Rectangular information lossless linear dispersion codes

This paper extends square M×M linear dispersion codes (LDC) proposed by Hassibi and Hochwald to T×M non-square linear dispersion codes of the same rate M, termed uniform LDC, or U-LDC. This paper establishes a unitary property of arbitrary rectangular U-LDC encoding matrices and determines their connection to the traceless minimal nonorthogonality criterion for space-time codes. The U-LDC are then applied to rapid fading channels by constructing trace-orthonormal versions, or TON-U-LDC for 2L and 4L input symbols, where L is a positive integer. Compared to a variety of state-of-the-art codes, the proposed codes are found to perform well in both block and rapid fading channels. In rapid fading, the symbol-wise time diversity order of a T × M, TON-U-LDC for 2L input symbols is shown to be min (T,2M).