Systems and methods for parametric PV-level modeling and read threshold voltage estimation

1. A memory system comprising:

a memory device including a plurality of cells; and

a controller configured to:

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 cumulative distribution function (CDF) values, selected from among a plurality of CDF values, which correspond to the CMF samples, each of the first and second CDF values representing a skew normal distribution;

estimate first and second probability distribution parameter sets corresponding to the first and second CDF values, respectively;

determine first and second probability density function (PDF) values corresponding to the first and second CDF values using the first and second probability distribution parameter sets, respectively; and

estimate, as an optimal read threshold voltage, a read threshold voltage corresponding to a cross-point of the first and second PDF values.

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 has a specific percentage of a particular binary value of data stored in the cells.

4. The memory system of claim 3 , wherein each of the first and second probability distribution parameter sets include location, scale and shape of a curve associated with the skew normal distribution.

5. The memory system of claim 3 , wherein each of the first and second probability distribution parameter sets is estimated by a neural network, which is trained to output multiple probability distribution parameter sets corresponding to multiple CDF values, respectively.

6. The memory system of claim 5 , wherein the neural network is trained to receive each of the multiple CDF values and output each of the multiple probability distribution parameter sets based on a synthetic model.

7. The memory system of claim 3 , wherein each of the first and second PDF values is determined by a neural network, which is trained to receive the first and second probability distribution parameter sets and output the first and second PDF values corresponding to the first and second probability distribution parameter sets, respectively.

8. The memory system of claim 3 , wherein the first PDF value is the same as the second PDF value.

9. The memory system of claim 8 , wherein the optimal read threshold voltage corresponds to a cross-point of a first read threshold voltage having the first PDF value and a second read threshold voltage having the second PDF value.

10. A method for operating a memory system including a memory device including a plurality of cells and a controller, the method comprising:

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 cumulative distribution function (CDF) values, selected from among a plurality of CDF values, which correspond to the CMF samples, each of the first and second CDF values representing a skew normal distribution;

estimating first and second probability distribution parameter sets corresponding to the first and second CDF values, respectively;

determining first and second probability density function (PDF) values corresponding to the first and second CDF values using the first and second probability distribution parameter sets, respectively; and

estimating, as an optimal read threshold voltage, a read threshold voltage corresponding to a cross-point of the first and second PDF values.

11. The method of claim 10 , wherein further comprising:

performing a next read operation on the cells using the optimal read threshold voltage.

12. The method of claim 10 , wherein each CMF sample has specific percentage of a particular binary value of data stored in the cells.

13. The method of claim 12 , wherein each of the first and second probability distribution parameter sets include location, scale and shape of a curve associated with the skew normal distribution.

14. The method of claim 12 , wherein each of the first and second probability distribution parameter sets is estimated by a neural network, which is trained to output multiple probability distribution parameter sets corresponding to multiple CDF values, respectively.

15. The method of claim 14 , wherein the neural network is trained to receive each of the multiple CDF values and output each of the multiple probability distribution parameter sets based on a synthetic model.

16. The memory system of claim 12 , wherein each of the first and second PDF values is determined by a neural network, which is trained to receive the first and second probability distribution parameter sets and output the first and second PDF values corresponding to the first and second probability distribution parameter sets, respectively.

17. The method of claim 12 , wherein the first PDF value is the same as the second PDF value.

18. The method of claim 17 , wherein the optimal read threshold voltage corresponds to a cross-point of a first read threshold voltage having the first PDF value and a second read threshold voltage having the second PDF value.