This is more of a computer science / information theory question than a straightforward programming one, so if anyone knows of a better site to post this, please let me know.
Let's say I have an N-bit piece of data that will be sent redundantly in M messages, where at least M-1 of those messages will be received successfully. I am interested in different ways of encoding the N-bit piece of data in fewer bits per message. (this is similar to RAID but at a much smaller level, where N = 8 or 16 or 32)
Example: suppose N = 16 and M = 4. Then I could use the following algorithm:
1st and 3rd message: send "0" + bits 0-7
2nd and 4th message: send "1" + bits 8-15
If I can guarantee that 3 messages of the 4 will get through, then at least one message from each group will get through. Thus I can make this work with 9 bits or less, there's probably a way to do this with fewer total bits but I'm not sure how.
Are there some simple encoding/decoding algorithms to do this kind of thing? Does this problem have a name? (if I know what it's called, I can google it!)
note: in my particular case, the messages either arrive correctly or do not arrive at all (no messages arrive with errors).
(edit: moved 2nd part to a separate question)