Random Coding Union Bounds for LDPC Coded MIMO Systems

Under the assumption of random coding, we derive a closed-form union bound on the error performance of MIMO systems. The distance spectrum of random block codes, instead of that of LDPC or turbo codes, is used in this paper for the purpose of closed-form derivation. As compared with the simulation results, the bound is useful as a performance benchmark for a concatenated coding scheme over MIMO systems in which the LDPC or turbo code serves as the outer code to drive an inner space-time modulation block. In addition, the derived closed-form error exponent and cutoff rate are consistent with Gallager´s random coding exponent and the information-theoretic channel capacity in a variety of modulation and channel scenarios