Error Probability Bounds for Bit-Interleaved Space–Time Trellis Coding Over Block-Fading Channels

In this correspondence, we investigate the error probability bounds of a bit-interleaved space-time trellis coding (BISTTC) scheme, which concatenates bit-interleaved coded modulation (BICM) with a space-time trellis code (STTC). We focus on general block-fading channels, wherein each data packet or frame spans a number of independent fading blocks. BICM applied to such channel environments can effectively exploit both time and frequency selectivity, while a STTC maximizes the spacial diversity order. The exact pairwise error probability (PEP) and weight enumeration function (WEF) of BISTTC are used to evaluate the error bound. Due to the concatenation of an outer error correction code (ECC) and a STTC, the overall WEF of BISTTC is obtained by combining the WEF of the outer code with that of the STTC through an uniform interleaver. The main challenge here is to compute the WEF of a STTC for block-fading channels with reasonable complexity. We rely on constructing a composite state transition matrix based on a number of single-step virtual trellises, each corresponding to an independent fading block within a frame. We discuss how this approach reduces storage and computational requirements in the bound analysis, compared to the existing method of obtaining the state transition matrix through accumulation of single-step transition matrices. The derived bound is applicable to both spatially uncorrelated and correlated channels as well as to both flat and frequency-selective block-fading channels. The bound is shown to provide a reasonably close estimate of the simulated performance based on the turbo equalizer-like iterative processing of soft information between the STTC decoder and the ECC decoder.