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Design of the output buffer is one of the most important tasks in implementing an adaptive data compression system. Upon proper design of the buffer including such parameters as size, inputoutput data rates, and occupancy control, rests the overall compression efficiency and error performance of the system. The binomial distribution is used to derive an exact model for a synchronous buffer. The Poisson distribution, which provides a reasonable model for a high-speed asynchronous buffer, is shown to yield an error greater than 10 percent in required buffer length for synchronous buffers. Design requirements such as probabilities of overflow and underflow, buffer length, and average buffer fill are derived as functions of compression ratio φ and the ratio of input-output transmission rates . It is shown that the buffer queuing behavior is a function of the ratio , as well as and φ independently. The derived results indicate that restricting buffer overflow by increasing the buffer size is inefficient. Control is suggested in which the aperture of the compression algorithm is changed to control the buffer fill. The design requirements are determined for the zero-order predictor and the first-order interpolator with two degrees of freedom. Using the buffer equations derived and the compression ratio-aperture relationship, the design of a buffer is described. It is shown that doubling the aperture with a resultant doubling in rms error reduces the buffer probability of overflow by a factor of 100.