Limited-Shift-Full-Rank Matrices With Applications in Asynchronous Cooperative Communications

Shift-full-rank (SFR) matrices are matrices that have full row rank no matter how their rows are shifted. SFR matrices have been used lately as generator matrices for a family of space-time trellis codes to achieve full diversity in asynchronous cooperative communications, where the numbers of columns of the SFR matrices correspond to the memory sizes of the trellis codes and an upper bound is assumed for all the possible delays during each packet (frame) transmission. In this paper, we study a variation of SFR matrices with relaxed conditions: limited-shift-full-rank (LT-SFR) matrices, i.e., the matrices that keep full row rank when the shifts of their rows are within some range called delay tolerance. As the generator matrices for the previously proposed space-time trellis codes, LT- SFR matrices can already guarantee asynchronous full diversity of the corresponding codes.