Design of Distributed Protograph LDPC Codes for Multi-Relay Coded-Cooperative Networks

This paper studies protograph low-density paritycheck coded cooperation (CC) schemes for two-hop multi-relay systems with L relays over Nakagami-m quasi-static fading (QSF) channels. We propose two CC schemes, namely schemes I and II, with different maximum code rates to satisfy different transmission requirements. We further design a family of distributed rate-compatible root-protograph (RCRP) codes to achieve full diversity in CC-based multi-relay QSF channels. In particular, our RCRP codes with L + 1 sub-codewords can realize full diversity in scheme I, and our RCRP codes with two sub-codewords can achieve full diversity in scheme II with a maximum-ratio combiner. In addition, we estimate the asymptotic word error rate and bit error rate of our RCRP codes using a generalized protograph extrinsic information transfer algorithm, which is able to characterize the error performance of finite-length codewords accurately. Analysis and simulation show that our RCRP codes can achieve outage-limit-approaching performance in both multi-relay CC architectures. This makes the RCRP coding framework extremely attractive for multirelay cooperative communication applications with slow-varying fading.