Optimum block length for data transmission with error checking

The efficiency of a block-checking system of data transmission, in which an answer-back block-checking signal is provided to acknowledge each block of characters, or to ask for a repeat if an error is detected, is investigated. Curves of data transmission efficiency, as a function of the number of characters in a message block, are shown to have sharper peaks as the distance and error probabilities are increased. For comparison, efficiency curves are plotted for a 7-bit single-error-detecting code and for a 10-bit single-error-correcting code. A family of curves of optimum block length is given for different probabilities of error and different reply times.