I'm doing a research on the the physical effect of unbalancing the fraction of 1's and 0's in digital communications. Can anyone quote a specific FEC code that adds for example up to 20% overhead to the original bit sequence and increases the fraction of ones over 50% (before passing through the scrambler)?

For instance, consider a balanced 10 Gbit/s data stream being encoded by an FEC encoder with 20% overhead. The resulting 12 Gbit/s data are unbalanced where the encoder has added more 1's such that the output fraction of the 1's is increased up to 54% (before getting re-balanced by a scrambler).

If no exact case occurs, is there any similar case that can be quoted?