Signal combining for relay transmission with rateless codes

The invention of practical rate-less codes in the form of Luby transform and Raptor codes has facilitated the implementation of decode-and-forward relaying schemes which permit the relay to autonomously switch between listening and collaboration phase. Considering the classical three-node relay network employing such a flexible decode-and-forward mechanism, in this paper we investigate signal combining strategies for the destination node. In particular, we compare information and energy combining considered previously in the literature and introduce a new, so-called mixed combining scheme, which is a hybrid of the two former strategies. Assuming general finite-size signal constellations we show that mixed combining is advantageous over the pure combining schemes in terms of achievable rate given the same total transmit energy. A comparison of the associated constellation-constrained capacities with simulated rates achieved for relay transmission with moderate-length Raptor codes underscores (i) the relevance of the capacity-based analysis and (ii) the suitability of rate-less codes for relay transmission.