Read threshold optimization systems and methods using model-less regression

1. A memory system comprising:

a memory device including a plurality of cells; and

a controller, coupled to the memory device, configured to:

perform multiple read operations on the plurality of cells using multiple read threshold voltage values;

measure probability values for the multiple read threshold voltage values;

estimate a threshold voltage distribution curve based on the multiple read threshold voltage values and the measured probability values using a set regression formula;

determine a read threshold voltage value corresponding to a set point on the threshold voltage distribution curve; and

perform a read operation on the plurality of cells using the read threshold voltage value.

2. The memory system of claim 1 , wherein the controller is configured to:

perform a first read operation, of the multiple read operations, on the plurality of cells using a first read threshold voltage value; and

perform a second read operation, of the multiple read operations, on the plurality of cells using a second read threshold voltage value.

3. The memory system of claim 2 , wherein the first read threshold voltage value includes a successful, previously-used read threshold voltage value.

4. The memory system of claim 2 , wherein the second read threshold is used for a read retry operation.

5. The memory system of claim 4 , wherein the second read threshold value has a high priority among multiple read retry threshold voltage values, which are stored in a read retry table for the read retry operation.

6. The memory system of claim 1 , wherein the controller:

measures probability values for the multiple read threshold voltage values using a probability mass function (PMF); and

estimates the threshold voltage distribution curve by applying the set regression formula to the multiple read threshold voltage values and the measured probability values.

7. The memory system of claim 6 , wherein the controller:

determines a cumulative mass function (CMF) values for a current read threshold voltage value and a previous read threshold voltage value; and

determines a difference between the CMF values for the current and previous read threshold voltage values as a PMF probability value for the current read threshold voltage value.

8. The memory system of claim 7 , wherein each CMF value is determined based on a number of cells and the number of a particular binary value among the cells, which are associated with a read operation using each read threshold voltage value.

9. The memory system of claim 6 , wherein the set regression formula includes a function of multiple read threshold voltage values and probability values, and

wherein the controller estimates the threshold voltage distribution curve by applying the set regression formula to the multiple read threshold voltage values and the measured probability values.

10. The memory system of claim 9 , wherein the controller evaluates the set regression formula in steps, each of which has a set uniform size, and determines a lowest value among all points evaluated as the set point on the threshold voltage distribution curve.

11. A method for operating a memory system comprising:

performing multiple read operations on a plurality of cells using multiple read threshold voltage values;

measuring probability values for the multiple read threshold voltage values;

estimating a threshold voltage distribution curve based on the multiple read threshold voltage values and the measured probability values using a set regression formula;

determining a read threshold voltage value corresponding to a set point on the threshold voltage distribution curve; and

performing a read operation on the plurality of cells using the read threshold voltage value.

12. The method of claim 11 , wherein the performing of the multiple read operations comprises:

performing a first read operation, of the multiple read operations, on the plurality of cells using a first read threshold voltage value; and

performing a second read operation, of the multiple read operations, on the plurality of cells using a second read threshold voltage value.

13. The method of claim 12 , wherein the first read threshold voltage value is a successful, previously-used read threshold voltage value.

14. The method of claim 12 , wherein the second read threshold is used for a read retry operation.

15. The method of claim 14 , wherein the second read threshold has a high priority among multiple read retry threshold voltage values, which are stored in a read retry table for the read retry operation.

16. The method of claim 11 , wherein the measuring of the probability values comprises measuring the probability values for the multiple read threshold voltage values using a probability mass function (PMF), and

wherein the estimating of the threshold voltage distribution curve comprises estimating the threshold voltage distribution curve by applying the set regression formula to the multiple read threshold voltage values and the measured probability values.

17. The method of claim 16 , wherein the measuring of the probability values comprises:

determining a cumulative mass function (CMF) values for a current read threshold voltage value and a previous read threshold voltage value; and

determining a difference between the CMF values for the current and previous read threshold voltage values as a PMF probability value for the current read threshold voltage value.

18. The method of claim 17 , wherein each CMF value is determined based on a number of cells and the number of a particular binary value among the cells, which are associated with a read operation using each read threshold voltage value.

19. The method of claim 16 , wherein the set regression formula includes a function of multiple read threshold voltage values and probability values, and

wherein the estimating of the threshold voltage distribution curve includes applying the set regression formula to the multiple read threshold voltage values and the measured probability values.

20. The method of claim 19 , wherein the determining of the read threshold voltage value comprises:

evaluating the set regression formula in steps, each of which a set uniform size; and

determining a lowest value among all points evaluated as the set point on the threshold voltage distribution curve.