Batched network coding with adaptive recoding for multi-hop erasure channels with memory

In this paper, we study the achievable throughput of batched temporal network coding in multi-hop erasure channels, where network coding is applied only within small coding blocks and each communication hop is modeled as a Gilbert-Elliott (GE) packet erasure channel. The GE channel is a 2-state Markov model that is commonly used for channels with memory. While channel memory does not affect the end-to-end capacity of multi-hop erasure channels, we show that it degrades the end-to-end throughput, when batched network coding with finite batch size is applied, due to the higher variance in erasures within one coding block. On the other hand, if the initial channel state information is available, the channel variance can be significantly reduced. We show that this fact can be utilized for improving the efficiency of the recoding operations at the intermediate nodes, and hence improve the end-to-end throughput of batched network coding schemes. Specifically, we propose adaptive recoding operations, where the network coded packets are adaptively generated based on the number of received packets and the initial channel state for each coding block. The simulation results show that the proposed adaptive recoding scheme significantly enhances the end-to-end throughput of batched network coding over multi-hop GE channels.