arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2002.04438cs.ITcs.SImath.IT
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网络上编码数据包的概率转发

Probabilistic Forwarding of Coded Packets on Networks

B. R. Vinay Kumar, Navin Kashyap

摘要:

我们考虑的情况下,通过无噪声通信链路连接的节点的网络广播信息。网络中的源节点有一些数据包要广播。它将这些数据分组编码成$n$编码分组,使得网络中接收到$n$编码分组中的任何$k$的任何节点将能够检索所有原始数据分组。源将$n$编码的分组发送到其单跳邻居。网络中的每一个其他节点都遵循概率转发协议,在该协议中,它以一定的概率$p$将先前未接收到的分组转发给其所有邻居。如果至少接收到$n$编码分组的$k$的节点的预期分数接近于$1$,则我们说来自源的信息经历“接近广播”。选择转发概率$p$,以便最小化近距离广播所需的传输的预期总数。我们研究如何,对于一个给定的$k$,这个最小的转发概率和相关的预期的数据包传输的总数随$n$。我们具体分析了两种网络拓扑结构:二叉树和正方形网格编码数据包的概率转发。对于树,我们的分析表明,对于固定的$k$,预期的传输总数随着$n$的增加而增加。另一方面,在网格上,明智地选择$n$可以显著减少近距离广播所需的预期传输总数。在其他的连通网络拓扑结构中也观察到类似于网格的行为,例如随机几何图和随机正则图

英文摘要:

We consider a scenario of broadcasting information over a network of nodes connected by noiseless communication links. A source node in the network has some data packets to broadcast. It encodes these data packets into $n$ coded packets in such a way that any node in the network that receives any $k$ out of the $n$ coded packets will be able to retrieve all the original data packets. The source transmits the $n$ coded packets to its one-hop neighbours. Every other node in the network follows a probabilistic forwarding protocol, in which it forwards a previously unreceived packet to all its neighbours with a certain probability $p$. We say that the information from the source undergoes a ``near-broadcast'' if the expected fraction of nodes that receive at least $k$ of the $n$ coded packets is close to $1$. The forwarding probability $p$ is chosen so as to minimize the expected total number of transmissions needed for a near-broadcast. We study how, for a given $k$, this minimum forwarding probability and the associated expected total number of packet transmissions varies with $n$. We specifically analyze the probabilistic forwarding of coded packets on two network topologies: binary trees and square grids. For trees, our analysis shows that for fixed $k$, the expected total number of transmissions increases with $n$. On the other hand, on grids, a judicious choice of $n$ significantly reduces the expected total number of transmissions needed for a near-broadcast. Behaviour similar to that of the grid is also observed in other well-connected network topologies such as random geometric graphs and random regular graphs

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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