Histogram-Based Flash Channel Estimation
  Current generation Flash devices experience significant read-channel degradation from damage to the oxide layer during program and erase operations. Information about the read-channel degradation drives advanced signal processing methods in Flash to mitigate its effect. In this context, channel estimation must be ongoing since channel degradation evolves over time and as a function of the number of program/erase (P/E) cycles. This paper proposes a framework for ongoing model-based channel estimation using limited channel measurements (reads). This paper uses a channel model characterizing degradation resulting from retention time and the amount of charge programmed and erased. For channel histogram measurements, bin selection to achieve approximately equal-probability bins yields a good approximation to the original distribution using only ten bins (i.e. nine reads). With the channel model and binning strategy in place, this paper explores candidate numerical least squares algorithms and ultimately demonstrates the effectiveness of the Levenberg-Marquardt algorithm which provides both speed and accuracy. 
Haobo Wang, Tsung-Yi Chen, and Richard D. Wesel
cs.IT math.IT