Trellis-coded quantization designed for noisy channels

Trellis-coded quantization (TCQ) of memoryless sources is developed for transmission over a binary symmetric channel. The optimized TCQ coder can achieve essentially the same performance as Ayanoglu and Gray's (1987) unconstrained trellis coding optimized for the binary symmetric channel, but with a much lower implementation complexity for transmission rates above 1 b/sample. In most cases, the optimized TCQ coder also provides larger signal-to-noise ratio than Farvardin and Vaishampayan's (1991) channel-optimized vector quantization. Algorithms are developed for the joint design of trellis-coded quantization/modulation (TCQ/TCM). The jointly designed TCQ/TCM system outperforms the straightforward cascade of separately designed TCQ and TCM systems. The improvement is most significant at low channel signal-to-noise ratio. For a first-order Gauss-Markov source, the predictive TCQ/TCM performance can exceed that of optimum pulse amplitude modulation     

On finite-state vector quantization for noisy channels

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.     

Shape-gain vector quantization for noisy channels with applicationsto image coding

A new design procedure for shape-gain vector quantizers (SGVQs) which leads to substantially improved robustness against channel errors without increasing the computational complexity is proposed. This aim is achieved by including the channel transition probabilities in the design procedure, leading to an improved assignment of binary codewords to the coding regions as well as a change of partition and centroids. In contrast to conventional design, negative gain values are also permitted. The new design procedure is applied to adaptive transform image coding. Simulation results are compared with those obtained by the conventional design procedure. The new algorithm is particularly useful for heavily distorted or fading channels     

A study of vector quantization for noisy channels

Several issues related to vector quantization for noisy channels are discussed. An algorithm based on simulated annealing is developed for assigning binary codewords to the vector quantizer code-vectors. It is shown that this algorithm could result in dramatic performance improvements as compared to randomly selected codewords. A modification of the simulated annealing algorithm for binary codeword assignment is developed for the case where the bits in the codeword are subjected to unequal error probabilities (resulting from unequal levels of error protection). An algorithm for the design of an optimal vector quantizer for a noisy channel is briefly discussed, and its robustness under channel mismatch conditions is studied. Numerical results for a stationary first-order Gauss-Markov source and a binary symmetric channel are provided. It is concluded that the channel-optimized vector quantizer design algorithm, if used carefully, can result in a fairly robust system with no additional delay. The case in which the communication channel is nonstationary (as in mobile radio channels) is studied, and some preliminary ideas for quantizer design are presented     

Innovations-based MAP detection for time-varyingfrequency-selective channels

By using the innovations process, this paper provides a unification and extension of the existing maximum a posteriori (MAP) detectors (MAPDs). The practically important topics of linear modulations, time-varying frequency-selective channels, differential phase detection, and fractional sampling are accounted for. The MAPDs are derived under different conditions of optimality and a priori knowledge as follows: when the MAP criterion is applied to the constellation mapper's input bits or output symbols, when all observations or only a fixed number of future observations (i.e. fixed-lag MAPDs) from a transmission are available, when the time-varying channel impulse response is perfectly known, and when only the Gaussian-distributed channel's mean and autocovariance and the noise variance are known. As these quantities are actually unknown, their estimation in the context of MAP detection is also discussed. The MAPDs are characterized through simulation and a novel, unified analysis. Although MAPDs are less suited to hardware implementation than the traditional maximum-likelihood sequence detectors, the MAPDs can accept nonuniform a priori bit or symbol probabilities and provide soft outputs. In this way, the MAPDs are well suited to iterative decoding, and so they will become increasingly integral to high-performance receiver designs     

Trellis coded vector quantization

A vector generalization of trellis coded quantization (TCQ), called trellis coded vector quantization (TCVQ), and experimental results showing its performance for an i.i.d. Gaussian source are presented. For a given rate, TCVQ yields a lower distortion that TCQ at the cost of an increase in implementation complexity. In addition, TCVQ allows fractional rates, which TCQ does not     

Coding for noisy channels with input-dependent insertions

Tree encoding and sequential decoding are considered for noisy channels that respond a random number of times to each input. Such channels appear in mathematical models of certain speech recognition systems. The decoding error probability and the channel capacity are bounded by extension of the methods of Jelinek and Zigangirov to noisy multilevel channels with input-dependent insertions. Certain analytical difficulties peculiar to the channels in question are indicated.     

