Random Coding Union Bounds and Error Exponents for Concatenated MIMO Systems

An assumption of random block codes is made for the closed-form derivation of union upper bounds. The random code works as the outer code for concatenation with the inner space-time modulation over the multi-input multi-output (MIMO) fading channels. From the union bound expression, we further obtain the closed-form expressions of error exponent and cut-off rate for MIMO channels. The error exponent is compared with Gallager´s classical error exponent which is generally evaluated in the Monte Carlo method. The obtained bounds can be useful to serve as space-time code design tools or as performance prediction measures for the MIMO systems which employ turbo-like block codes as the outer code to drive the inner space-time code.