Delay invariant convolutional network codes

In this work, we define delay invariant convolutional network codes which guarantee multicast communication at asymptotically optimal rates in networks with arbitrary delay patterns. We show the existence of such a code over every symbol field. Moreover, the code can be constructed with high probability when coding coefficients are independently and uniformly chosen from a sufficiently large set of coding operations. On the other hand, if the symbol field is no smaller than the number of receivers, we devise a method to efficiently construct a delay invariant convolutional network code with scalar coding coefficients.