Performance Measures for Compressed and Coded Space Telemetry Systems

The considerations involved in the combination of 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 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 that 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 and identification data as well as coding redundancy. 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; the effect of errors in time information; the use of the strict monotonicity of the time information for error control; the probability distribution of the source; the biterror 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.