[sdenton4]

sure, at a communication complexity of 2N+k, where k is the hash size.... Error correcting codes allow much shorter error-free communications, with lower probability of failure than your method.

Consider an N bit stream of data, with a probability mu of any given bit being flipped. Then the probability of your stream containing an error is gamma := 1-(1-mu)^N. Since you're sending the identical stream twice, there's a 1-(1-gamma)^2 chance that your overall transmission is unrecoverable. The hash will tell you that the transmission failed, but not how to correct it. Furthermore, there's a probability that your hash has a bit flipped somewhere, too...

An error correcting code makes a guarantee that if up to m bits are flipped, the original message can be recovered exactly. A Reed-Solomon code can correct up to m errors while adding just 2m bits to the message length; even with a pretty conservative upper bound on the number of expected errors, this should be way less than 2N+k.