We study the convergence behavior of iterative decoding of a serially concatenated code. We rederive a existing analysis technique called EXIT chart [15] and show that for certain decoders the construction of an EXIT chart simplifies tremendously. The findings are extended such that simple irregular codes can be constructed, which can be used to improve the converence of the iterative decoding algorithm significantly. An efficient and optimal optimization algorithm is presented. Finally, some results on thresholds on the decoding convergence are outlined.

We study the convergence behavior of turbo decoding, turbo equalization, and turbo bit-interleaved coded modulation in a unified framework, which is to regard all three principles as instances of iterative decoding of two serially concatenated codes. There is a collection of measures in the recent literature, which trace the convergence of iterative decoding algorithms based on a single parameter. This parameter is assumed to completely describe the behavior of the soft-in soft-out decoders being part of the iterative algorithm. The measures observe different parameters and were originally applied to different types of decoders. In this paper, we show how six of those measures are related to each other and we compare their convergence prediction capability for the decoding principles mentioned above. We observed that two measures predict the convergence very well for all regarded decoding principles and others suffer from systematic prediction errors independent of the decoding principle.

A number of important advances have been made in the area of joint equalization and decoding of data transmitted over intersymbol interference channels. Turbo equalization is an iterative approach to this problem, in which a maximum a-posteriori probability (MAP) equalizer and a MAP decoder exchange soft information in the form of prior probabilities over the transmitted symbols. A number of reduced-complexity methods for turbo-equalization have recently been introduced in which MAP equalization is replaced with sub-optimal, low-complexity approaches. In this paper, we explore a number of low-complexity soft-input/soft-output (SISO) equalization algorithms based on the minimum mean square error (MMSE) criterion. This includes the extension of existing approaches to general signal constellations and the derivation of a novel approach requiring less complexity than the MMSE-optimal solution. All approaches are qualitatively analyzed by observing the mean-square error averaged over a sequence of equalized data. We show that for the turbo equalization application the MMSE-based SISO equalizers perform well compared to a MAP equalizer while providing a tremendous complexity reduction.