无线信息流的组合算法
Combinatiorial Algorithms for Wireless Information Flow
摘要：
描述无线中继网络的单播容量是信息论中一个长期存在的问题。由于无线信道固有地广播信号并且在传输之间存在干扰，所以由于在网络中引起的复杂信号交互而出现困难。最近，Avestimehr，Diggavi和Tse提出了一种线性确定性模型，该模型考虑了无线信道的共享特性，重点关注信号相互作用而不是背景噪声。他们将图的最小割最大流定理推广到确定性信道的网络，并证明了容量可以使用信息理论工具来实现。他们表明，在这种情况下，最小割的值是描述源-目的地割的所有邻接矩阵的最小秩。在本文中，我们开发了一个多项式时间算法，发现中继编码策略，以实现线性确定性（无线）网络中的最小割值，单播连接的情况下。我们的算法关键使用信道之间的线性独立的概念来计算容量在多项式时间。此外，我们可以通过在中间结点使用非常简单的单符号处理来实现容量，从而建设性地产生有限长度策略，其实现线性确定性（无线）中继网络的单播容量。
英文摘要：
A long-standing open question in information theory is to characterize the unicast capacity of a wireless relay network. The difficulty arises due to the complex signal interactions induced in the network, since the wireless channel inherently broadcasts the signals and there is interference among transmissions. Recently, Avestimehr, Diggavi and Tse proposed a linear deterministic model that takes into account the shared nature of wireless channels, focusing on the signal interactions rather than the background noise. They generalized the min-cut max-flow theorem for graphs to networks of deterministic channels and proved that the capacity can be achieved using information theoretical tools. They showed that the value of the minimum cut is in this case the minimum rank of all the adjacency matrices describing source-destination cuts. In this paper, we develop a polynomial time algorithm that discovers the relay encoding strategy to achieve the min-cut value in linear deterministic (wireless) networks, for the case of a unicast connection. Our algorithm crucially uses a notion of linear independence between channels to calculate the capacity in polynomial time. Moreover, we can achieve the capacity by using very simple one-symbol processing at the intermediate nodes, thereby constructively yielding finite length strategies that achieve the unicast capacity of the linear deterministic (wireless) relay network.
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