Fast solving of systems of linear equations in decoding of LDPC codes

Abstract

In this thesis, a method is proposed, which is suitable for fast solving of sparse systems of linear equations over finite extension fields for the purpose of improving the speed of decoding related tasks for LDPC codes. The aim of the study is to optimize the Gaussian elimination algorithm for sparse systems of equations, which would solve the problem more efficiently than the standard approach. The proposed method is implemented in the Java language. Its performance is analyzed and tested experimentally.