[gji]

I'm pretty sure the way analog degrees are freedom are mapped onto symbols is very important. In principle, if you have infinite SNR over a limited bandwidth, you can have infinite rate of data transfer - e.g. if you can have infinitely fine voltage resolution (in reality limited by the thermal noise floor, but you can always increase transmit power). So in that sense the mapping between information and bandwidth depends on SNR.

From the wiki page on QAM: "Arbitrarily high spectral efficiencies can be achieved with QAM by setting a suitable constellation size, limited only by the noise level and linearity of the communications channel." [https://en.wikipedia.org/wiki/Quadrature_amplitude_modulatio...]

[gugagore]

Unfortunately I used bandwidth informally (how most people use it), to mean something measured in bits per second, not Hertz.

You're absolutely right that SNR plays a role. But I don't see why you need to map to symbols.