Union Bounds to Error Probabilities of LDPC-Coded Q-ary Modulation Systems over Fast Fading MIMO Channels

Closed-form union bounds are derived for the error performance of low-density parity-check (LDPC) coded Q-ary modulation systems over fast fading multi-input multi-output (MIMO) channels. The LDPC codewords are mapped onto space-time modulation blocks, referred to as associated space-time (AST) codewords, in one-to-one correspondence. Based on this relationship, the distance spectrum of the AST code is identified in a combinatorial manner, and each AST codeword possessing the same distance metric renders the identical pairwise error probability. The union bound is obtained in a closed form and can be efficiently evaluated by the method of polynomial expansion. In addition, the analysis is extended to the system with random coding which contributes to a concise expression of the error exponent. Numerical results are presented for different channel scenarios and modulation schemes, which indicate that the bounds are useful to benchmark the practical performance of iterative detection and decoding algorithms.