Recursively indexed differential pulse code modulation

The performance of a differential pulse code modulation (DPCM) system with a recursively indexed quantizer (RIQ) under various conditions, with first order Gauss-Markov and Laplace-Markov sources as inputs, is studied. When the predictor is matched to the input, the proposed system performs at or close to the optimum entropy constrained DPCM system. If one is willing to accept a 5 percent increase in the rate, the system is very forgiving of predictor mismatch

On Predictive Coding for Erasure Channels Using a Kalman Framework

We present a new design method for robust low-delay coding of autoregressive (AR) sources for transmission across erasure channels. It is a fundamental rethinking of existing concepts. It considers the encoder a mechanism that produces signal measurements from which the decoder estimates the original signal. The method is based on linear predictive coding and Kalman estimation at the decoder. We employ a novel encoder state-space representation with a linear quantization noise model. The encoder is represented by the Kalman measurement at the decoder. The presented method designs the encoder and decoder offline through an iterative algorithm based on closed-form minimization of the trace of the decoder state error covariance. The design method is shown to provide considerable performance gains, when the transmitted quantized prediction errors are subject to loss, in terms of signal-to-noise ratio (SNR) compared to the same coding framework optimized for no loss. The design method applies to stationary auto-regressive sources of any order. We demonstrate the method in a framework based on a generalized differential pulse code modulation (DPCM) encoder. The presented principles can be applied to more complicated coding systems that incorporate predictive coding as well

Study and simulation of low rate video coding schemes

The semiannual report is included. Topics covered include communication, information science, data compression, remote sensing, color mapped images, robust coding scheme for packet video, recursively indexed differential pulse code modulation, image compression technique for use on token ring networks, and joint source/channel coder design

Mismatched DPCM Encoding of Autoregressive Processes

A method is developed for computing the mean squared error distortion of differential pulse code modulation applied to Gaussian autoregressive sources. This extends previous work wherein the code predictor was matched to the source. A two-dimensional version of the projection method is developed for the computation of the stationary distribution of the joint source-state process, from which distortion can be readily evaluated. An iterative algorithm is used to optimize the quantizer for a given source and predictor. The results show that the matched predictor is very nearly optimal but not exactly so, and that DPCM is fairly robust to mismatch of the prediction coefficient to the correlation coefficient of a first-order autoregressive source. © 1990 IEE

Predictive Quantization of Autoregressive and Composite Random Processes.

This thesis is concerned with the Differential Pulse Modulation (DPCM) encoding of Autoregressive and Composite random processes. The goal in our study is to compute the average distortion introduced by the code between the input process and the reproduction process and optimize the parameters of the code so as to minimize the average distortion. For the case of an autoregressive source and a matched DPCM code a well known approximation technique has been previously used for the evaluation of the code's distortion. However, the validity of this approximation method has not been justified before, and it has only been applied in the matched case. We establish a framework in which this approximation technique can be viewed as the projection method for the numerical solution of integral equations. We then obtain sufficient conditions under which the approximation technique can be rigorously justified. Mismatched DPCM encoding of autoregressive processes is studied next. We assume a first order predictor, and study the asymptotically stationary joint input-reproduction process. It is demonstrated that for small values of the prediction coefficient the stationary distribution of this process is singularly continuous. We conjecture that when the prediction coefficient is large, this distribution is absolutely continuous. For the latter case a two dimensional version of the projection method is developed to solve the Chapman-Kolmogorov equation for the stationary distribution. We then develop a recursive algorithm for evaluating distortion and optimizing the code. Finally we study the DPCM encoding of regenerative composite sources with Markovian mode processes. Two methods are developed for the evaluation of the code's average distortion. The first method provides insight into the code's operation in the sense that it describes the code's distortion on the composite source in terms of the code's transient distortion on individual mode processes. The second method can be utilized to optimize the code parameters. Numerical results are obtained using the second method only. Our results are consistent with the simulation results obtained by other authors. The main advantage of our procedure over simulation is that we can use our algorithm recursively to optimize the code parameters, whereas such can not be easily achieved through simulation.Ph.D.Systems scienceUniversity of Michiganhttp://deepblue.lib.umich.edu/bitstream/2027.42/161442/1/8712182.pd