An automatic‐repeat request policy for a data transmission system with three types of error probabilities
Kazumi Yasui, Toshio Nakagawa, Hiroaki Sandoh · Electronics and Communications in Japan (Part III Fundamental Electronic Science) · 1996
Abstract In the data transmission, in general, the data error is inevitable due to the interference to the communication channel, e.g., temporary disconnection, the noise, and the distortion. Then the error control is indispensable in order to maintain a high quality of data and various methods have been devised from the viewpoint of reliability improvement. Among those, automatic‐repeat request (ARQ) is applied frequently to the point‐to‐point data transmission system, since the error can be controlled relatively simply. This paper assumes that the data error occurs at random, usually in the transmission system; and a transmission model is discussed where the generaton of the error is enhandced greatly by the occurrence of the intermittent faults and their potential period. In other words, it is assumed that the transmission system has three states, i.e., normal, temporary fault, and permanent fault. An ARQ model then is defined in which the error of the unit data arises with different probabilities in those states. When an error occurs, retransmissions are attempted for up to (N ‐ 1) times. If all retransmission trials fail, the transmission of the unit data is restarted from the initial state after the specified period. Using the probability genertive function, the mean time until the transmission of the unit data succeeds is derived. the optimal number N of retransmission trials that minimize the above mean time is determined analytically. Discussions are then made on the result using numerical examples.