Aren’t polar coordinates still n-1 + 1 for radius for n-dim vector? If so I understand that angles can be quantized better but when radius r is big the error is large for highly quantized angles right? What am I missing?
Trivially, with r=0, the error is 0, regardless of how heavily the direction is quantized. Larger r means larger absolute error in the reconstructed vector.
It is expected that bigger vectors have proportionally bigger error, nothing can be done by the quantizer about that.