Time extended block network erasure control code: A path-time network-channel code

In this paper, time-extended block network error/erasure control coding (TBNEC) for robust multicast communications in a directed acyclic network is proposed. The proposed codes jointly exploit the network path diversity and the time diversity due to an extended coding period. Time extended Singleton bound, on the total number of manageable symbol errors/erasures on all network edges within a coding-period is introduced. A TBNEC design scheme is presented to attain the new bound. Next, new bound on the total number of manageable symbol erasures in a certain network edge within a coding-period is introduced. Subsequently, improved TBNEC codes are designed to attain this bound. Finally, we show that the improved TBNEC code asymptotically achieves the multicast capacity of a symbol erasure network with independent edges and no interference.