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

在过去的几年中，广播信道的预编码和网络编码的领域发展迅速，但彼此独立。虽然，这两种方案的程序和目标在许多方面是双重的，但有些方案已经从一个领域转化为另一个领域。继续这方面的工作将导致新的办法，也将导致更好地理解计划本身。基于秩度量的随机线性网络信道的编码方法也在过去几年中迅速发展。基于当前项目的发现，很明显，预编码、网络编码和信道编码之间存在相互依赖性。因此，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，已经公布了多个示例，其中预编码、网络编码和信道编码的任务彼此相遇或互补。然而，到目前为止，没有完整的图片的相互作用，这些领域和组合的各自的计划是可用的。因此，在该项目的拟议延续期间的主要目标是详细了解（模型）预编码，网络编码和信道编码的相互作用。我们的目标是联合设计和优化的计划在这三个领域的交叉点。首先，将评估差分预编码与合适的（秩度量）卷积码的级联。一种对信道变化鲁棒的设计是期望的。其次，必须更详细地理解格码与预编码的组合或代替预编码的使用。整数强迫和格点约简的相似性和差异性必须详细地计算出来。第三，必须设计用于无线回程中的多流预编码和双侧格型约简的新设计。最后，基于广义级联码理论，需要在不同度量上构造新的格码。将研究与空时编码等其他应用的联系。

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.