On performance bounds for serially concatenated codes with the general inner code and interleaver

We investigate the union bound for symbol interleaved serially concatenated codes (SCC) with non-uniform error properties. We calculate the distance spectrum of the SCC using the input difference symbol sequence spectrum (DSSS) of the inner code. Then we modify the trellis search algorithm for general codes to calculate the DSSS. We also show the mapping approach between difference symbols with the different alphabet size. For the symbol interleaver, we use the multinomial coefficient to calculate the probability of the permuted sequence. Numerical results for symbol interleaved serially concatenated continuous phase modulation (SCCPM) show that the bound is tight in the medium to high signal-to-noise ratio (SNR) region.