Asymptotic Analysis of Spatial Coupling Coding for Compute-and-Forward Relaying

Compute-and-forward (CAF) relaying is effective to increase bandwidth efficiency of wireless two-way relay channels. In a CAF scheme, a relay is designed to decode a linear combination composed of transmitted messages from other terminals or relays. Design for error-correcting codes and its decoding algorithms suitable for CAF relaying schemes remain as an important issue to be studied. As described in this paper, we will present an asymptotic performance analysis of LDPC codes over two-way relay channels based on density evolution (DE). Because of the asymmetric characteristics of the channel, we use the population dynamics DE combined with DE formulas for asymmetric channels to obtain BP thresholds. Additionally, we also evaluate the asymptotic performance of spatially coupled LDPC codes for two-way relay channels. The results indicate that the spatial coupling codes yield improvements in the BP threshold compared with corresponding uncoupled codes for two-way relay channels. Finally, we will compare the mutual information rate and rate achievability between the CAF scheme and the MAC separation decoding scheme. We demonstrate the possibility that the CAF scheme has higher reliability in the high-rate region.