The Upper Bounds of the Confidence Intervals of Bit Error Probabilities Based on a Markov Chain Bit Error Model

Abstract

Confidence intervals for the bit error probability of an actual PCM telemetry data can be determined based on the analysis of received redundant bits. The procedure usually requires the assumption of independence of bit errors. However, bit errors may occur in clusters under various conditions of multipath, injection of nonthermal noise of long duration, and bit jitters. As a representation of bit errors in clusters, a Markov chain model is introduced. Some results on the confidence interval of bit error probability are obtained as functions of a Markovian parameter, which designates the degree of departure from the binomial model. The computations are quite laborious compared to the case of the binomial model. This paper gives step-by-step instructions for computing the probabilities that r error bits occur among mn received bits which can then be used for the derivation of the confidence interval.