Combinatorial Union-Bound Analysis on the Concatenation of LDPC/Turbo Codes and Space-Time Codes over Fast Fading MIMO Channels

A performance evaluation framework based on the maximum-likelihood (ML) union bound is proposed for the concatenated coding scheme where the outer linear block code, low-density parity-check (LDPC) or Turbo code, drives a sequence of inner space-time codes. The outer code can be partitioned in a combinatorial manner such that all codewords in one subset/subcode are associated with an identical pairwise error probability. The union bound is therefore the summation of all distinct pairwise error probabilities, each of which is weighted by the cardinality of the corresponding subset. The cardinality is computable by making use of the statistical property of an ensemble of codes, and an approach of polynomial expansion is proposed for efficient evaluation of the closed-form union bound. Numerical results are presented for different channel scenarios and modulation schemes, which indicate that the ML union bounds are useful to benchmark the performance of practical iterative detection and decoding algorithms.