Capturing a 16.368MHz data stream with a MCU running at 32MHz
I doubt your processor will be able to read data and store it in each cycle (given that the 16.368 MHz is more than half the 32 MHz clock, some inputs will have to be processed in sequential processor cycles.

A more powerful processor (e.g. Teensy 3.2) can run at 96 MHz, and with DMA may be able to process the inputs fast enough.