A controller includes an interface and storage circuitry. The interface communicates with a memory that includes memory cells that store data in multiple programming levels, and that are organized in Word Lines (WLs). Each WL connects to one or more cell-groups of the memory cells. The memory cells in some cell-groups suffer from an impairment that has a different severity for reading data units of different bit-significance values. The storage circuitry assigns multiple parity groups to data units stored in cell-groups belonging to consecutive WLs, so that a same parity group is assigned to data units of different bit-significance values in neighboring groups of Nwl consecutive WLs. Upon detecting a failure to access a data unit of a given parity group, due to the impairment, the storage circuitry recovers the data unit using other data units assigned to the given parity group, and that are stored in other cell-groups.