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Two general classes of operations for the purpose of compressing the output of a message source are considered: (1) Entropy-reducing (ER) transformation, and (2) Information-preserving (IP) transformation (redundancy removal). The type (1) transformation, when acceptable, can yield substantial compression gains in telemetry applications while the type (2) transformation can yield substantial gains for certain types of source statistics. A new concept, adaptive coding, is introduced. It is shown that for quasi-stationary source statistics it is possible to obtain estimates of the statistics and to use these subsequently for efficient coding. A general statistical measure for monitoring the efficiency of the adaptive procedure is presented and a decision rule, based on this statistic, for updating the coding is defined. It is shown that the statistical estimates need not be precise since the coding efficiency remains reasonably insensitive to small errors; hence, only violent changes in the source statistics must be detected. A number of configurations for performing adaptive and non-adaptive compression are discussed in detail. Some of these procedures, such as predictive coding, are well known while others are new. In particular, a practical configuration is presented for compressing the output of many sensors which have the statistical structure; no changes in the signal for relatively long time intervals and very rapid changes for relatively short time intervals. It is concluded that this approach has the advantage over variable rate commutation procedures in that short message bursts can always be detected without increasing the communications channel capacity.