Asymptotic Analysis on Spatial Coupling Coding for Two-Way Relay Channels

TL;DR

This paper analyzes the asymptotic performance of LDPC and spatially coupled LDPC codes in two-way relay channels using density evolution, showing that spatial coupling improves decoding thresholds.

Contribution

It provides the first asymptotic analysis of spatially coupled LDPC codes for two-way relay channels, demonstrating threshold improvements over uncoupled codes.

Findings

Spatially coupled LDPC codes have higher BP thresholds than uncoupled codes.

Density evolution with population dynamics effectively analyzes asymmetric two-way relay channels.

Spatial coupling enhances error correction performance in two-way relay communication.

Abstract

Compute-and-forward relaying is effective to increase bandwidth efficiency of wireless two-way relay channels. In a compute-and-forward scheme, a relay tries 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 compute-and-forward relaying schemes are still important issue to be studied. In this paper, we will present an asymptotic performance analysis on LDPC codes over two-way relay channels based on density evolution (DE). Because of the asymmetric nature of the channel, we employ the population dynamics DE combined with DE formulas for asymmetric channels to obtain BP thresholds. In addition, 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.