On the weight distribution of recursive systematic convolutional codes

An analytical bound to bit error probability of turbo codes can be derived by weight distribution of recursive systematic convolutional codes. In this paper, the conditional weight enumerating function of terminated recursive systematic convolutional codes is computed. This form can be expressed as a function of number of information bits, and can reduce the computational complexity of calculation of error bounds. Applying these results, it is shown that improved error bound can be obtained by the conditional weight enumerating function of parallel concatenated convolutional codes.