Xavier Jaspar

Joint Source–Channel Turbo Techniques for Discrete-Valued Sources: From Theory to Practice

The principles which have been prevailing so far for designing communication systems rely on Shannons source and channel coding separation theorem. This theorem states that source and channel optimum performance bounds can be approached as close as desired by designing independently the source and channel coding strategies. However, this theorem holds only under asymptotic conditions, where both codes are allowed infinite length and complexity. If the design of the system is constrained in terms of delay and complexity, if the sources are not stationary, or if the channels are nonergodic, separate design and optimization of the source and channel coders can be largely suboptimal. For practical systems, joint source-channel (de)coding may reduce the end-to-end distortion. It is one of the aspects covered by the term cross-layer design, meaning a rethinking of the layer separation principle. This article focuses on recent developments of joint source-channel turbo coding and decoding techniques, which are described in the framework of normal factor graphs. The scope is restricted to lossless compression and discrete-valued sources. The presented techniques can be applied to the quantized values of a lossy source codec but the quantizer itself and its impact are not considered.

New iterative decoding of variable length codes with turbo-codes

A new joint source-channel (JSC) turbo-decoding scheme, with three soft-in/soft-out (SISO) modules, is presented for variable length coded sources protected by a turbo-code. This new scheme offers the advantage to combine the powerfulness of the used turbo-code with the robustness of the reversible variable length codes (VLC), and moreover with a decoding complexity close (or less) to the one of the turbo-code alone. The performance due to the turbo-code alone leads to an increased freedom in the VLC design depending on the application -, and suggests to revisit the VLC distance criteria investigated in R. Bauer and J. Hagenauer (March 2001). The decoding algorithm for this three SISO modules scheme is briefly presented in the framework of the Bayesian networks. Compared with previous JSC turbo-decoders and with a classical turbo-code, simulation results show the relevance and the superior performance of the proposed scheme.

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.

Joint source-channel codes based on irregular turbo codes and variable length codes

Variable length codes (VLCs), used in data compression, are very sensitive to error propagation in the presence of noisy channels. To address this problem, several joint source channel turbo techniques have been proposed in the literature. In this paper, we focus on pairs of source/VLC of low redundancy, i.e., when there is a good match between the source statistics and the length distribution of the VLC. It is a case not considered extensively in the literature so far and the classical concatenation of a VLC and a convolutional code is not satisfying. Through EXIT chart and interleaving gain analysis, we show that the introduction of a repetition code between the VLC and the convolutional code considerably improves global performance. In particular, excellent symbol error rates are obtained with reversible VLCs which are used in recent source codecs.

Performance and convergence analysis of joint source-channel turbo schemes with variable length codes

Recently, we proposed a joint source-channel (JSC) turbo (de)coder combining a variable length code (VLC) and a turbo code, and applied it to image transfer (Jaspar, X. and Vandendorpe, L., SCC Conf., p.279-86, 2004; ICC Conf., p.2606-10, 2004). Simulation results showed that this scheme gave better performance and lower decoding complexity than previous ones. The paper assesses the performance of such a scheme at all signal-to-noise ratios on the channel. Analytical tools are provided for the understanding and optimization of a wide variety of similar schemes currently explored in the literature. More precisely, the bit, symbol and frame distance spectra are developed for VLCs and for VLCs turbo-concatenated with an error correcting code (ECC), in order to get bounds on the corresponding error rates. Also EXIT charts are extended to three dimensions in order to analyze the turbo-convergence of the scheme.

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.

Random bit flipping and EXIT charts for nonuniform binary sources and joint source-channel turbo systems

Joint source-channel turbo techniques have recently been explored a lot in literature as one promising possibility to lower the end-to-end distortion, with fixed length codes, variable length codes, and (quasi) arithmetic codes. Still, many issues remain to be clarified before production use. This short contribution clarifies very concisely several issues that arise with EXIT charts and nonuniform binary sources (a nonuniform binary source can be the result of a nonbinary source followed by a binary source code). We propose two histogram-based methods to estimate the charts and discuss their equivalence. The first one is a mathematical generalization of the original EXIT charts to nonuniform bits. The second one uses a random bit flipping to make the bits virtually uniform and has two interesting advantages: (1) it handles straightforwardly outer codes with an entropy varying with the bit position, and (2) it provides a chart for the inner code that is independent of the outer code.

Distributed Source Coding with Optimized Irregular Turbo Codes

We address the problem of distributed source coding of binary sources with side information at the decoder. We propose a compression scheme using irregular turbo codes. We optimize them by maximizing the distance between the two curves of their EXIT charts for given statistics and a compression rate close to the Slepian-Wolf limit in order to increase the robustness of the scheme. This optimized irregular code enables us to achieve compression rates superior to the ones achieved by previously proposed turbo schemes without increasing the decoding complexity.

Performance Bounds and Distance Spectra of Variable Length Codes in Turbo/Concatenated Systems

Variable length codes (VLCs), used in data compression, are very sensitive to error propagation in the presence of noisy channels. Addressing this problem with joint source-channel turbo techniques has been proposed in the literature and looks quite promising. But to date, most code-related conclusions are based on simulations. This paper states and proves several theoretical results about the robustness of prefix VLCs concatenated with linear error correcting codes (ECC), assuming a maximum likelihood decoder. Especially, an approximate and asymptotically tight distance spectrum of the concatenated code (VLC+ECC) is rigorously developed. Together with the union bound, it provides upper bounds on the symbol and frame/packet error rates.

calculating turbo-decoding performance characteristics for adaptive channel coding

Low complexity performance characterizations of error-correcting codes are needed to better exploit their potential when adapting a communication system to channel conditions or to service requirements. For the case of turbo-codes, existing performance characterizations are often too complex or not flexible enough to be used for real-time adaptation. This paper presents a new technique for evaluating the performance of turbo-codes, that may fit the need for flexibility and low-complexity. It enables the determination of the error-free decoding threshold and of the number of iterations to achieve error-free decoding. Its complexity is far lower than that of existing methods and its accuracy is very satisfying.