Decoding techniques for correcting errors using soft information

A data storage apparatus that decodes encoded data to perform error correction, wherein the data storage apparatus comprises:

• means for generating syndrome values for error events in an input sequence using a first error correction code;
• means for generating reliability information by selecting a most likely error event for each span of a symbol in the input sequence having a minimum error metric value among the error events that have a first syndrome value, and by selecting a most likely error event for each span of the symbol in the input sequence having a minimum error metric value among the error events that have a second syndrome value;
• means for applying a second error correction code to provide corrected syndrome values using the reliability information;
• and
• means for selecting a most likely symbol corresponding to an error event having a smallest error metric value among the error events having syndrome values consistent with the corrected syndrome values.