# Multi-Phase Adaptive Recoding: An Analogue of Partial Retransmission in Batched Network Coding +
## 5 Conclusions  
Previous literature in BNC did not consider multi-phase transmission. When feedback is available, the fire-and-forget strategy is not the best choice. How to make use of the feedback for BNC is still an open problem, as there are too many different components involved in the deployment of BNC in real systems.  
In this paper, we investigated one possible use of feedback for adaptive recoding, together with a preliminary protocol design that can support multi-phase recoding. The information carried by the feedback is the rank of the batch at the node, which is simply a small integer. From our numerical evaluations, we can see that multi-phase recoding has a significant throughput gain when compared with the traditional fire-and-forget scheme. By simulating the decoding time, we found that the conventional throughput optimization for BNC may not be able to reflect the delay induced by the protocol and the recoding scheme. This suggests that in future works, the decoding time might be a more important objective to be optimized than the throughput, and it is likely to be a joint optimization problem with the design of the protocol. We also highlight a message that instead of making more transmissions, one direction to enhance the efficiency of BNC is to craft a well-designed inner code and feedback mechanism, as proposed in this paper.  
As this work is a preliminary study on multi-phase recoding, further investigations are necessary for different network setups and conditions. For example, we considered independent packet loss to simplify the formulation. Although it is common to make this assumption in the literature, a more accurate channel model should help in optimizing the gain of recoding, especially when there is a dependency between the recoding phases. The formulation of innovation rank distributions for other channel models is a major component in multi-phase recoding. Potential approaches include distributionally robust optimization for Markov chains [125] and advanced statistical models, e.g., [126]. The evaluation of the performance gap between the accurate and inaccurate channel models is another research direction. We will leave all these optimal strategies and the model development as open problems.  
We remark that the protocol we proposed is not standardized yet. Inconsistencies in implementations on how to use feedback may lead to unpredicted behaviors. However, BNC deployments usually have specialized purpose in self-contained networks that the owners have full control of, e.g., smart lamppost networks. This is because network coding requires recoding at intermediate nodes and it is not feasible to ask the public to replace all existing network infrastructures. This way, the consistency of protocol implementation can be maintained. However, a standard should be proposed in the future to avoid inconsistency when combining networks with different BNC implementations. On the other hand, optimization on the design is needed. For demonstration purposes, we assumed that a feedback packet is sent at every timeslot. This is not a good solution because every feedback packet consumes network resources. Delaying the feedback, however, would delay the trigger of recoding. The investigations of advanced feedback mechanism and its impact are left as future work.