The Generalized UMP BP-Based Algorithm and its Modifications for Non-binary LDPC Codes

Abstract

An uniformly most powerful (UMP) belief propagation (BP)-based algorithm and its modifications are presented for decoding non-binary LDPC codes. We propose the generalized of the UMP BP-based and its modified UMP BP-based decoding algorithms for non-binary LDPC codes using the Hadamard transform as an extension of binary case. The generalized UMP BP-based algorithm has less complexity than the generalized BP algorithm, but has performance degradations. To improve performance, we modify the generalized UMP BP-based algorithm using the similar way as in binary case. Simulation results show that the generalized UMP BP-based algorithm and its modifications are effective decoding methods for non-binary LDPC codes.