On the Rate Versus ML-Decoding Complexity Tradeoff of Square LDSTBCs with Unitary Weight Matrices

The low decoding complexity structure of Linear Dispersion Space Time Block Codes (LDSTBCs) with unitary weight matrices is analyzed. It is shown that given n = 2alpha, the maximum number of groups in which the information symbols can be separated and decoded independently is (2a + 2), and as we lower the number of different groups to (2k + 2), 0 les k les alpha, we get higher rate codes. We also find the analytic expression for rates that such codes can achieve for any chosen group number, thus completely characterizing the rate-ML-decoding-complexity tradeoff for this class of codes. The proof of the result also includes a method for constructing such optimal rate achieving codes. Interestingly, this analysis produces some low decoding complexity codes with rate greater than one.