On Broadcast Stability of Queue-Based Dynamic Network Coding Over Erasure Channels

The transmission of packets is considered from one source to multiple receivers over single-hop erasure channels. The objective is to evaluate the stability properties of different transmission schemes with and without network coding. First, the throughput limitation of retransmission schemes is discussed and the stability benefits are shown for randomly coded transmissions, which, however, need not optimize the stable throughput for finite coding field size and finite packet block size. Next, a dynamic scheme is introduced for distributing packets among virtual queues depending on the channel feedback and performing linear network coding based on the instantaneous queue contents. The difference of the maximum stable throughput from the min-cut rate is bounded as function of the order of erasure probabilities depending on the complexity allowed for network coding and queue management. This queue-based network coding scheme can asymptotically optimize the stable throughput to the max-flow min-cut bound, as the erasure probabilities go to zero. This is realized for a finite coding field size without accumulating packet blocks at the source to start network coding. The comparison of random and queue-based dynamic network coding with plain retransmissions opens up new questions regarding the tradeoffs of stable throughput, packet delay, overhead, and complexity.