TY - JOUR
T1 - Limited-shift-full-rank matrices with applications in asynchronous cooperative communications
AU - Shang, Yue
AU - Xia, Xiang Gen
PY - 2007/11
Y1 - 2007/11
N2 - 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. A systematic construction of SFR matrices, including the shortest (square) SFR (SSFR) matrices, has been also previously proposed. In this paper, we study a variation of SFR matrices with a relaxed condition: limited-shift-full-rank (LT-SFR) matrices, i.e., the matrices that have full row rank no matter how their rows are shifted as long as the shifts are within some range called delay tolerance. As the generator matrices for the previously proposed space-time trellis codes, LT-SFR matrices can guarantee asynchronous full diversity of the corresponding codes when the timing errors are within the delay tolerance. Therefore, due to the relaxed condition imposed on LT-SFR matrices, more eligible generator matrices than SFR matrices become available.
AB - 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. A systematic construction of SFR matrices, including the shortest (square) SFR (SSFR) matrices, has been also previously proposed. In this paper, we study a variation of SFR matrices with a relaxed condition: limited-shift-full-rank (LT-SFR) matrices, i.e., the matrices that have full row rank no matter how their rows are shifted as long as the shifts are within some range called delay tolerance. As the generator matrices for the previously proposed space-time trellis codes, LT-SFR matrices can guarantee asynchronous full diversity of the corresponding codes when the timing errors are within the delay tolerance. Therefore, due to the relaxed condition imposed on LT-SFR matrices, more eligible generator matrices than SFR matrices become available.
KW - Asynchronous cooperative communications
KW - Cooperative diversity
KW - Distributed space-time coding
KW - Limited-shift-full-rank (LT-SFR) matrices
KW - Shift-full-rank (SFR) matrices
KW - relay networks
UR - http://www.scopus.com/inward/record.url?scp=36348976519&partnerID=8YFLogxK
U2 - 10.1109/TIT.2007.907510
DO - 10.1109/TIT.2007.907510
M3 - Article
AN - SCOPUS:36348976519
SN - 0018-9448
VL - 53
SP - 4119
EP - 4126
JO - IEEE Transactions on Information Theory
JF - IEEE Transactions on Information Theory
IS - 11
ER -