Precoding for Broadcasting with Linear Network Codes

A technique based on linear precoding is introduced for broadcasting on linear networks. The precoding allows the different message components of a broadcast message to be separated and decoded at the desired sink nodes, thus providing a systematic design methodology for broadcasting over a given network with a given linear network code. To achieve a good throughput, however, the network code itself must also be chosen judiciously. Motivated by several recent results on random network codes, we propose a combination of precoding and random linear network codes. This approach does not require a centralized coordination for network code design. One of the advantages of this approach is that by simply changing the precoding matrix (together with associated decoding strategies), different broadcast objectives can be achieved without tampering with the network code, therefore one can manage the network operation by controlling the origin and destination nodes of the network and without manipulating the network interior. Together, random network codes and linear precodings provide a simple yet powerful methodology for broadcast over linear networks.