On quantization of noisy signals

Quantized noise distributions derived from continuous signals with additive noise are studied. Two noise sources are considered, quantized image noise derived from the continuous input noise source and noise due to quantization roundoff error. These are treated as statistically independent sources. An analytic solution for the quantized noise probability density is obtained. The analytic solution is estimated by two expressions valid for normally distributed noise over different ranges of variance. The estimates have excellent agreement in the region of overlapping validity. Quantized noise variance is related to the continuous noise variance from normally distributed noise using these expressions. A table and plots of useful values are included. These results are helpful in choosing a quantization interval for a particular application. They can also be used to determine quantizer output noise level and signal-to-noise ratio in digital applications     

Adaptive quantization for fading channels with feedback

The effect of the presence of a feedback channel on the transmission of information was first considered by Shannon, who showed that the capacity of a memoryless channel is not increased by the existence of a feedback link even if the feedback link is noiseless. Later it was shown that the information on a feedback channel can be used to improve considerably the performance of channel coding. In this work we study the transmission of an information source through a fading channel with feedback, modeled by a finite-state channel in the Gilbert-Elliot sense. We show that by employing the feedback information in the quantizer design for this finite-state channel, one can achieve lower overall distortion compared to the case where feedback is not available. The feedback channel is used to estimate the channel state using a hidden Markov model, and a quantizer matched to the channel state is chosen based on this information.     

On the partial MAP detection with applications to MIMO channels

We investigate a multidimensional detection problem with a partial information of the a posteriori probability, which is referred to as the partial maximum a posteriori probability (MAP) detection problem. We show that the maximum likelihood (ML) detection of a higher dimension can be reduced to the ML detection of a lower dimension with cancellation under a certain condition through the formulation of the partial MAP detection problem. Using this, we can propose a computationally efficient algorithm to apply to the detection problem for multiple input multiple output (MIMO) channels including multiple transmit and multiple receive antenna (MTMR) channels and intersymbol interference (ISI) channels. It is shown that the proposed method has less error propagation effect, and its performance is close to that of the full ML detection with a lower computational complexity.     

Image coding using robust quantization for noisy digitaltransmission

A robust quantizer is developed for encoding memoryless sources and transmission over the binary symmetric channel (BSC). The system combines channel optimized scalar quantization (COSQ) with all-pass filtering, the latter performed using a binary phase-scrambling/descrambling method. Applied to a broad class of sources, the robust quantizer achieves the same performance as the Gaussian COSQ for the memoryless Gaussian source. This quantizer is used in image coding for transmission over a BSC. The peak signal-to-noise ratio (PSNR) performance degrades gracefully as the channel bit error rate increases.     

Trellis coded quantization of memoryless and Gauss-Markov sources

Trellis-coded quantization (TCQ) is developed and applied to the encoding of memoryless and Gauss-Markov sources. The theoretical justification for the approach is alphabet-constrained rate distortion theory, which is a dual to the channel capacity argument that motivates trellis-coded modulation (TCM). The authors adopt the notions of signal set expansion, set partitioning, and branch labeling of TCM, but modify the techniques to account for the source distribution, to design TCQ coders of low complexity with excellent mean-squared-error (MSE) performance. For a memoryless uniform source, TCQ provides an MSE within 0.21 dB of the distortion-rate bound at all positive (integral) rates. The performance is superior to that promised by the coefficient of quantization for all of the best lattices known in dimensions 24 or less. For a memoryless Gaussian source, the TCQ performance at rates of 0.5, 1, and 2 b/sample is superior to all previous results the authors found in the literature. The encoding complexity of TCQ is very modest. TCQ is incorporated into a predictive coding structure for the encoding of Gauss-Markov sources. Simulation results for first-, second-, and third-order Gauss-Markov sources are presented     

