Abstract:

Based on network coding, a method for constructing codes in multicast networks with link failure is proposed. More specifically, disjoint paths ( is larger than the multicast rate so that multicast transmissions can work well even at most link failures occur) are selected for each receiver, and the global coding vectors of any input links should be linearly independent. Then the receivers can obtain right symbols, and avoid link failure. By using some results available of MDS codes, the minimal finite field which is enough to implement network coding for different multicast rate is obtained. To design codes of multicast network and implement network coding, a generator matrix of a maximum distance separable（MDS） code is constructed based on the obtained minimal finite field, and its column vectors are allocated to input links of receivers as their coding vectors.

Key words: network coding, link failure, maximum distance separable codes, finite field