We describe three-dimensional error correcting codes for encoding data to be stored in volumetric optical memories. Data are stored and retrieved in multiple pages where each page is a two-dimensional information bit array. This three- dimensional encoding, also called z-encoding, provides error detection and correction regarding error events which may span multiple pages. We discuss codes that can provide the same level of error protection to all the information bits in a page and codes that support unequal error protection such that selected groups of information bits are provided different levels of protection. The bit error rate performance of these codes is analyzed and simulated. For raw bit error rates ranging from 10$+$MIN@5$/ to 10$+$MIN@4$/, these codes provide corrected bit error rates ranging from 10$+$MIN@14$/ to 10$+$MIN@12$/, respectively. The codes can be implemented in a bit-serial and bit-parallel fashion.
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