Are we being presented with a 'solution' to a not fully defined problem and then requested to flesh out the solution. I looked at it and thought 'I created a TOG for an ATmega328P, two of them would do it easily' [TOG - top octave generator, generates the 12 tones from D8 (4694.8Hz) to C9 (8368.2Hz) - used in old electronic organs]. But they are (a) not in the specified frequency range (b) continuous (c) come out of separate pins (d) square wave. So could that be modified to do the job? So then one asks, why use frequency division multiplexing (FDM) versus time division multiplexing. It is way more complex. A simple 1200 baud FSK signal would move 16 bits in 13ms, does it need to be quicker? If so, why? Although it requires parallel to serial conversion by the sender and serial to parallel conversion by the receiver, these are simple tasks offloaded to sub $1 parts.
I think we need a better definition of the problem. I know there was a partial explanation a few posts back, but it left out things like what data rate is required (more than 1200 bit/sec?), what delays are tolerable, how far the signal needs to propagate (is there a significant path delay), if there are errors, (a) that's OK (like in VoIP) (b) should be detected but don't require correction (c) need a forward correction like trellis encoding (d) could deal with as a simple ACK/NAK resend (if there's little latency, this could be achieved in less than 100ms). What is the significance of 16 bit? What SNR is this to work within. Is it a one off to fit a specific situation or should it allow for future mods and what might they be?
This is the bane of the system analyst. Brings to mind the story of the advertised job, financial manager pay $2 million p.a. Candidate asks what the job entails. "First figure out how you get paid".