We propose a novel multipath multi-hop adaptive and causal random linear network coding (AC-RLNC) algorithm with forward error correction. This algorithm generalizes our joint optimization coding solution for point-to-point communication with delayed feedback. AC-RLNC is adaptive to the estimated channel condition, and is causal, as the coding adjusts the retransmission rates using a priori and posteriori algorithms. In the multipath network, to achieve the desired throughput and delay, we propose to incorporate an adaptive packet allocation algorithm for retransmission, across the available resources of the paths. This approach is based on a discrete water filling algorithm, i.e., bit-filling, but, with two desired objectives , maximize throughput and minimize the delay. In the multipath multi-hop setting, we propose a new decentralized balancing optimization algorithm. This balancing algorithm minimizes the throughput degradation, caused by the variations in the channel quality of the paths at each hop. Furthermore, to increase the efficiency, in terms of the desired objectives, we propose a new selective recoding method at the intermediate nodes. We derive bounds on the throughput and the mean and maximum in-order delivery delay of AC-RLNC, both in the multipath and multipath multi-hop case. In the multipath case, we prove that in the non-asymptotic regime, the suggested code may achieve more than 90% of the channel capacity with zero error probability under mean and maximum in-order delay constraints, namely a mean delay smaller than three times the optimal genie-aided one and a maximum delay within eight times the optimum. In the multipath multi-hop case, the balancing procedure is proven to be optimal with regards to the achieved rate. Through simulations, we demonstrate that the performance of our adaptive and causal approach, compared to selective repeat (SR)-ARQ protocol, is capable of gains up to a factor two in throughput and a factor of more than three in mean delay and eight in maximum delay. The improvements on the throughput delay trade-off are also shown to be significant with regards to the previously developed singlepath AC-RLNC solution.

中文翻译：

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多路径多跳通信的带反馈自适应因果网络编码

我们提出了一种具有前向纠错的新颖的多径多跳自适应和因果随机线性网络编码（AC-RLNC）算法。该算法概括了我们的联合优化编码解决方案，用于具有延迟反馈的点对点通信。AC-RLNC适应估计的信道状况，并且是因果关系的，因为编码使用先验和后验算法来调整重传速率。在多路径网络中，为了实现所需的吞吐量和延迟，我们建议在路径的可用资源中合并用于重新传输的自适应数据包分配算法。该方法基于离散水填充算法，即位填充，但是有两个期望的目标 ，最大化吞吐量并最大程度地减少延迟。在多路径多跳设置中，我们提出了一种新的分散式均衡优化算法。该平衡算法将吞吐量下降降到最低，该吞吐量下降是由每个跃点上路径的信道质量变化引起的。此外，为了提高效率，就所需目标而言，我们在中间节点处提出了一种新的选择性重新编码方法。在多径和多径多跳情况下，我们得出了AC-RLNC的吞吐量以及平均和最大顺序交付延迟的界限。在多径情况下，我们证明了在非渐近状态下，在均值和最大有序延迟约束下，建议的代码可以实现零误码概率超过90％的信道容量，也就是说，平均延迟小于最佳辅助频率的三倍，最大延迟小于最佳频率的八倍。在多路径多跳的情况下，就达到的速率而言，平衡过程被证明是最佳的。通过仿真，我们证明了与选择性重复（SR）-ARQ协议相比，我们的自适应和因果方法的性能能够使吞吐量提高2倍，平均延迟提高3倍，平均延迟提高8倍。最大延迟。对于先前开发的单路径AC-RLNC解决方案，还显示了吞吐量延迟权衡方面的显着改进。我们证明，与选择性重复（SR）-ARQ协议相比，我们的自适应和因果方法的性能能够使吞吐量提高2倍，平均延迟提高3倍，最大延迟提高8倍。对于先前开发的单路径AC-RLNC解决方案，还显示了吞吐量延迟权衡方面的显着改进。我们证明，与选择性重复（SR）-ARQ协议相比，我们的自适应和因果方法的性能能够使吞吐量提高2倍，平均延迟提高3倍，最大延迟提高8倍。对于先前开发的单路径AC-RLNC解决方案，还显示了吞吐量延迟权衡方面的显着改进。