LDPC turbo decoder using generalized belief propagation over two-dimensional inter-symbol interference channel
Kenta Kasai, Hashimoto Akiyoshi · 2017
Due to many small cycles in factor graphs, detection and decoding over two-dimensional inter-symbol interference (2D-ISI) channels has been considered difficult. It is reported that generalized belief propagation (GBP) detection for 2D-ISI performs much better than BP. However, conventional studies for GBP for 2D-ISI were restricted to the separate uses of detection and decoding. Joint usage of detection and decoding were proposed in [1] but hard-decisions are inserted between detector and decoder. This makes a gap to the optimal performance. In this paper, we study full-joint use of GBP for detector and decoder for 2D-ISI, i.e., we use only soft-messages. Furthermore, we clarify a necessary condition with respect to the region graph that messages converge to a GBP fixed point. We found most of regions graph proposed in the literature do not satisfy the convergence condition. This prevents the full-joint use of GBP for 2D-ISI. Moreover, we propose a method to construct region graphs which satisfy the condition. Numerical experiments show that the proposed joint detector and decoder perform better than the conventional separate detector and decoder [2] in a simple 2D-ISI channels.