This thesis focuses on interference management methods for interference channels, in particular on interference alignment. The aim is to contribute to the understanding of issues such as the performance of the interference alignment scheme and lattice codes for interference channels. Interference alignment is studied from two perspectives. One is the signal space perspective where precoding methods are designed to align the interference in half of the received subspace. Cadambe and Jafar found precoding matrices to achieve the theoretical degrees of freedom. However, using an interference suppression technique over the Cadambe and Jafar scheme, yields poor performance. Thus, in this thesis precoding methods such as singular value decomposition and Tomlinson-Harashima precoding are proposed to improve performance. The second perspective is on the signal scale, where structured codes are used to align interference. For this, lattice codes are suitable. In this research, the problem was initially approached with a many-to-one interference channel. Using lattices, joint maximum-likelihood decoding of the desired signal and the sum of the interference signals is used, and the union bound of the error probability for user 1 is derived, in terms of the theta series. Later, a symmetric interference channel is studied. Jafar built a scheme for every level of interference, where interference was aligned and could be cancelled. In this thesis, Barnes-Wall lattices are used since they have a similar structure to the scheme proposed by Jafar, and it is shown to be possible to improve the performance of the technique using codes constructed with Barnes-Wall lattices. Finally, previous work has found the generalized degrees of freedom for a two-user symmetric interference channel using random codes. Here, we obtain the generalized degrees of freedom for that channel setting using lattice Gaussian distribution.
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