The focus of this paper is the modeling of a class of stationary non-Gaussian auto-regressive processes that often find applications in statistical signal processing. We propose a general simulation procedure for constructing a time series model with a near-Laplace marginal distributions. Our approach is based on a class of Monte Carlo rejection algorithms. A theoretical analysis of the average complexity of the proposed algorithms for simulating the time series model is included.

The paper examines the impact of the additive correlated noise on the accuracy of a signal reconstruction algorithm originating from the Whittaker-Shannon sampling interpolation formula. The proposed reconstruction method is a smooth post-filtering correction of the classical Whittaker-Shannon interpolation series. We assess the global accuracy of the proposed reconstruction algorithm for long memory stationary errors being independent on the sampling rate. We also examine a class of long memory noise processes for which the correlation function depends on the sampling rate. Exact rates at which the reconstruction error tends to zero are evaluated. We apply our theory to the problem of designing non-parametric lack-of-fit tests for verifying a parametric assumption on a signal. The theory of the asymptotic behavior of quadratic forms of stationary sequences is utilized in this case

We investigate joint source-channel decoding for vector quantization over the finite-state Markov channel. In particular, we consider the decoding problem in which the channel state information is not available to the decoder. Based on hidden Markov modeling of the channel output, two decoding strategies are proposed. The first one is a soft-decoder which estimates the source reconstruction vectors directly from the observed channel output samples. The second one is a hard-decoder based on joint MAP estimation of channel symbols and channel states. Application of these decoders to wireless channels with multipath fading is also investigated. Simulation results are provided for a flat fading wireless channel and a Gauss-Markov source.

We consider the extension of the Whittaker-Shannon interpolation reconstruction formula to the case of band-limited signals observed in the presence of correlated noise. Observing that in this situation the classical sampling expansion gives inconsistent reconstruction, we apply a postfiltering strategy yielding a smooth correction of the interpolation series. We assess the accuracy of the method by the global L/sub 2/ error. A large class of dependent noise processes is taken into account. This includes short and long memory errors. Whereas the short memory errors have relatively small influence on the reconstruction accuracy, the long-memory errors can dramatically slow down the convergence rate. We explain this phenomenon by evaluating the speed at which the reconstruction error tends to zero.

Finite-state vector quantization (FSVQ) over a noisy channel is studied. A major drawback of a finite-state decoder is its inability to track the encoder in the presence of channel noise. In order to overcome this problem, we propose a nontracking decoder which directly estimates the code vectors used by a finite-state encoder. The design of channel-matched finite-state vector quantizers for noisy channels, using an iterative scheme resembling the generalized Lloyd algorithm, is also investigated. Simulation results based on encoding a Gauss-Markov source over a memoryless Gaussian channel show that the proposed decoder exhibits graceful degradation of performance with increasing channel noise, as compared with a finite-state decoder. Also, the channel-matched finite-state vector quantizers are shown to outperform channel-optimized vector quantizers having the same vector dimension and rate. However, the nontracking decoder used in the channel-matched finite-state quantizer has a higher computational complexity, compared with a channel-optimized vector-quantizer decoder. Thus, if they are allowed to have the same overall complexity (encoding and decoding), the channel-optimized vector quantizer can use a longer encoding delay and achieve similar or better performance. Finally, an example of using the channel-matched finite-state quantizer as a backward-adaptive quantizer for nonstationary signals is also presented.

Summary form only given. Channel optimized vector quantization (COVQ) has received considerable attention as an approach to joint source-channel coding. COVQ for hidden Markov channels was studied, with application in wireless communication over fading channels. The optimal VQ decoding was considered for finite state channels when the channel state is not explicitly observed at the receiver. A hidden Markov model (HMM) with a continuous observation space is constructed for the channel by assuming both channel input and channel state are first-order Markov process. A recursive-decoding algorithm is derived for computing the minimum mean square error (MMSE) optimal estimate for the source vector, based on the observed channel output sequence. In simulation experiments, the performance of a communications system based on the proposed quantizer is investigated for a Gauss-Markov signal source and a frequency non-selective Rayleigh fading channel. The results indicate that for fading channels, proposed soft-decoding based COVQ can results in a substantial improvement of performance over detection based COVQ.

The problem of recovering bandlimited signals from discrete and noisy data is studied. A nonlinear signal processing algorithm based on thresholding noisy data prior to reconstruction is proposed for improving the accuracy and robustness of reconstruction. The upper bound and the exact formula for mean integrated squared error of the proposed reconstruction scheme is established. The performance of the proposed reconstruction scheme is compared to that of the classical Whittaker-Shannon interpolation scheme.

In this paper, finite-state vector quantization (FSVQ) over noisy channels is studied. In particular a robust, time-recursive algorithm is proposed for reconstructing the output from a finite-state encoder, observed through a noisy channel. In contrast to an ordinary finite-state decoder, the proposed decoder exhibits graceful degradation of performance with increasing channel noise. We also consider the iterative optimization of encoder and decoder for designing channel optimized FSVQ. Simulation results based on Gauss-Markov source and additive white Gaussian noise channel are presented, and it is shown that robust FSVQ designed by methodology introduced here can outperform memory less channel optimized vector quantization at the same rate. Soft-decoding at the receiver, which provides an additional performance gain, is also considered.

A Lloyd-style iterative algorithm for designing predictive vector quantizers optimized to both source and channel is presented. We consider communication systems which use waveform channels and soft-decoding at the receiver. Based on reasonable assumptions, a set of conditions for the optimality of the predictive encoder and decoder, including the linear predictor, is derived. Simulation results based on a Gauss-Markov source and additive white Gaussian noise channel are presented. These results show that, when hard-decoding is used, the predictive codes designed here perform nearly identically to those obtained by gradient-search optimization techniques. It is also demonstrated that soft-decoding based systems designed with the proposed algorithm significantly outperform the hard-decoding systems.