Carrierless amplitude/phase modulation (CAP) is a viable alternative for digital subscriber loop (DSL) systems such as high-speed DSL, asymmetric DSL, and very high-speed DSL. In this paper, two novel orthogonal-based modulation schemes are introduced for the DSL environment. In the first technique, the conventional two-dimensional (2-D) CAP-16 line code is extended to a three-dimensional (3-D) scheme. The 3-D system is designed so that the new overall transfer matrix maintains perfect reconstruction (PR) of the transmitted information. The system is designed by solving a minimax optimization problem by using the sequential quadratic programming algorithm; this searches the whole space of signals under the PR condition and the DSL constraints. The 3-D CAP system leads to a 50% increase in throughput at the expense of the output signal-tonoise ratio (SNR) degradation by 3-1 dB. It should be noted that this increase in throughput can also be achieved by a CAP64 system. Nevertheless, the dynamic range of the proposed 3-D CAP approach is 7.4 dB less than CAP-64, which leads to faster equalization. Furthermore, the equalizer performance in the 3-D case is 1-3 dB better, depending on channel and noise considerations. Another application of the multidimensional CAP approach, referred to as orthogonality division multiple access (ODMA) is presented. In this approach, the CAP system is extended to more than three dimensions by maintaining the same overall symbol rate as in the 2-D case. The ODMA system allows multiple-access operation of the DSL communication link with minimal hardware penalty. The performance of the ODMA system for the multiple-access environment is found to match the conventional 2-D CAP, allowing suitable multiple-access topology with minimal complexity overhead. The ODMA system complexity is compared with discrete multitone and is found to have 25% less complexity for the same bit rate. Theoretical analysis of the ODMA system using zero-forcing equalization shows that the equalization process yields better SNR as the number of dimensions increases, asymptotically approaching the intersymbol interference-free matched filter bound. Index Terms-Digital subscriber loops, orthogonality division multiple access, perfect reconstruction, three-dimensional CAP, transmultiplexors.