Interrelations between Channel Coding and Precoding in Transmission Strategies for Broadcast Channels and in Network Coding

近年来，广播信道预编码和网络编码领域发展迅速，但又相互独立。虽然这两种方案的程序和目的在许多方面是双重的，但一些方案已经从一个领域转到另一个领域。继续开展这方面的工作将导致新的办法，也将使人们更好地了解各项计划本身。基于秩度量的随机线性网络信道编码方法近年来也得到了迅速发展。基于当前项目的发现，预编码、网络编码和信道编码之间明显存在相互依赖关系。因此，对这三个领域的联合分析将产生新的见解、新的结果和新的方法。最近，已经发表了一些例子，其中预编码、网络编码和信道编码的任务相互满足或互补。但是，到目前为止，还没有关于这些领域的相互作用和各自方案组合的完整图景。因此，该项目的主要目标是详细了解（模型）预编码、网络编码和信道编码之间的相互作用。目的是联合设计和优化在这三个领域的交叉点运行的方案。首先，将评估差分预编码与合适的（秩-度量）卷积编码的连接。一个设计健壮的渠道变化的愿望。其次，点阵码与预编码相结合或代替预编码的使用必须得到更详细的理解。整数强迫和晶格约简的异同必须详细地加以研究。第三，必须设计用于无线回程的多流预编码和双面格约简的新设计。最后，基于广义连接码理论，提出了不同度量上的格码的新结构。将研究与其他应用（如空时编码）的联系。

Over the last years, the fields of precoding for the broadcast channel and network coding have developed rapidly but independently of each other. Although, the procedures and aims of both scenarios are dual in many aspects, some schemes already have been translated from one field to the other. A continuation of this line of work will lead to new approaches and also to a better understanding of the schemes per se. Coding methods for the random linear network channel based on the rank metric also developed rapidly over the last years. Based on the findings of the current projects it became obvious that there exist interdependencies between precoding, network coding, and channel coding. Therefore the joint analysis of these three areas will generate novel insights, novel results, and novel methods. Recently, a number of examples have been published where the tasks of precoding, network coding, and channel coding meet or complement each other. However, up to now, no complete picture of the interaction of these fields and combinations of the respective schemes is available. Hence, the main objective during the proposed continuation of the project is the detailed understanding of the interaction of (modulo-type) precoding, network coding, and channel coding. The aim is a joint design and optimization of schemes operating at the intersections of these three fields. First, the concatenation of differential precoding with suited (rank-metric) convolutional codes will be assessed. A design robust to channel variations is aspired. Second, the use of lattice codes in combination with or instead of precoding has to be understood in much more detail. The similarities and differences of integer forcing and lattice reduction have to be worked out in detail. Third, new designs for multiple-stream precoding and both-sided lattice reduction to be used in the wireless backhaul have to be designed. Finally, new constructions for lattice codes over different metrics based on the theory of generalized concatenated codes are required. The connection to other applications such as space-time coding will be studied.