Many redundancy removal algorithms employ some sort of run length code. Blocks of timing words are coded with synchronization words inserted between blocks. The probability of incorrectly reconstructing a sample because of a channel error in the timing data is a monotonically nondecreasing function of time since the last synchronization word. In this paper we compute the "probability that the accumulated magnitude of timing errors equal zero" as a function of time since the last synchronization word for a zero-order predictor (ZOP). The result is valid for any data source that can be modeled by a first-order Markov chain and any digital channel that can be modeled by a channel transition matrix. An example is presented.

We consider optimum uniform data quantization for noisy channels. We present a general formulation for natural encoding that results in simple expressions for the mean-square error. Specifically, we show that the optimum location of the center of the quantizer is at the mean of the distribution for all error rates. The optimum levels for quantization and the corresponding mean-square error are presented for Gaussian and uniform data. For the latter the width of the optimum quantizer for noisy channels is shown to be smaller than the entire range of probability distribution.

In a communications system the total system error is of importance. One measure of system error is the mean-square error between the input signal and the output signal. The total mean-squared error includes sampling error, quantization error, and channel error. The work reported here considers all three errors in differential pulsecode modulation (DPCM) systems and compares the results obtained with standard pulse-code modulation (PCM) systems. The total meansquared error is determined using well-defined system parameters such as quantizer levels, signal-to-noise ratio (SNR), sampling rate, etc. Using the derived formulas the design of DPCM systems is facilitated along with various tradeoff studies. The error equations are determined for both uniform and nonuniform quantizers. The error due to channel noise is obtained in closed form for both cases. DPCM and PCM are compared for three different reconstruction filters, the zero-order hold (ZOH), the linear interpolator (LI), and the ZOH followed by a low-pass filter. The optimum prediction coefficient is shown to depend on the channel noise. The optimum prediction coefficient improves the performance of DPCM systems considerably. DPCM is shown to perform better than PCM in all cases. Simulation results are presented, which verify the theoretical results.

The Karhunen-Loève transformation is applied to multispectral data for information extraction, SNR improvement, and data compression. When applied in the spectral dimension, the transform provides a set of uncorrelated principal component images very useful in automatic classification and human interpretation. Significant improvements in SNR and estimates of the noise variance are also shown to be possible in the spectral dimension. Data compression results using the transform on one-, two-, and three-dimensional blocks over three general types of terrain are presented.

We show that the error signal incurred by block quantizing stationary data is nonstationary under some conditions. Examples are presented that indicate that the mean square error is largest at the block edges. When block quantizers are used to encode pictures at low bit rates, this effect tends to make the block edges visible in the reconstructed picture.

An upper bound on the rate-distortion function for discrete ergodic sources with memory is developed by partitioning the source sample space into a finite number of disjoint subsets and bounding the rates for each subset. The bound depends only on the mean vectors and covariance matrices for the subsets and is easy to compute. It is tighter than the Gaussian bound for sources that exhibit clustering of either the values or covariances of successive source outputs. The bound is evaluated for a certain class of pictorial data using both one-dimensional and two-dimensional blocks of picture elements. Two-dimensional blocks yield a tighter bound than one-dimensional blocks; both result in a significantly tighter bound than the Gaussian bound.

Published papers and reports dealing with data compression, picture properties and models, picture coding and transmission, image enhancement, and human visual information processing are listed.

A number of schemes for implementing a fast multiplier are presented and compared on the basis of speed, complexity, and cost. A parallel multiplier designed using the carry-save scheme and constructed from 74 series integrated circuits is described. This multiplier multiplies 10-bit by 12-bit binary numbers with a worst- case multiplication time of 520 ns. The cost of the integrated circuits was less than $ 500.

A recent paper by Crimmins et al. deals with minimization of mean-square error for group codes by the use of Fourier transforms on groups. In this correspondence a method for representing the groups in a form suitable for machine calculation is shown. An efficient method for calculating the Fourier transform of a group is also proposed and its relationship to the fast Fourier transform is shown. For groups of characteristic two, the calculation requires onlyN \log_2 Nadditive operations whereNis the order of the group.

Still pictures can be modeled as realizations of a two-dimensional random field. Similarly, pictures that unfold with time across an aperture can be modeled as realizations of three-dimensional fields. Correlated sources can be found by looking at different regions of the spectrum or at different areas of a picture. Under the assumption that the sources are Gaussian a method is presented for finding the rate distortion function for all such sources, under a mean-square-error criterion, in terms of their power spectral densities. In particular, the rate distortion functions for a pair of correlated processes and for a two-dimensional random field are derived.

An optimum system for transmitting a sample function from a stationary second order process over the BSC in real time is formulated under the mean-integral-square error criterion. The optimum number of channel bits and the optimum assignment of these bits to the samples is determined for the SGM process withR(\tau) = \exp(-|\tau}). The system error is evaluated and compared to the error performances of systems using time sampling with and without data compression. Shannon's information rate is also computed for these systems and compared to the theoretical limit and to Goblick's BSQC digitizer. We also present a waveform representation technique based on Hotelling's method of principal components. The waveform-to-vector converter consists of a time sampler followed by a digital filter, and the vector-to-waveform reconstructor consists of a digita filter followed by a linear interpolator. Performance is shown to be comparable to KL sampling.