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Matrix Factorization in MIMO Systems and Machine Learning

Many applications of digital signal processing rely on multiplications of a stream of unknown vectors with a single fixed matrix. Examples of such applications include MIMO precoding in a wireless communication system, signal detection, and machine learning using, e.g., an artificial neural network. As the dimensions grow large, which is the case in such applications, the matrix-vector multiplication operation becomes burdensome in terms of complexity and energy consumption.

By allowing some preprocessing of the matrix, highly efficient algorithms can be implemented to perform the matrix-vector multiplication. In this context, a new and innovative multiplicative matrix decomposition has been developed and patented by the chair. In particular, the matrix is approximated by a product of matrices, where each factor matrix comprises a restricted set of powers of two. For large rectangular matrices already a few factors are sufficient to obtain a very good approximation. Furthermore, all factor matrices but the first one can be made sparse. This leads to an algorithm of low complexity and low memory usage.

The concept has been proved by a basic implementation of the matrix decomposition. However, there is plenty of room for improvement. For example, as the first factor cannot be made sparse, other techniques have to be employed to speed up the multiplication. A candidate approach is to employ bit pattern matching in binary multiplication, i.e. to identify recurring patterns in the multiplicands and store and reuse the results associated to them. Hence, a possible topic for a thesis in this field is to implement and refine this method for the described matrix factorization problem.

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