CRII: CIF: Towards a Systematic Interference Alignment Approach for Network Information Flow

通信和存储网络在现代生活的各个方面发挥着不可或缺的作用。高效通信和存储基础设施的设计在很大程度上依赖于在其各个组件之间进行高效信息流的算法。多单播网络容量表征问题是一种信息论抽象，它抓住了几个通信和存储系统中信息流的基本挑战。尽管最优码在多个单播网络中具有重要意义，但它的发展仍然是信息论中一个极具挑战性的未解决问题。最近，最初在无线系统环境中发现的干扰对齐的想法已经被证明是多单播网络编码中的重要工具。然而，揭示基于干扰对齐的可实现编码方案仍然是一门艺术；基于对齐的解决方案通常必须基于所考虑的特定网络场景而仔细地手工制作。缺乏基于系统对齐的方法已将该想法的影响限制在网络拓扑和配置的狭窄类别。本项目的目标是通过开发基于系统干扰对齐的多单播网络编码算法来填补这一空白。该项目将包括对几个网络玩具模型的研究，这些模型是为揭示调整的作用而量身定做的。从玩具模型中获得的见解将被结合到基于有向无环图的一般网络的网络编码算法中。这些算法的性能将通过解析和数值方法进行研究。建议的工作包括通过研究网络信息理论领域的典型问题，对网络信息理论领域的基础贡献，特别是对网络编码这一子主题的贡献。该项目的发展将影响数据中心、内容分发网络和无线通信网络的设计。开展的研究将通过同行评议的会议和期刊进行传播。开发的算法的源代码将向公众开放。

Communication and storage networks play an integral role in various aspects of modern life. The design of an efficient infrastructure of communication and storage relies significantly on algorithms for efficient information flow among its various components. The multiple unicast network capacity characterization problem is an information theoretic abstraction that captures the fundamental challenges in information flow in several communication and storage systems. Despite its importance, development of optimal codes in multiple unicast networks is a challenging unsolved problem in information theory. Recently the idea of interference alignment, which was originally discovered in the context of wireless systems, has been shown to be an important tool in multiple unicast network coding. However, uncovering interference alignment based achievable coding schemes remains an art; alignment-based solutions typically must be carefully handcrafted based on the specific network scenario under consideration. A dearth of systematic alignment based approaches has restricted the impact of this idea to a narrow class of network topologies and configurations. The objective of this project is to fill this gap by developing systematic interference alignment based algorithms for multiple unicast network coding. The project will include the study of several toy models of networks, which are tailor-made to expose the role of alignment. Insights obtained from the toy models will be incorporated into network coding algorithms for general networks over directed acyclic graphs. The performance of the algorithms developed will be studied through analytical and numerical methods.The proposed work involves fundamental contributions to the field of network information theory, specifically to the sub-topic of network coding, through the study of canonical problems in the field. The developments of the project will impact the design of data centers, content distribution networks and wireless communication networks. The research developed will be disseminated through peer-reviewed conferences and journals. The source code for algorithms developed will be made available to the public.