The Effects of Channel Errors in DPCM Systems and Comparison with PCM Systems

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.