On optimal quantization of noisy sources

Problems in optimal multidimensional quantization of sources corrupted by noise are addressed. Expressions for the optimum quantizer values and the optimum quantization rule for the weighted squared error distortion measure are found and calculated for the Gaussian signal in additive independent Gaussian noise problem. Some properties of the optimum quantizer, and its relations with the optimal estimator for the general problem, are derived     

Optimal bit allocation for noisy channels

An asymptotic expression for the optimal bit allocation for noisy channels is derived using high-resolution quantisation theory. Theoretically determined bit allocation based on the derived expression is presented.     

DS-CDMA system with joint channel estimation and MAP detection intime-selective fading channels

In this paper, maximum a posteriori (MAP) detection is applied to a direct-sequence code-division multiple-access (DS-CDMA) system jointly with identification and estimation of time-selective fading channels. By sampling the outputs of the matched filter and combining antenna array elements, strong and time-varying multiple-access interference (MAI) is characterized and suppressed instantaneously. The decision statistics for MAP detection are obtained from the conditional probability density function of the prediction error. The prediction is accomplished by approximating the fading channel with a constrained nonlinear state model. Unknown parameters such as auto-regressive (AR) process coefficients, noise covariance matrices, and the antenna array vector are estimated based on received sample vectors only. Also, differential modulation is applied to eliminate the need for pilot insertion. Through computer simulations, near-optimum bit error rates (BERs) are found     

Optimum quantization for detection

Vector quantization is a procedure widely used in communications. The problem has been solved for the basic detection situation using the locally optimal procedure and with some constraints on the quantization scheme. It is stated in its widest sense, which consists of finding the partition of the observation space and the values associated with it in such a way that the detection performance is optimal. It is solved completely with the deflection criterion, and the solution introduces the concept of quantization by a likelihood ratio procedure     

Robust vector quantization for wireless channels

This study focuses on two issues: parametric modeling of the channel and index assignment of codevectors, to design a vector quantizer that achieves high robustness against channel errors. We first formulate the design of a robust zero-redundancy vector quantizer as a combinatorial optimization problem leading to a genetic search for a minimum-distortion index assignment. The performance is further enhanced by the use of the Fritchman (1967) channel model that more closely characterizes the statistical dependencies between error sequences. This study also presents an index assignment algorithm based on the Fritchman model with parameter values estimated using a real-coded genetic algorithm. Simulation results indicate that the global explorative properties of genetic algorithms make them very effective in estimating Fritchman model parameters, and use of this model can match index assignment to expected channel conditions     

Trellis coded modulation schemes for shadowed Rician fading channels

The Canadian mobile satellite (MSAT) channel has been modelled as the sum of lognormal and Rayleigh components to represent foliage attenuation and multipath fading, respectively. The paper derives a Chernoff based error bound on the performance of trellis coded modulation (TCM) schemes operating on this channel.<>     

Splitting algorithms in noisy channels with memory

Multi-access networks are considered in which the shared channel is noisy. The authors assume a slotted-time collision-type channel, Poisson infinite-user model, and binary feedback. Due to the noise in the shared channel, the received signal may be detected as a collision even though no message or a single message is transmitted. This kind of imperfect feedback is referred to as error. A common assumption in all previous studies of multi-access algorithms in channels with errors is that the channel is memoryless. The authors consider the problem of splitting algorithms when the channel has memory. They introduce a two-state, first-order Markovian model for the channel and analyze the operation of the tree collision-resolution algorithm in this channel. They obtain a stability result, i.e., the necessary conditions on the channel parameters for stability of the algorithm. Assuming that the stability conditions hold, they calculate the throughput of the algorithm. Assuming that the stability conditions hold, they calculate the throughput of the algorithm. Extensions to more general channel moders are discussed