Design and performance analysis of joint source-channel turbo schemes with variable length codes

We proposed in Jaspar et al. (2004) a joint source-channel (JSC) turbo-(de)coder combining a variable length code (VLC) with a turbo-code. The simulation results showed the better performance and the lower decoding complexity of this new scheme over the previous ones. In this paper, we provide tools for the analysis and the performance prediction of this scheme. The bit, symbol and frame distance spectra are developed for VLC and for the more general case of VLC turbo-concatenated with an error correcting code (ECC). These spectra are then used to get the union bounds on the bit, symbol and frame error probabilities, and to shed some light on previous simulation-based results. These tools are also valid for a wide variety of other similar schemes currently explored in the literature and, hence, can be used to analyze and to compare them.