Robust network coding against path failures
In this study, an approach for robust network coding is introduced for multicast in a directed acyclic network in the presence of network edge failures. The proposed designs aim at combating the resulting path failures, which result in interestingly scalable solutions. A robust network coding scheme (RNC1) is proposed that, devising a rate-path diversity trade-off for the receivers, attains the post-failure capacity of the network with high probability. The scheme is receiver based and can also be applied for correcting random erasures. Next, a rate-guaranteed robust network coding scheme (RNC2) is proposed. The code guarantees the maximum rate for a predetermined number of path failures. The scheme, of course, attains the refined Singleton bound for the edge failure model. A path failure may not necessarily reduce the network capacity, as the remaining intact edges within the network may still facilitate backup paths from the source to the sinks. We introduce RNC3 to employ such backup paths in addition to the original paths and guarantee multicast at a certain rate in the presence of all edge/path failure patterns that do not reduce the capacity below this rate. All the three proposed schemes for multicast are robust to a number of edge failures that may, in general, exceed the refined Singleton bound. Our analyses indicate that the design complexities and the required field sizes grow as a function of the number of network paths, as opposed to the number of network edges because of prior schemes.
