Impact of Variable Length Codes on the Interleaving Gain of Turbo Systems: The Concept of Bounded Spectrum

When a telecommunication system is constrained in terms of delay and complexity, it is usually wise to allow some cross-layer cooperation between the source and channel layers. In this context, the success of joint source-channel turbo techniques has been attested several times in the literature, in particular to transmit variable length code (VLC) streams which are very sensitive to error propagation. Capitalizing on previously developed performance upper bounds, this paper investigates whether the VLC can contribute to the interleaving gain of concatenated codes just as a convolutional code with non-catastrophic encoder would. To this end, the important concept of bounded VLC spectrum is introduced and is proved to be a sufficient condition for the VLC to contribute indeed to the interleaving gain. This concept is also proved to be closely related to non-catastrophic VLCs and, under certain assumptions, to the well known concept of statistically synchronizable VLCs.