You're omitting an important thing - MCU has own clock, wastes different time on program execution, but incoming data is sent async, so it can't wait for MCU to become ready, so my guess, how it all should work, is as follows:

As pulse arrives, we start recording it as fast as possible, after pulse sequence finished, we just count numbers of 1's and 0's recorded, and based on that, decide what to do with decoded data. Considering total sequence duration and speed, I guess, external sram or eeprom might be needed?