Systems and methods for non-parametric PV-level modeling and read threshold voltage estimation
Embodiments provide a scheme for non-parametric PV-level modeling and an optimal read threshold voltage estimation in a memory system. A controller is configured to: generate multiple optimal read threshold voltages corresponding to multiple sets of two cumulative distribution function (CDF) values, respectively; perform read operations on the cells using a plurality of read threshold voltages; generate cumulative mass function (CMF) samples based on the results of the read operations; receive first and second CDF values, selected from among a plurality of CDF values, each CDF value corresponding to each CMF sample; and estimate an optimal read threshold voltage corresponding to the first and second CDF values, among the multiple optimal read threshold voltages.
1. A memory system comprising:
a memory device including a plurality of cells; and
a controller configured to:
generate multiple optimal read threshold voltages corresponding to multiple sets of two cumulative distribution function (CDF) values, respectively;
perform read operations on the cells using a plurality of read threshold voltages;
generate cumulative mass function (CMF) samples based on the results of the read operations;
receive first and second CDF values, selected from among a plurality of CDF values, each CDF value corresponding to each CMF sample; and
estimate an optimal read threshold voltage corresponding to the first and second CDF values, among the multiple optimal read threshold voltages.
2. The memory system of claim 1 , wherein the controller is further configured to perform a next read operation on the cells using the optimal read threshold voltage.
3. The memory system of claim 1 , wherein each CMF sample indicates a percentage of a particular binary value of data stored in the cells.
4. The memory system of claim 1 , wherein the controller is configured to estimate the optimal read threshold voltage through a training operation including:
receiving a set of first and second CDF values corresponding to first and second program voltage (PV) levels, respectively;
determining a first read threshold voltage corresponding to a cross-point of the first and second PV levels; and
finding, as an optimal read threshold voltage, a second read threshold voltage corresponding to the set of first and second CDF values such that a difference between the first read threshold voltage and the second read threshold voltage is minimized.
5. The memory system of claim 4 , wherein the difference is calculated based on a set loss function.
6. The memory system of claim 4 , wherein the first and second PV levels are obtained through measurements from the cells.
7. The memory system of claim 4 , wherein the first and second PV levels are obtained through a synthetic model associated with the cells.
8. A method for operating a memory system having a memory device including a plurality of cells and a controller, the method comprising:
generating multiple optimal read threshold voltages corresponding to multiple sets of two cumulative distribution function (CDF) values, respectively;
performing read operations on the cells using a plurality of read threshold voltages;
generating cumulative mass function (CMF) samples based on the results of the read operations;
receiving first and second CDF values, selected from among a plurality of CDF values, each CDF value corresponding to each CMF sample; and
estimating an optimal read threshold voltage corresponding to the first and second CDF values, among the multiple optimal read threshold voltages.
9. The method of claim 8 , further comprising:
performing a next read operation on the cells using the optimal read threshold voltage.
10. The method of claim 8 , wherein each CMF sample indicates a percentage of a particular binary value of data stored in the cells.
11. The method of claim 8 , wherein the estimating of the optimal read threshold voltage is performed through a training operation including:
receiving a set of first and second CDF values corresponding to first and second program voltage (PV) levels, respectively;
determining a first read threshold voltage corresponding to a cross-point of the first and second PV levels; and
finding, as an optimal read threshold voltage, a second read threshold voltage corresponding to the set of first and second CDF values such that a difference between the first read threshold voltage and the second read threshold voltage is minimized.
12. The method of claim 11 , wherein the difference is calculated based on a set loss function.
13. The method of claim 11 , wherein the first and second PV levels are obtained through measurements from the cells.
14. The method of claim 11 , wherein the first and second PV levels are obtained through a synthetic model associated with the cells.