Errors encountered in digital transmission over most real communication channels are not independent but appear in clusters. Such channels are said to exhibit memory, i.e., statistical dependence in the occurrence of errors; and thus cannot be adequately represented by the classical memoryless binary symmetric channel. The existence of memory implies additional capacity. To exploit this through efficient coding schemes, it is necessary to describe and model the underlying statistical structure of the error process. This paper reviews various channel models, noting the interaction between channel modeling and error control.

Models for channels with memory and their applications to error control

The design of speech coders that produce high-quality highly intelligible speech at 6 to 16 kb/s while retaining robustness to background and transmission impairments is an area of current research interest Differential encoding structures employing adaptive quantization and adaptive prediction constitute one of the most promising approaches to achieving these design objectives This paper focuses on the design and analysis of adaptive predictors for differential encoders Several differential encoding systems, including adaptive predictive coding, differential pulse-code modulation, noise feedback coding, direct feedback coding, and prediction error coding, are described and related Adaptive quantizers are briefly discussed and quantitative and qualitative indicators of speech coder performance are defined The channel model, the speech model, and the research problem statements used in the design of differential encoders and adaptive predictors are presented The nomenclature and theory of forward and backward adaptive prediction are developed, and several new backward adaptive algorithms based on various assumptions are presented A detailed survey of theoretical and simulation results on adaptive prediction for speech differential encoders is given, and the effects of background and transmission impairments on these systems are discussed, Finally, the impact of adaptive predictors on rate distortion theory motivated coders is indicated Numerous areas for future research are highlighted

Adaptive prediction in speech differential encoding systems

A field test has been made in order to better understand the digital mobile radio channel. At the mobile receiver (450 MHz, 1200 bits/s) recordings were made of the digital signal and the field strength. These recordings were later analyzed by a computer. Some existing models for digital channels have been tested. Theoretically motivated probability density functions for the fading envelope have also been considered. A new model for the digital channel is proposed. This model is a memoryless binary symmetric channel (BSC) with field strength dependent crossover error probability. This model fits very well to the recorded data.

Characteristics of a digital mobile radio channel

The problem of optimal carrier recovery and detection of digitally phase modulated signals on fading channels by using a nonstructured approach is presented, i.e. no constraint is placed on the receiver structure. First, the optimal receiver is derived for digitally phase-modulated signals when transmitted over a frequency-nonselective fading channel with memory. The memory results from the fact that usually the coherence time of the channel is larger than the symbol period. Symbols adjacent in time cannot be detected independently and therefore the well-known quadratic receiver is not optimal in this case. A maximum a posteriori (MAP) detector is derived and explicitly utilizes the channel memory for carrier recovery. The derivation shows that the optimal carrier recovery is, under certain conditions, a Kalman filter. Some attractive properties of this carrier recovery unit (including the absence of hang up) are discussed. Then the error rate of several digital modulation schemes is calculated taking the performance of the filter into account. The differences in susceptibility of the modulation schemes to carrier phase jitter are specified. >

A systematic approach to carrier recovery and detection of digitally phase modulated signals of fading channels

Two important classes of coding schemes that use the spatial correlation of picture elements in reducing data redundancy are the differential pulse-code modulation (DPCM) and the unitary transform coding techniques. We will study the performance of an n th order DPCM system for n ranging from 1 to 22 and compare it to the performance of the unitary-transform techniques (Hadamard, Fourier, and KarhunenLoeve) in coding two monochrome still pictures. We will also consider the sensitivities of the coding systems to picture-to-picture variations.

Comparison of nth-Order DPCM Encoder With Linear Transformations and Block Quantization Techniques

In this paper, an adaptive receiver with memory for fading communication channels is considered. The receiver consists of an estimator and a detector. The estimator is a finite-memory MMSE estimator with decision-feedback which minimizes the probability of error of the receiver. Asymptotic approximations are employed to derive an adaptive decision role based on the estimate. An example is presented where the receiver with memory is shown to perform better than an optimum receiver without memory.

A Receiver with Memory for Fading Channels

A Markov gap model is proposed for real digital communication channels. Analytic properties of the model are investigated and compared with data from VHF and troposcatter channels. The model is also simulated, and the satistics of the simulated data are compared favorably with those of the real data.

Markov Gap Models for Real Communication Channels

This paper presents some theoretical properties of a predictive quantizing system for the transmission of random signals. Expressions for the mean-squared error are derived for some input processes. It is shown that for the Gaussian case the predictive system gives no improvement over the conventional system. The class of linear Markov processes is also considered, and an example is presented which clearly illustrates the limited region of improvement for the predictive system. The relation of the improvement to the correlation of the input samples is also illustrated.

Some Properties of a Predictive Quantizing System

A variable length feedback scheme for binary constant antipodal signals with an upper bound on the decision time is proposed. In addition to the noiseless decision feedback channel a noiseless information feedback channel is used for energy saving. The performance of the scheme is derived, and the probability of error as a function of the average energy per symbol is compared to existing systems. Two of the existing systems may be obtained as limiting cases of the combined scheme considered here.

A. Haddad

Papers

A Receiver with Memory for Fading Channels

Markov Gap Models for Real Communication Channels

Some Properties of a Predictive Quantizing System

A Binary Sequential Communication Scheme With Information Feedback