Detection of a Pulse pattern with Matched filter I am working on a hobby transmitter-receiver project. Presence of 4 pulses in T seconds is regarded as 1(not any number of pulses, should match below):

lack of pulses during that T seconds is regarded as bit 0. This is how transmitter block sends out information.
This signal is transmitted over a lossy channel so what I receive is r = alpha.s + noise , which is then digitized and passed to a DSP. Noise is not necessarily Gaussian (not sure of it's distribution).
1- Can I use matched filter(done in DSP) to detect if s was the Bit 1 shown above or Bit 0?
2- When should I sample the middle of match filter response? Does this need to be synched to start of every bit?
I am not sure what other method could be robust and reliable for decoding this.
IF a 1 is always represented by the waveform in the figure, you can use that waveform as the matched filter response.
However, it sounds like the waveform could be anything as long as there are some pulses in it. In that case, the matched filter should be a single pulse, and you'll have to count how many pulses were detected afterwards.
The non-Gaussian noise can be a problem; if you don't know anything about its distribution, you'll probably just have to build a prototype and test it. You may end up having to design a filter tailored to the specific noise distribution in your system.