Decodability of Network Coding with Time-Varying Delay and No Buffering

In the traditional information transmission through a network, an intermediate node was only allowed to duplicate input information and output the duplication. In contrast, in the transmission with the network coding, an intermediate node is able to code the input information from multiple links and outputs the coded information. The multicast using the network coding can achieve higher information rate than the traditional multicast [1]. Hence the network coding is attracting much attention as a method for multicast. Furthermore, it is known that linear coding in each node is sufficient to multicast in such a rate [2]. Accordingly in this paper, we only deal with the linear network coding. In the following, the network coding refers to the linear network coding, and the single source multicast is considered. For practical realization of the network coding, we should consider delay in the information transmission and delay is not always constant in time. Because of timevarying delay, a sink may sometimes fail to decode transmitted information depending on the structure of the network and coding. However, in most of past research of the network coding, it was assumed that there is constant delay that does not change in time or that there is no delay of information transmission [1]–[4]. The drawback in these researches is that each node have to wait for coding until all the information reaches to the node when there is time-varying delay. This means that the buffer for coding by nodes is necessary and that transmission delay unnecessary accumulates in every node. As a research considering time-varying delay, Chou et al. proposed a scheme by employing generation [5]. In the scheme, packets containing information multicasted at the