Memory system and control method

A memory system comprising:

• a non-volatile memory;
• and
• a memory controller configured to:
• encode data to be written into the non-volatile memory using an error-correction code that includes a Hamming code;
• obtain a hard-read value of data read from the non-volatile memory using a read voltage;
• obtain a plurality of soft-read values of data read from the non-volatile memory using a plurality of read voltages;
• based on the hard-read value and the soft-read values, obtain a soft decision input data, each value of which indicates a likelihood that a corresponding bit of the read data is either 0 or 1;
• obtain a hard decision data of the soft decision input data;
• obtain a syndrome using the hard decision data and a parity check matrix of the error-correction code;
• decoding the hard decision data using a predetermined decoding method to obtain decoded words that are different from each other;
• obtain a plurality of metrics each of which indicates a distance between one of the decoded words and the soft decision input data;
• generate a metric array using the obtained metrics;
• and
• based on a relationship of each value of the metric array with a smallest one of the metrics and a second smallest one of the metrics, obtain a soft decision output data corresponding to the soft decision input data, as a decoding result of the read data.