Optimal distributed codes with delay four and constant decoding complexity

A novel transmission scheme based on the non-orthogonal selection decode-and-forward protocol is presented in this paper for cooperative relay networks. The proposed scheme assumes a low rate feedback channel from the destination to the relays. Benefited from the feedback information, an optimal distributed code that has an extremely short delay equal to four is constructed, and the same code can be applied to networks with arbitrary number of relays to yield optimal cooperative diversity gains. The proposed code is sphere-decodable with decoding complexity again independent of the number of relays. In particular, when operating at multiplexing gain ≥ 1/2, the lattice decoder at the destination has a zero complexity exponent, meaning a constant decoding complexity and independent of transmission rate. Analyses for the decoding complexity of other existing diversity-optimal distributed codes are also provided. It is shown that these codes have a linear growth in delay and an exponential growth in decoding complexity as the number of relays increases.