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We report on research to code speech at 16 kbit/s with the goal of having the quality of the coded speech be equal to that of the original. Some of the original speech had been corrupted by noise and distortions typical of long-distance telephone lines. The basic structure chosen for our system was adaptive predictive coding. However, the rigorous requirements of this work led to a new outlook on the different aspects of adaptive predictive coding. We have found that the pitch predictor is not cost-effective on balance and may be eliminated. Solutions are presented to deal with the two types of quantization noise: clipping and granular noise. The clipping problem is completely eliminated by allowing the number of quantizer levels to increase indefinitely. An appropriate self-synchronizing variable-length code is proposed to minimize the average data rate; the coding scheme seems to be adequate for all speech and all conditions tested. The granular noise problem is treated by modifying the predictive coding system in a novel manner to include an adaptive noise spectral shaping filter. A design for such a filter is proposed that effectively eliminates the perception of granular noise.