Code design for the relay channel and factor graph decoding

Recent information theoretical results have shown a considerable improvement in the performance of communication systems through the use of relaying and cooperation. Despite a collection of strong information theoretical results on the relay channel, there has been almost no attention to real code design for the relay channel. In this paper, we present a powerful modular code design approach for the relay channel and corresponding decoding algorithms based on the factor graph representation of the code. For most of the relay channel conditions, the constructed codes with a low-complexity simple relay protocol outperforms any possible code design for the direct channel by achieving an E_b/N₀ below the minimum required E_b/N₀ of single-link transmission. Moreover, the designed codes achieve a gap of less than 1 dB (at a BER of 10^-6) to the Shannon limit for the relay channel with a code length of only 2 × 10⁴ bits.