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An information theory approach to the theory and practice of linear predictive coded (LPC) speech compression systems is developed. It is shown that a traditional LPC system can be viewed as a minimum distortion or nearest-neighbor system where the distortion measure is a minimum discrimination information between a speech process model and an observed frame of actual speech. This distortion measure is used in an algorithm for computer-aided design of block source codes subject to a fidelity criterion to obtain a 750-bits/s speech compression system that resembles an LPC system but has a much lower rate, a larger memory requirement, and requires no on-line LPC analysis. Quantitative and informal subjective comparisons are made among our system and LPC systems.