[CELT-dev] On guessing theta

[Benjamin M. Schwartz]

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Currently, the encoder does l = normalize(L), r = normalize(R), M = l+r, m
= normalize(M), etc.  The trick will not work in this case.  Here's why:

dot(m,s) = c*dot(M,S) for some constant c.
dot(M,S) = dot(l+r,l-r) = dot(l,l) + dot(r,l) - dot(l,r) - dot(r,r) = 1 +
dot(r,l) - dot(r,l) - 1 = 0

so dot(m,s) is always zero.  The trick described previously does not work
when dot(m,s) = 0, so theta must be transferred explicitly.

However, this orthogonality is still useful.  If m is encoded in N
dimensions, then from this orthogonality s can be encoded in N-1
dimensions.  That means that transmitting theta no longer represents an
extra degree of freedom.

Maybe you're already doing this. I have no idea.

- --Ben
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