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In LPC analysis, the speech signal is divided into frames each of which is represented by a vector of estimated vocal tract parameters, assumed to be constant throughout the frame. For many sounds, these parameters do not change significantly from one frame to the next, and some of them can often be adequately represented by previously transmitted values. In the LPC coding systems described in this paper, a number of alternative representations are considered for each frame. These representations (vectors) are combinations of PARCOR coefficients from the current frame and from previous frames. Several consecutive frames are analyzed at once, and all the possible sequences of PARCOR coefficient vectors are examined. The sequence which minimizes a preselected cost function is chosen for transmission, resulting in a reduced overall data rate. The examination of all the decision sequences is equivalent to a decision tree search, which is most efficiently accomplished through dynamic programming. Using these techniques, LPC encoded speech at 1200 bits/s is demonstrated to be of quality comparable to a constant rate LPC vocoder at 2400 bits/s.