The approach behind the design of codes which meet the channel capacities of \text{BSC} or the binary erasure channel \text{BEC} have been to correct a lesser number of errors with a high probability, and to achieve the highest possible rate. Shannon's theorem gives us the best rate which could be achieved over a \text{BSC}_{p}, but it does not give us an idea of any explicit codes which achieve that rate. In fact such codes are typically constructed to correct only a small fraction of errors with a high probability, but achieve a very good rate. The first such code was due to George D. Forney in 1966. The code is a concatenated code by concatenating two different kinds of codes.
