Cyclic interference alignment in multi-user communication networks

In this thesis a novel channel model is developed on the basis of a polynomial ring representation - the cyclic polynomial channel model (CPCM). The proposed model is inspired by interference alignment by propagation delay, the algebraically convenient description of cyclic codes, and by the linear deterministic channel model (LDCM) as introduced by Avestimehr et al. The CPCM describes multi-user communication systems with interference. Therein, each transmitted signal experiences an individual cyclic shift and at the receivers, those shifted signals interfere with each other. Several multi-user communication systems are investigated from an information-theoretic perspective applying the CPCM. These systems range from elementary unidirectional multi-user channels to multi-way and multi-hop networks with relays. We derive optimal communication strategies to achieve the maximal data-rates. These schemes involve interference alignment, signal alignment, interference neutralization, orthogonal multiple-access and linear coding schemes. Utilizing the CPCM is convenient for an approximation of optimal communication schemes when compared to the conventional Gaussian MIMO channel model and the LDCM. We define separability conditions to allow for linear decodability at the receivers. This step assists us in classifying the intricate interference patterns of multiple users and it facilitates the derivation of feasibility and optimality of the proposed communication schemes. As a result it is shown that optimal solutions exist in a compact form, even for channels with arbitrary cyclic shifts. This thesis provides a comprehensive theoretical analysis and optimal coding schemes for various multi-user interference networks modelled with arbitrary cyclic shifted communication links.