Analytic expression for the exact bit error probability of the (7,5) convolutional code

Analytic expressions for the bit error probabilities of the (7,5) convolutional code as functions of the crossover probability of the binary symmetric channel (BSC) are derived for a maximum likelihood (ML) decoder. In addition to classical nonsystematic encoders without feedback we consider also recursive systematic encoders, which became especially important as component encoders in concatenated coding schemes.