That's an interesting question. I don't know if Lincos, which is the most conspicuous attempt at creating a self-explanatory language for aliens, included any kind of compression. Self-explanatory compression seems difficult to achieve, though maybe once you have the motion of equality, you can start giving examples of equivalent plain and compressed texts.

Then any damage to these instructions will be critical.

Copies of it could be distributed throughout the data. However I'm not sure what tolerance to damage is expected. How long is this disc supposed to last? How much damage will occur in that time? What's the tradeoff between compressing the data and it's expected lifespan?