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On the Capacity of the Finite Field Counterparts of Wireless Interference Networks

机译：无线干扰网络有限现场对方的能力

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摘要

This paper explores how degrees of freedom (DoF) results from wireless networks can be translated into capacity or linear capacity results for their finite field counterparts that arise in network coding applications. The main insight is that scalar (SISO) finite field channels over (mathbb {F}_{!p^n}) are analogous to (ntimes n) vector (MIMO) channels in the wireless setting, but with an important distinction—there is additional structure due to finite field arithmetic, which enforces commutativity of matrix multiplication and limits the channel diversity to (n) , making these channels similar to diagonal channels in the wireless setting. Within the limits imposed by the channel structure, the DoF optimal precoding solutions for wireless networks can be translated into capacity or linear capacity optimal solutions for their finite field counterparts. This is shown through the study of capacity of the 2-user X channel and linear capacity of the 3-user interference channel. Besides bringing the insights from wireless networks into network coding applications, the study of finite field networks over (mathbb {F}_{!p^n}) also touches upon important open problems in wireless networks (finite SNR, finite diversity scenarios) through interesting parallels between (p) and SNR, and (n) and diversity.
机译：本文探讨了如何将无线网络产生的自由度（DoF）转换为网络编码应用中出现的有限域对应物的容量或线性容量结果。主要见解是（mathbb {F} _ {！p ^ n}）上的标量（SISO）有限场信道类似于无线设置中的（n×n）向量（MIMO）信道，但有一个重要区别-是由于有限域算术而产生的附加结构，该算法增强了矩阵乘法的可交换性并将信道分集限制为（n），从而使这些信道类似于无线设置中的对角信道。在信道结构所施加的限制内，可以将无线网络的DoF最佳预编码解决方案转换为其对应的有限域容量或线性容量最佳解决方案。通过研究2用户X信道的容量和3用户干扰信道的线性容量可以看出这一点。除了将无线网络的见解带入网络编码应用之外，对（mathbb {F} _ {！p ^ n}）上的有限域网络的研究还涉及到无线网络中的重要开放性问题（有限SNR，有限分集方案）。 （p）与SNR，以及（n）与分集之间有趣的相似之处。

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