This paper puts forth a class of new transceiver designs for interleaved frequency division multiple access (IFDMA) systems. These transceivers are significantly less complex than conventional IFDMA transceiver. The simple new designs are founded on a key observation that multiplexing and demultiplexing of IFDMA data streams of different sizes are coincident with the IFFTs and FFTs of different sizes embedded within the Cooley-Tukey recursive FFT decomposition scheme. For flexible resource allocation, this paper puts forth a new IFDMA resource allocation framework called Multi-IFDMA, in which a user can be allocated multiple IFDMA streams. Our new transceivers are unified designs in that they can be used in conventional IFDMA as well as multi-IFDMA systems. Two other well-known multiple-access schemes are localized FDMA (LFDMA) and orthogonal FDMA (OFDMA). In terms of flexibility in resource allocation, Multi-IFDMA, LFDMA, and OFDMA are on an equal footing. With our new transceiver designs, however, IFDMA has the following advantages (besides other known advantages not due to our new transceiver designs): 1) IFDMA/Multi-IFDMA transceivers are significantly less complex than LFDMA transceivers; in addition, IFDMA/Multi-IFDMA has better Peak-to-Average Power Ratio (PAPR) than LFDMA; 2) IFDMA/Multi-IFDMA transceivers and OFDMA transceivers are comparable in complexity; but IFDMA/Multi-IFDMA has significantly better PAPR than OFDMA.