Abstract: 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. !13
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机译：摘要：我们描述了三维纠错码，用于编码要存储在体积光学存储器中的数据。数据在多个页面中存储和检索，其中每个页面都是二维信息位数组。这种三维编码（也称为z编码）提供了有关可能跨越多个页面的错误事件的错误检测和纠正。我们讨论了可以为页面中的所有信息位提供相同级别的错误保护的代码，以及支持不平等错误保护的代码，以便为选定的信息位组提供不同级别的保护。对这些代码的误码率性能进行了分析和仿真。对于从10 $ + $ MIN @ 5 $ /到10 $ + $ MIN @ 4 $ /的原始误码率，这些代码提供了从10 $ + $ MIN @ 14 $ /到10 $ + $的更正误码率。 MIN @ 12 $ /。可以以位串行和位并行的方式实现代码。 ！13
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