A memory system includes an encoder and a decoder. The encoder is configured to generate multi-dimensionally-coded data to be written into the non-volatile memory. Data bits of the multi-dimensionally-coded data are grouped into first and second dimensional codes with respect to first and second dimensions, respectively. The decoder is configured to, with respect to each of the first and second dimensional codes included in read multi-dimensionally-coded data, generate a syndrome value of the dimensional code, generate low-reliability location information, generate a soft-input value based on the syndrome value and the low-reliability location information, decode the dimensional code through correction of the dimensional code using the soft-input value, and store modification information indicating a bit of the dimensional code corrected through the correction and reliability information indicating reliability of the correction. The decoder generates the soft-input value also based on the modification information and the reliability information in the memory.