Digital data is stored in an analog memory device using coded modulation techniques. The memory device includes a number of memory cells, each capable of storing one of a number of different levels. A given set of b information bits to be stored in the memory device is first coded in a convolutional or block coder to generate a set of coded bits which includes more than b bits. The set of coded bits is then mapped to one or more corresponding levels, and the one or more levels are each stored in a separate cell of the memory device. In a one-dimensional embodiment, the coding may involve applying a rate 1/2 convolutional code to i least significant bits, i=1, 2, . . . , and mapping the resulting b+i coded bits to one of 2b+i distinct levels in a one-dimensional AM signal set. In embodiments of the invention which utilize multidimensional signal sets, a given set of bits is mapped to a signal in an m-dimensional signal set, with or without coding of the bits, and each of the m dimensions of the selected signal is then stored as a level in a separate cell of the analog memory device. The invention increases the storage capacity of the memory device for a given readout error probability, or alternatively improves the error probability for a given storage capacity. Readout performance may be further improved by using a multiple read-and-sum unit to generate a readout value for a given stored level based on a sum or average of several different readouts of the stored level.