In　this　paper,　we　investigate　the　performance　of　the　protograph　low-density　parity-check　(LDPC)　codes　concatenated　with　space-time　block　code　(STBC)　over　Rayleigh　fading　channels.　We　firstly　extend　the　modified　protograph　extrinsic　information　transfer　(PEXIT)　algorithm　in　order　to　analyze　the　convergence　performance　of　protograph　codes.　Based　on　the　extended　PEXIT　algorithm　and　Gaussian　approximation,　we　further　derive　the　asymptotic　bit-error-rate　(BER)　expression　of　protograph　codes.　Utilizing　the　PEXIT　algorithm,　theoretical　and　simulated　BERs,　we　compare　the　performance　of　two　classical　protograph　codes,　i.e.,　accumulate-repeat-by-3-accumulate　(AR3A)　code　and　accumulate-repeat-by-4-jagged-accumulate　(AR4JA)　code,　regular　LDPC　code,　and　optimized　irregular　LDPC　codes,　and　illustrate　that　the　AR3A　code　is　superior　to　other　three　codes.　Additionally,　we　discuss　the　impact　of　the　number　of　receive　antennas　(i.e.,　N-R)　on　the　system　performance　and　verify　that　the　theoretical　analyses　hold　as　N-R　varies.　As　a　result,　the　AR3A　code　stands　out　as　a　good　candidate　for　wireless　communication　applications　with　multiple　antennas.