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Irregular low-density parity-check (LDPC) codes have shown exceptionally good performance for single antenna systems over a wide class of channels. In this paper, we investigate their application to multiple antenna systems in flat Rayleigh fading channels. For small transmit arrays, we focus mainly on space-time coding with 2p-ary LDPC codes, where p equals the number of encoded bits transmitted by the transmit antenna array during each signaling interval. For large transmit arrays, we study a layered space-time architecture using binary LDPC codes as component codes of each layer: We show through simulation that, when applied to multiple antenna systems with high diversity order, LDPC codes of quasi-regular construction are able to achieve higher coding gain and/or diversity gain than previously proposed space-time trellis codes, space-time turbo codes, and convolutional codes in a number of fading conditions. Extending the work of density evolution with Gaussian approximation, we study 2p-ary LDPC codes on multiple antenna fading channels, and search for the optimum 2p-ary quasi-regular codes in quasi-static fading. We also show that on fast fading channels, 2p-ary irregular LDPC codes, though designed for static channels, have superior performance to nonbinary quasiregular codes and binary irregular codes specifically designed for fast fading channels.