We show that military standard (MIL-STD) shaped-offset quadrature phase-shift keying (SOQPSK), a highly bandwidth-efficient constant-envelope modulation, can be represented in the form of a cross-correlated trellis-coded quadrature modulation. Similarly, we show that offset QPSK (OQPSK) can be decomposed into a "degraded" trellis encoder and a memoryless mapper. Based on the representations of OQPSK and MIL-STD SOQPSK as trellis-coded modulations (TCMs), we investigate the potential coding gains achievable from the application of simple outer codes to form a concatenated coding structure with iterative decoding. For MIL-STD SOQPSK, we describe the optimum receiver corresponding to its TCM form and then propose a simplified receiver. The bit-error rate (BER) performances of both receivers for uncoded and coded MIL-STD SOQPSK are simulated and compared with that of OQPSK and Feher-patented QPSK (FQPSK). The asymptotic BER performance of MIL-STD SOQPSK is also analyzed and compared with that of OQPSK and FQPSK. Simulation results show that, compared with their uncoded systems, there are significant coding gains for both OQPSK and MIL-STD SOQPSK, obtained by applying iterative decoding to either the parallel concatenated coding scheme or the serial one, even when very simple outer codes are used.