Mapping for multi-state programming of memory devices

A data storage system, comprising:

• a first memory;
• and
• one or more controllers configured to cause:
• generating, based on a first set of data, a first mapped data and a second mapped data based on a Gray code encoding;
• writing to the first memory, in a first mode, the first mapped data;
• generating a second set of data, based on the first mapped data and the second mapped data;
• and
• writing to the first memory, in a second mode, data based on the second set of data,
• wherein:
• the first mapped data is representable in first rows and one or more columns;
• the second mapped data is representable in second rows and at least one column;
• the at least one column of the second mapped data includes more transitions than any one of the one or more columns of the first mapped data;
• and
• each transition corresponds to a change between neighboring data.

An apparatus, comprising:

• a first memory;
• means for generating, based on a first set of data, a first mapped data and a second mapped data based on a Gray code encoding;
• means for writing to the first memory, in a first mode, the first mapped data;
• means for generating a second set of data, based on the first mapped data and the second mapped data;
• and
• means for writing to the first memory, in a second mode, data based on the second set of data,
• wherein:
• the first mapped data is representable in first rows and one or more columns;
• the second mapped data is representable in second rows and at least one column;
• the at least one column of the second mapped data includes more transitions than any one of the one or more columns of the first mapped data;
• and
• each transition corresponds to a change between neighboring data.