BER analysis of MLC NAND Flash memories based on an asymmetric PAM model

The reliability of multilevel NAND Flash memories, which are used extensively on solid-state drives, is strongly affected by their aging, ie. the number of applied program/erase cycles (P/E). A multilevel memory uses discrete voltage levels to represent the various bit patterns and, at the beginning of the life-time of such a device, these voltage levels demonstrate distributions with very small variances, resulting to very low symbol and bit-error-ratio (BER). As the number of applied P/E cycles increases, the variance of the voltage levels also increases and that results to increased BER. In this paper, we present a general model for four-level NAND Flash memories that can be used to estimate the memories´ BER as a function of the used NAND technology and the aging process. For that purpose, we use asymmetric Pulse Amplitude Modulation with data-dependent channel noise and we provide analytic expressions for the behavior of such memories, and we associate their aging with noise conditions and used technology.