Error correction coding utilizing numerical base conversion for modulation coding

A method of decoding data retrieved from a medium comprising steps of:

• (a) error correction decoding the retrieved data;
• and
• (b) converting symbols represented in a first base in the retrieved data to symbols represented in a second base.

A system for communicating data comprising:

• an encoder having a base converter module that converts input data from a first base to a second base and an error correction code encoding module that performs ECC encoding operations on the converted input data to create error correction encoded input data;
• and
• a communicating module that communicates the error correction encoded input data to a medium.

A disc drive comprising:

• a communication module that writes encoded data to a disc in the disc drive;
• and
• means for converting unencoded data in a first numerical base to error correction coded encoded data in a second numerical base, wherein the unencoded data and the error correction coded encoded data each comprise a plurality of symbols.