### BER performance for a (7,4) Hamming code

The BER curves for uncoded and coded BPSK are shown here for the k = 4, n = 7 Hamming code. The curves have been normalized for equal energy per information bit (pre-coding), bearing in mind that the energy per transmitted bit is less than the energy per information bit by a factor equal to the code rate R. The mathematics required to work out the performance of some of these codes is very complex and often it is only possible to derive approximate results or run simulations over very long periods of time. The improvement in Eb/N0 performance of the coded vs uncoded systems, at a specified BER, is termed the coding gain. Note that: |

#### Eb(precoded) = Eb(postcoded) / R