods 
(for example, this could represent the voiced/unvoiced decision, though 
codec2 does not use that parameter this way). If the bit is set, you 
decode one set of parameters using one set of codebooks, and if it's 
unset, you decode another set of parameters using a completely different 
set of codebooks. If you get that bit wrong, then your interpretation of 
all the remaining bits will be wrong, and you'll decode complete garbage.

That kind of design is obviously at odds with the goal of being robust 
to bit errors, so it's probably not appropriate to do too much of that 
in codec2, but there's still obvious places where some bits are more 
important than others (e.g., the MSb of Wo_index will be more important 
than the LSb).

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