On network coding with finite channel state information

Ming Xiao, M. Skoglund
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引用次数: 5

Abstract

We study network coding for wireless networks with finite channel state information (CSI) at intermediate nodes (relays). Based on the CSI of the relay-sink channels, we adapt the network codes at the relays. For a specific network with two sources, four relays and two sinks, the analytic results show that one bit CSI of all relay-sink channels (global CSI) can reduce complexity (field size), and simultaneously decrease the erasure probability. Then, we generalize the results to relay networks with M users, N relays and J sinks. We show that fixed network codes without CSI cannot achieve instantaneous min-cut, i.e., min-cut under current channel state. We also show that with one bit global CSI, we can achieve instantaneous min-cut by adapting the network codes using an alphabet size L, where L is the number of sinks connecting to a relay. Yet, the fixed MDS network codes use an alphabet size L(M−1N−1). For the networks with perfect or imperfect source-relay channels, adaptive network codes with one bit global CSI have lower erasure probability than the codes without CSI. Thus, one bit global CSI can reduce the erasure probability, and simultaneously reduce coding complexity.
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有限信道状态信息下的网络编码
本文研究了中间节点(中继)具有有限信道状态信息的无线网络的网络编码问题。根据中继接收信道的CSI,对中继上的网络编码进行调整。分析结果表明,对于具有两个源、四个中继和两个接收器的特定网络,所有中继-接收器通道的1位CSI(全局CSI)可以降低复杂性(字段大小),同时降低擦除概率。然后,我们将结果推广到具有M个用户、N个中继和J个接收器的中继网络。我们证明了没有CSI的固定网码不能实现瞬时最小割,即当前信道状态下的最小割。我们还表明,使用一位全局CSI,我们可以通过使用字母大小L来调整网络代码来实现瞬时最小切断,其中L是连接到继电器的接收器数量。而固定MDS网络码使用的是字母大小L(M−1N−1)。对于具有完全或不完全源中继信道的网络,具有1位全局CSI的自适应网络码比不具有全局CSI的自适应网络码具有更低的擦除概率。因此,1位全局CSI可以降低擦除概率,同时降低编码复杂度。
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