Optimal distributed concatenated space-time block codes for two-way relaying networks

In this paper, we consider a half-duplex amplify-and-forward two-way relaying network consisting of two sources with each having a single antenna and N relays with each having two antennas. For such a system with a general distributed linear dispersion code, a tight lower bound of pairwise error probability (PEP) of the maximum likelihood (ML) detector is derived, showing that diversity gain function cannot decay faster than ln^N SNR/SNR^2N, where SNR is signal to noise ratio. Particularly for N = 2^b, a new distributed concatenated space-time block code (STBC) is proposed and its asymptotic PEP formula is attained, showing that the code presented in this paper achieves the maximum diversity gain, i.e., meeting the lower bound of the diversity gain function, as well as the maximum coding gain.