I work in Sattelite Communications and we use these algorithims by default. We call it forward error correction. I would assume that they would use a much less aggressive algorithim, maby 1 correction bit per 8-16 bits rather than a 1 for 1 data, or a 1 for 2 data that you see for dirty links in the space operations. See http://en.wikipedia.org/wiki/Viterbi_algorithm or http://en.wikipedia.org/wiki/Reed%E2%80%93Solomon_error_correction.
The additional throughput is not from compression but from not having to TCP resend entire packets and probably also prevents the TCP window from resetting.