  A single source network is said to be memory-free if all of the internal
nodes (those except the source and the sinks) do not employ memory but merely
send linear combinations of the symbols received at their incoming edges on
their outgoing edges. In this work, we introduce network-error correction for
single source, acyclic, unit-delay, memory-free networks with coherent network
coding for multicast. A convolutional code is designed at the source based on
the network code in order to correct network-errors that correspond to any of a
given set of error patterns, as long as consecutive errors are separated by a
certain interval which depends on the convolutional code selected. Bounds on
this interval and the field size required for constructing the convolutional
code with the required free distance are also obtained. We illustrate the
performance of convolutional network error correcting codes (CNECCs) designed
for the unit-delay networks using simulations of CNECCs on an example network
under a probabilistic error model.
