In　wireless　communications,　spatial　diversity　techniques,　such　as　space-time　block　code　(STBC)　and　multiple　input　multiple-output　(MEMO),　have　attracted　much　attention　in　recent　years　because　they　possess　powerful　robustness　against　signal　fading.　In　this　paper,　we　investigate　the　performance　of　the　protograph　low-density　parity-check　(LDPC)　codes　over　space-time　block　code　(STBC)　Rayleigh　fading　channels.　Taking　into　consideration　the　Alamouti　STBC　structure,　we　propose　a　modified　protograph　extrinsic　information　transfer　(PEXIT)　algorithm　in　order　to　analyze　the　convergence　performance　of　protograph　codes　in　such　scenarios.　We　further　compare　the　decoding　thresholds　and　bit　error　rates　(BERs)　of　two　typical　protograph　codes,　i.e.,　accumulate-repeat-by-3-accumulate　(AR3A)　code　and　accumulated-repeat-by-4-jagged-accumulate　(AR4JA)　code,　with　the　regular　LDPC　code　and　optimized　irregular　LDPC　codes.　The　results　illustrate　that　the　AR3A　code　outperforms　other　three　codes　in　the　high　signal-to-noise-ratio　(SNR)　region.　As　a　consequence,　the　AR3A　code　appears　to　be　a　better　candidate　for　use　in　the　wireless　communication　systems　with　multiple　antennas.