One of the more interesting projects I ever had to complete was while awaiting clearance when I first started working for the NRO years back in ground processing algorithms (no longer work there, by the way). One of the long time guys gave us an assignment to implement the BCH error-correcting code, and then iteratively optimize it until we were able to implement the algorithm for computing the code published in a company proprietary whitepaper that was more efficient than any of the publicly published algorithms. That was just everything that is fun about programming. The actual production implementation corrected up to 8 bits per block, though I can't remember the block size any more.

Ground processing was a totally separate program and contract from mission control, though, so my team only ever received data from the satellites. We never sent data to them.