Joint source-channel turbo techniques and variable length codes

Efficient multimedia communication over mobile or wireless channels remains a challenging problem. To deal with that problem so far, the industry has followed mostly a divide and conquer approach, by considering separately the source of data (text, image, video, etc.) and the communication channel (electromagnetic waves across the air, a telephone line, a coaxial cable, etc.). The goal is always the same: to transmit (or store) more data reliably per unit of time, of energy, of physical medium, etc. With today's applications, the divide and conquer approach has, in a sense, started to show its limits. Let us consider, for example, the digital transmission of an image. At the transmitter, the first main step is data compression, at the source level. The number of bits that are necessary to represent the image with a given level of quality is reduced, usually by removing details in the image that are invisible (or less visible) to the human eye. The second main step is data protection, at the channel level. The transmission is made ideally resistant to deteriorations caused by the channel, by implementing techniques such as time/frequency/space expansions. In a sense, the two steps are quite antagonistic --- we first compress then expand the original signal --- and have different goals --- compression enables to transfer more data per unit of time/energy/medium while protection enables to transfer data reliably. At the receiver, the "reversed" operations are implemented. This separation in two steps dates back to Shannon's source and channel coding separation theorem in 1948 and has encouraged the division of the research community in two groups, one focusing on data compression, the other on data protection. This separation has also seduced the industry for the design, thereby supported by theory, of layered communication protocols. But this theorem holds only under asymptotic conditions that are rarely satisfied with today's multimedia content and mobile channels. Therefore, it is usually wise in practice to drop this strict separation and to allow at least some cross-layer cooperation between the source and channel layers. This is what lies behind the words joint source-channel techniques. As the name suggests, these techniques are optimized jointly, without a strict separation. Intuitively, since the optimization is less constrained from a mathematical standpoint, the solution can only be better or equivalent. In this thesis, we investigate a promising subset of these techniques, based on the turbo principle and on variable length codes. The potential of this subset has been illustrated for the first time in 2000, with an example that, since then, has been successfully improved in several directions. Unfortunately, most decoding algorithms have been so far developed on an ad hoc basis, without a unified view and often without specifying the approximations made. Besides, most code-related conclusions are based on simulations or on extrinsic information analysis. A theoretical framework on the error correcting properties of variable length codes in turbo systems is lacking. The purpose of this work, in three parts, is to fill in these gaps up to a certain extent. The first part presents the literature in this field and attempts to give a unified overview. The second part proposes a transmission system that generalizes previous systems from the literature, with the simple addition of a repetition code. While most previous systems are designed for bit streams with a high level of residual redundancy, the proposed system has the interesting flexibility to handle easily different levels of redundancy. Its performance is then analyzed for small levels of redundancy, which is a case not tackled extensively in the literature. This analysis leads notably to the discovery of surprising interleaving gains with reversible variable length codes. The third part develops the mathematical framework that was motivated during the second part but skipped on purpose for the sake of clarity. We first clarify several issues that arise with non-uniform bits and the extrinsic information charts, and propose and discuss two methods to compute these charts. Next, several theoretical results are stated on the robustness of variable length codes concatenated with linear error correcting codes. Notably, an approximate average distance spectrum of the concatenated code is rigorously developed. Together with the union bound, this spectrum provides upper bounds on the symbol and frame/packet error rates. These bounds are then analyzed from an interleaving gain standpoint and it is proved that the variable length code improves the interleaving gain if its spectrum is bounded.