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

The noisy-channel coding theorem says you can actually achieve the Shannon capacity for the channel. It does not say the channel has nonzero capacity!

If you randomize 100% of the bits in the channel, 50% of them will be unchanged, so you only flip a random 50% of the bits. It should be obvious that you can't send any data over such a channel -- its Shannon capacity is zero.