On the information about message arrival times required for in-order decoding

Suppose that messages arrive at a source A according to a point process at random times X₁, X₂, …, X_n , to be transmitted to a receiver B, and are decoded at B at times Y₁,Y₂, …, Y_n, where Y_i⩾X_i, i=1, …, n. The fact that B is able to decode message i at time Y_i means that by time Y_i, B must have been informed that message i had arrived at A. Thus B must have received some infermation about the times at which messages arrived at A, apart from the information about the contents of the messages. The amount of information about the message arrival times that the receiver must receive was first analyzed by Gallager (1976), who reasoned that this information must be at least equal to I(X₁ , …, X_n; Y₁, …, Y_n). We refine Gallager´s approach by imposing the constraint that the messages be decoded at the receiver in the same order they arrived at the source, for example in a virtual circuit connection in a network or on a point-to-point channel