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

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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.