The considerations involved in combining data compression and error control coding in space telemetry are analyzed through the use of two performance measures, D and R, which are similar to those measures used by Shannon for his rate distortion function. The average distortion D is a function of the source probability distribution, the overall system transitional probability matrix, and a cost matrix which signifies the relative importance of different types of data errors. The rate-ratio R is the reciprocal of the overall system compression ratio and includes the data expansion effect of additional timing data, identification data, and coding redundancy. Different schemes for supplying the timing information in a compressed system are analyzed and compared. A new timing scheme is developed which requires, on the average, fewer time words for a large class of data sources. A method is developed for uniquely encoding and decoding an entire sequence of time words for compressed data, utilizing the strict monotonicity of the sequence. The effects of the following system parameters and properties on the overall distortion and rate-ratio are analyzed: the error-control usefulness of natural data redundancy, errors in time information, the error-control usefulness of time word monotonicity, the probability distribution of the source, the bit-error probability of a binary symmetric channel, and the word compression ratio. A rationale for comparing and choosing among three systems--uncompressed-uncoded, compressed-uncoded, and compressed-coded--is given in terms of the performance measures D and R.

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