An Analysis of Retransmission Systems

This paper presents an analysis of the throughput rate R and undetected block error rate ρ for each of three basic types of retransmission logics: 1) send and wait for confirmation, 2) send continuously repeating each individual unconfirmed message, and 3) send continuously repeating each unconfirmed message together with those which followed it. Formulas for R and ρ were obtained in terms of the probability of detected block error and the probability of misinterpreted confirmation or retransmission request. Several options for interpreting garbled service information were considered and the corresponding formulas for R and ρ were obtained. Block diagrams are presented which show the possible sequences of events and their probabilities for each type of logic. Analysis of the third logic required models based on seven-state and ten-state Markov processes. Tractable formulas were not obtainable in closed form but only as solutions to matrix equations. Approximate formulas for R and ρ were derived for this case. The results of this paper are used in a companion paper to compare the performance of forward error correcting codes and retransmission systems under various channel conditions.