Nonvolatile memory with on-chip encoding for foggy-fine programming

A non-volatile storage apparatus includes a plurality of non-volatile memory cells formed on a memory die, each non-volatile memory cell configured to hold a plurality of bits of data, and a control circuit formed on the memory die. The control circuit is configured to calculate parity data for data to be stored in the memory cells and program the memory cells to first distributions. The control circuit is also configured to read memory cells in the first distributions, recover the data from results of reading the memory cells in the first distributions combined with the parity data, and further program the memory cells from the first distributions to second distributions to store the data.