Which algorithm for extremely high non burst errors?

Question

I have a binary stream that has a very high error rate. The error rate is 50% meaning each bit has a 50% chance of being flipped. The error does not occur in bursts and is completely random, so Reed–Solomon codes wouldn't work well.

Which scheme or algorithm should I apply to the stream? I don't care about the overhead at all.

This is all theoretical, so there's no point in asking if I could just reduce the error of the stream.

EDIT

Don't say its not possible, the very first answer it tells you it is possible with noisy channel coding theorem.

Answer 1

If the error rate is 50%, then that's basically random noise isn't it? I mean, consider just trying to transmit a single bit. If you send an infinite stream of the right bit, with a 50% error rate you'll get half 1s and half 0s whether the right bit is 1 or 0.

If it's actually less than 50% (e.g. 50% of the bits will be "random" rather than "flipped") then you could just repeat the data - transmit each bit 128 times and work out which you get more of for each 100 bits received. That's the simple-to-code, hugely inefficient, not mathematical at all solution :)