Photonics-Based Cholesky Decomposition

Matrix decomposition approaches are the techniques that partition a complex matrix into its constituents in order to reduce the computational complexity of different matrix calculations. Among different decomposition techniques, Cholesky decomposition [1] , in which a Hermitian positive semi-definite matrix is decomposed into the product between a lower triangular matrix and its conjugate transpose, has been employed in different applications [2] . In particular, Cholesky decomposition has been widely used to compute the inverse of large matrices [3] , because of the advantages it offers terms of the computational complexity and memory requirements [4] . While matrix decomposition reduces the computational complexity, the hardware in which the decomposition is performed affects the overall efficiency and the time required to decompose the matrix. Photonics-based computation has been proposed as a promising approach that offers low-computational cost for ultra-fast data processing [5] . In this paper, a photonic computing architecture is proposed to improve the time and power efficiency of Cholesky decomposition. This is specifically attractive for wireless communication systems, where computational resources are limited and the data needs to be processed on the fly. The proposed architecture is based on Broadcast-and-Weight (B&W) protocol [6] , in which a bank of microring modulators and wavelength division multiplexing scheme are utilized to implement dot product in an optical platform. In the proposed architecture, a feedback control procedure is designed to set the weights by applying voltages to microring resonators.