卷积网络编码编译码理论的进一步研究

Convolutional network coding is one type of linear network coding which plays an important role in both theory and engineering applications. However, in order to become more practical, it still needs to deal with several issues, such as how to handle delay problems, how to design efficient encoding and decoding kernels in a decentralized manner, and how to guarantee efficient data transmission etc. By taking the unified theory of linear network coding as a new theoretical foundation, the delay-invariant convolutional network code as a new model, and the time-variant decoding of convolutional network codes as a new method, this project aims at further enriching the fundamental theory of convolutional network coding, and better design of various reliable, efficient, secure, low-complexity, and adaptive convolutional network codes. This project will emphasize on the following topics: (1) Establish the intrinsic connection between time-variant new decoding method and time-invariant conventional decoding method, and deduce how one decoding scheme yields the other. (2) By integrative application of both decoding methods, study the real practical implementation of delay-invariant convolutional network codes. (3) Formulate the frameworks of delay-invariant property incorporated secure convolutional network codes, static convolutional network codes, and variable-rate convolutional network codes. We believe that this project will provide a more complete theoretical and technical underpinning for the potential application of convolutional network coding in next generation communication networks.

卷积网络编码是一类具有重要理论和工程应用意义的线性网络编码。为了拉近与实际应用之间的距离，卷积网络编码的编、译码理论仍有许多地方需要进一步完善，其中包括如何可靠地处理时延问题，如何分散式地设计高效编、译码核，以及如何保证安全传输等。本项目将以广义线性网络编码理论作为研究理论新基础，以时延不变卷积网络编码模型作为研究新方向，以卷积网络编码时变译码作为研究新方法，进一步完善卷积网络编码基础理论，并设计研究各类可靠、高效、安全、低复杂度、强可适性的卷积网络编码编、译码新方案。本项目将重点研究：（1）时变译码新方法与时不变经典译码方法的内在理论联系及其相互转化关系；（2）时延不变卷积网络编码的实际编、译码方案；（3）结合时延不变性质的安全卷积网络编码、静态卷积网络编码以及速率可变卷积网络编码等编码体系。我们相信本项目的研究将为卷积网络编码实际应用于新一代通信网络提供更加完善的理论基础和技术支持。

卷积网络编码是网络编码理论中一类重要的线性网络编码。在本项目的资助下，项目组对卷积网络编码的理论基础与实际应用均展开了深入的研究，完善了卷积网络编码理论、拓宽了卷积网络编码潜在的应用场景。其中，论证了在有环图网络中通用卷积网络编码的最强线性独立性并通过拟阵的数学概念阐述了其拓扑意义；建立起卷积网络编码时变译码方法与时不变译码方法译码的等价性；提出有环线性确定型网络中信息流的概念并将卷积网络编码从图网络拓展至线性确定型网络；提出可应用于无线中继网络的基于爱森斯坦整数的卷积格型网络编码并设计了相对应的编译码方案。此外，首次通过多播网络实例揭示较小有限域上存在线性解并不能保证一个更大有限域上存在一个线性解。由于该成果看似是线性网络编码定理的一个悖论，受到众多网络编码领域研究同行们的关注，并对线性网络编码基础理论的完善开辟了一个新视角。在本项目支持下，项目组成员共发表7篇SCI期刊论文、7篇EI国际会议论文，项目负责人在IEEE举办的国际信息论年会(ISIT)、国际通信大会(ICC)等知名国际会议上作口头报告4次。