Emerging die-stacked DRAMs provide several factors higher bandwidth and energy efficiency than 2D DRAMs, making them excellent candidates for future memory systems. To be deployed in server and high-performance computing systems, however, die-stacked DRAMs need to provide equivalent or better reliability than existing 2D DRAMs. This includes protecting against channel and die faults, which have been observed in existing 2D DRAM production systems. In this paper, we observe that memory subsystems can be viewed as a multi-dimensional collection of memory banks in which faults generally affect memory banks that lie along a single dimension. For instance, in die-stacked DRAMs, a die consists of a group of DRAM banks that lie in a horizontal plane while a channel consists of a vertical group of banks spanning across multiple dies. We exploit this fault behavior to propose Parity Helix to efficiently protect against single-dimensional faults in multi-dimensional memory systems. Parity Helix shares the same error correction resources across all dimensions to minimize error correction overheads. For die-stacked DRAMs, our evaluation shows that compared to a straightforward extension of previous schemes, Parity Helix increases memory capacity by 16.7%, reduces memory energy per program access by 21%, on average, and by up to 45%.