Quantizing a filtered signal
Your low-pass filter's pass band is smaller than your signal's bandwidth, so it is destroying a significant portion of your signal.  Given that, you cannot reliably reproduce the original signal without using sophisticated techniques like error correction codes.

I would try increasing $\alpha$ to 2400 Hz.  Then the rolloff point will be 2400 * .5 = 1200.  The resulting signal should look much better.  If that filter bandwidth is too large you can find your sweet spot somewhere between 1200 and 2400 Hz.