On union bounds for random serially concatenated turbo codes with maximum likelihood decoding

The input-output weight enumeration (distribution) function of the ensemble of serially concatenated turbo codes is derived, where the ensemble is gen erated by a uniform choice over the interleaver and a uniform choice of the component codes from the set of time varying recursive systematic convolut ional codes. The conventional union bound is employed to obtain an upper bo und on the bit error probability of the ensemble of serially concatenated t urbo codes for the binary-input additive white Gaussian noise (AWGN) channe l with coherent detection of antipodal signal and maximum likelihood decodi ng. The influence of the interleaver length N and the memory length of the component codes m on the ensemble performance is investigated and compared with relevant results for parallel concatenated multiple-turbo codes.