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A number of important advances have been made in the area of joint equalization and decoding of data transmitted over intersymbol interference (ISI) 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 suboptimal, 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 with a MAP equalizer while providing a tremendous complexity reduction.Index Terms-Equalization, iterative decoding, low complexity, minimum mean square error.

Face masks muffle speech and make communication more difficult, especially for people with hearing loss. This study examines the acoustic attenuation caused by different face masks, including medical, cloth, and transparent masks, using a head-shaped loudspeaker and a live human talker. The results suggest that all masks attenuate frequencies above 1 kHz, that attenuation is greatest in front of the talker, and that there is substantial variation between mask types, especially cloth masks with different materials and weaves. Transparent masks have poor acoustic performance compared to both medical and cloth masks. Most masks have little effect on lapel microphones, suggesting that existing sound reinforcement and assistive listening systems may be effective for verbal communication with masks.

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Abstract-Turbo codes and the iterative algorithm for decoding them sparked a new era in the theory and practice of error control codes. Turbo equalization followed as a natural extension to this development, as an iterative technique for detection and decoding of data that has been both protected with forward error correction and transmitted over a channel with intersymbol interference (ISI). In this paper, we review the turbo equalization approach to coded data transmission over ISI channels, with an emphasis on the basic ideas, some of the practical details, and many of the research directions that have arisen from this offshoot, introduced by Douillard, et al. of the original turbo decoding algorithm. The subsequent relaxation of the maximum a posteriori (MAP) equalization algorithm to include linear and other simpler receivers sparked a decade and a half of research into iterative algorithms, spanning research problems ranging from trellis coded modulation to underwater acoustic communications.Index Terms-Equalization, iterative decoding, minimum mean square error, turbo equalization.

This paper considers the problem of piecewise linear prediction from a competitive algorithm approach. In prior work, prediction algorithms have been developed that are "universal" with respect to the class of all linear predictors, such that they perform nearly as well, in terms of total squared prediction error, as the best linear predictor that is able to observe the entire sequence in advance. In this paper, we introduce the use of a "context tree," to compete against a doubly exponential number of piecewise linear (affine) models. We use the context tree to achieve the total squared prediction error performance of the best piecewise linear model that can choose both its partitioning of the regressor space and its realvalued prediction parameters within each region of the partition, based on observing the entire sequence in advance, uniformly, for every bounded individual sequence. This performance is achieved with a prediction algorithm whose complexity is only linear in the depth of the context tree per prediction.Upper bounds on the regret with respect to the best piece-wise linear predictor are given for both the scalar and higher-order case, and lower bounds on the regret are given for the scalar case. An explicit algorithmic description and examples demonstrating the performance of the algorithm are given.

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A common problem that arises in adaptive filtering, autoregressive modeling, or linear prediction is the selection of an appropriate order for the underlying linear parametric model. We address this problem for linear prediction, but instead of fixing a specific model order, we develop a sequential prediction algorithm whose sequentially accumulated average squared prediction error for any bounded individual sequence is as good as the performance attainable by the best sequential linear predictor of order less than some M M M. This predictor is found by transforming linear prediction into a problem analogous to the sequential probability assignment problem from universal coding theory. The resulting universal predictor uses essentially a performance-weighted average of all predictors for model orders less than M M M. Efficient lattice filters are used to generate the predictions of all the models recursively, resulting in a complexity of the universal algorithm that is no larger than that of the largest model order. Examples of prediction performance are provided for autoregressive and speech data as well as an example of adaptive data equalization.