论文标题
合作X通道的DOF，并具有分布式计算的应用
DoF of a Cooperative X-Channel with an Application to Distributed Computing
论文作者
论文摘要
我们考虑使用$ \ sf k $发射器（TXS）和$ \ sf k $接收器（RXS）的合作X渠道，其中TXS和RXS分别分为大小$ \ sf r $。属于同一组的TXS合作将消息共同向所有其他组中的$ \ sf k- \ sf r $ rxs共同传递，每个RX单独解码其所有预期的消息。通过引入新的干扰一致性（IA）方案，我们证明，当$ \ sf k/\ sf r $是该渠道的整数时，该渠道的总和度（SDOF）在$ 2 \ sf r $的范围下，如果$ 2 \ sf r $，如果$ \ \ sf sf k/\ sf k/\ sf k/\ sf k/\ sf r \ \ sf r \ \ in \ in \ in \ {2,3,3，s $ \ f frac（ k- \ sf r） - \ sf r^2} {2 \ sf k-3 \ sf r} $如果$ \ sf k/\ sf k/\ sf r \ geq 4 $。我们还证明，SDOF由$ \ frac {\ sf k（\ sf k- \ sf r）} {2 \ sf k-3 \ sf r} $界定。拟议的IA方案在无线分布式MAPREDUCE框架中找到了应用程序，在该框架中，它可以改善与最新技术相比的标准化数据传递时间（NDT）。
We consider a cooperative X-channel with $\sf K$ transmitters (TXs) and $\sf K$ receivers (Rxs) where Txs and Rxs are gathered into groups of size $\sf r$ respectively. Txs belonging to the same group cooperate to jointly transmit a message to each of the $\sf K- \sf r$ Rxs in all other groups, and each Rx individually decodes all its intended messages. By introducing a new interference alignment (IA) scheme, we prove that when $\sf K/\sf r$ is an integer the sum Degrees of Freedom (SDoF) of this channel is lower bounded by $2\sf r$ if $\sf K/\sf r \in \{2,3\}$ and by $\frac{\sf K(\sf K-\sf r)-\sf r^2}{2\sf K-3\sf r}$ if $\sf K/\sf r \geq 4$. We also prove that the SDoF is upper bounded by $\frac{\sf K(\sf K-\sf r)}{2\sf K-3\sf r}$. The proposed IA scheme finds application in a wireless distributed MapReduce framework, where it improves the normalized data delivery time (NDT) compared to the state of the art.
