Theory and Application of DPCM and Comparison of DPCM With Other Time Predictive Techniques

JOSEPH EDWARD ESSMAN, Purdue University

Abstract

Differential pulse code modulation systems are analyzed using total mean-squared error as the measure of fidelity. The formulation of the total system error is done using sampled data and spectral techniques. Design formulae are obtained in terms of tangible system parameters such as sampling rates, quantizer levels, quantizer ranges, signal-to-noise, etc. The use of uniform and nonuniform quantization are considered. The formulae derived include the effects of channel errors when non- uniform quantization is used. Spectral densities for the various error terms in DPCM are obtained. The effects of channel errors using non-uniform quantizers are shown to result in an error spectral density which is not white. This result indicates the propagation of error in DPCM systems. Approximate results for the spectral density of the error term due to channel noise are obtained which is valid for a three or more bit quantizer. Simulation studies are performed to justify the assumptions of independence between the quantizing noise and the input signal; between the channel noise and the input signal; and between the channel noise and the quantizing noise.The derived formulae are used to obtain the total system error using three reconstruction filters-the zero-order-hold, the linear interpolator, and a zero-order-hold followed by a low pass filter. The optimum prediction coefficient is obtained for each reconstruct or for both the noiseless case and noisy case. For the noiseless case the optimum prediction coefficient is that prescribed by prediction theory. For the noisy case the optimum prediction coefficient differs from that prescribed by prediction theory depending on the signal-to-noise ratio. Rate distortion curves are presented for PCM and DPCM using the various reconstruction filters. The use of the optimum prediction coefficient in the noisy case results in the occurrence of the knee of the rate distortion curves at higher bit rates and lower error. Results are presented in terms of the bit savings obtained in using DPCM over PCM for equivalent performance of the two systems. In all cases it is seen that the performance of DPCM is superior to that of PCM. Simulation results are given for PCM and DPCM which verify the theoretical results.DPCM techniques are used to process still pictures consisting of scenes of a cameraman, a face, a crowd, a chest X-ray and an X-ray of a skull. Results are presented for various error criteria and for various number of quantizer levels. It is seen that three bits are sufficient for a good reproduction. Two bits appear to give usable results, particularly for the medical pictures. The effects of channel noise and using too high of a prediction coefficient are shown for the scene of the cameraman.The results of processing the various pictures by the Zero-Order- Predictor method (ZOP) and the Fan method are given. Since these methods require a buffer for temporary storage, experimental results are given to determine the optimum length of the timing word. The effects of channel noise, buffer underflows and buffer overflows are indicated for the scene of the cameraman. These types of predictive techniques are very sensitive to channel noise. The results of using the Fan method and the Zero-Order-Predictor method appear to be approximately equivalent. The primary degradation in both systems is due to streaking. This is less noticable in the Fan method.Comparisons between the pictures obtained using the Fan and ZOP methods with those obtained using DPCM indicate that DPCM can be trans- mitted with over one bit per picture element less. The pictures of the skull and the chest using DPCM techniques are of considerably higher quality than those obtained using the ZOP and Fan methods. For these pictures, two bits per picture element gives satisfactory results using DPCM techniques. The Fan and ZOP methods require over four bits per picture element to obtain usable results.

Degree

Ph.D.

Subject Area

Electrical engineering

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