Optimal read threshold estimation
An optimal read threshold estimation method includes determining a flip difference corresponding to an optimal step size Δ opt , estimating a first slope m 1 at a first read point and a second slope m 2 at a second read point, and obtaining an optimal read threshold (X LP opt ) as the intersection of a first line with the first slope m 1 and a second line with the second slope m 2 .
1. An optimal read threshold estimation method, comprising:
determining a flip difference corresponding to an optimal step size Δ opt ;
estimating a first slope m at a first read point and a second slope m 2 at a second read point, wherein the first read point is a read point to the left of an optimal read threshold X minbin opt , the second read point is a read point to the right of the optimal read threshold X minbin opt , the first slope m 1 and the second slope m 2 are slopes on the left side and right side of an estimated read threshold curve, respectively; and
obtaining an optimal read threshold estimation (X LP opt ) as the intersection of a first line with the first slope m 1 and a second line with the second slope m 2 .
2. The optimal read threshold estimation method according to claim 1 , wherein the flip difference is determined as 1 CD (R k −Δ opt /2, R k +Δ opt /2)/Δ opt at read points ((R k −Δ opt /2) and (R k +Δ opt /2)), where the R k denotes the read at Kth time, and 1 CD (R k−1 , R k ) is the function for ones count difference between R k−1 and R k .
3. The optimal read threshold estimation method according to claim 1 , wherein the slopes m and m 2 are estimated as:
m 1 =( F ( X minbin opt −L L +Δ m )− F ( X minbin opt −L L ))/Δ m
m 2 =( F ( X minbin opt +L R +Δ m )− F ( X minbin opt +L R ))/Δ m
where the values of L L , L R and Δ m are chosen depending upon a solid state storage, the L L denotes the shift on the left side of the estimated threshold X minbin opt , the L R is the shift on the right side of the estimated threshold X minbin opt , the Δ m is the step size, and
F ( X minbin opt −L L +Δ m )=1 CD ( X minbin opt −L L +Δ m −Δ opt /2, X minbin opt −L L +Δ m +Δ opt /2)/Δ opt ,
F ( X minbin opt −L L )=1 CD ( X minbin opt −L L −Δ opt /2, X minbin opt −L L +Δ opt /2)/Δ opt ,
F ( X minbin opt −L R +Δ m )=1 CD ( X minbin opt −L R +Δ m −Δ opt /2, X minbin opt −L R +Δ m +Δ opt /2)/Δ opt , and
F ( X minbin opt −L R )=1 CD ( X minbin opt −L R −Δ opt /2, X minbin opt −L R +Δ opt /2)/Δ opt .
4. The optimal read threshold estimation method according to claim 1 , wherein the first read point is (x 1 , y 1 ) and the second read point is (x 2 , y 2 ); and the optimal read threshold is obtained as:
X LP opt =( x 2 m 2 −x 1 m 1 +y 1 −y 2 )/( m 2 −m 1 )
where x 1 =X minbin opt −L L , x 2 =X minbin opt +L R , y 1 =F(x 1 ) and y 2 =F(x 2 ), the L L denotes the shift on the left side of the estimated threshold X minbin opt , the L R is the shift on the right side of the estimated threshold X minbin opt , x 1 m 1 is product of x 1 and m 1 , and x 2 m 2 is product of x 2 and m 2 .
5. The optimal read threshold estimation method according to claim 1 , wherein the step size Δ opt value is 12.
6. The optimal read threshold estimation method according to claim 1 , wherein the step size Δ opt value is determined based on a type of solid state storage.
7. The optimal read threshold estimation method according to claim 1 , further comprising, before the determining the flip difference, searching a minimum bin to find optimal read threshold estimates for three read thresholds.
8. The optimal read threshold estimation method according to claim 1 , wherein the solid state storage comprises a Multi-Level Cell (MLC) NAND, and two bits (low significant bit (LSB) and most significant bit (MSB)) are programmed on the NAND.
9. A system, comprising:
a solid state storage;
an optimal read threshold estimator; and
an interface suitable for communicating with the solid state storage and the optimal read threshold estimator;
the optimal read threshold estimator being suitable for:
determining a flip difference corresponding to an optimal step size Δ opt ; estimating a first slope m 1 at a first read point and a second slope m 2 at a second read point, wherein the first read point is a read point to the left of an optimal read threshold X minbin opt the second read point is a read point to the right of the optimal read threshold X minbin opt , the first slope m 1 and the second slope m 2 are slopes on the left side and right side of an estimated read threshold curve, respectively; and
obtaining an optimal read threshold estimation (X LP opt ) as the intersection of a first line with the first slope m 1 and a second line with the second slope m 2 .
10. The system according to claim 9 , wherein the flip difference is determined as 1 CD (R k −Δ opt /2, R k +Δ opt /2)/Δ opt at read points ((R k −Δ opt /2) and (R k +Δ opt /2)), where the R k denotes the read at Kth time, and 1 CD (R k−1 , R k ) is the function for ones count difference between R k−1 and R k .
11. The system according to claim 9 , wherein the slopes m 1 and m 2 are estimated as:
m 1 =( F ( X minbin opt −L L +Δ m )− F ( X minbin opt −L L ))/Δ m
m 2 =( F ( X minbin opt +L R +Δ m )− F ( X minbin opt +L R ))/Δ m
where the values of L L , L R and Δ m are chosen depending upon a solid state storage, the L L denotes the shift on the left side of the estimated threshold X minbin opt , the L R is the shift on the right side of the estimated threshold X minbin opt , the Δm is the step size, and
F ( X minbin opt −L L +Δ m )=1 CD ( X minbin opt −L L +Δ m −Δ opt /2, X minbin opt −L L +Δ m +Δ opt /2)/Δ opt ,
F ( X minbin opt −L L )=1 CD ( X minbin opt −L L −Δ opt /2, X minbin opt −L L +Δ opt /2)/Δ opt ,
F ( X minbin opt −L R +Δ m )=1 CD ( X minbin opt −L R +Δ m −Δ opt /2, X minbin opt −L R +Δ m +Δ opt /2)/Δ opt , and
F ( X minbin opt −L R )=1 CD ( X minbin opt −L R −Δ opt /2, X minbin opt −L R +Δ opt /2)/Δ opt .
12. The system according to claim 9 , wherein the first read point is (x 1 , y 1 ) and the second read point is (x 2 , y 2 ) and the optimal read threshold is obtained as:
X LP opt =( x 2 m 2 −x 1 m 1 +y 1 −y 2 )/( m 2 −m 1 )
where x 1 =X minbin opt −L L , x 2 =X minbin opt +L R , y 1 =F(x 1 ) and y 2 =F(x 2 ), where, the L L denotes the shift on the left side of the estimated threshold X minbin opt , the L R is the shift on the right side of the estimated threshold X minbin opt , x 1 m 1 is product of x 1 and m 1 , and x 2 m 2 is product of x 2 and m 2 .
13. The system according to claim 9 , wherein the step size Δ opt value is 12.
14. The system according to claim 9 , wherein the step size Δ opt value is determined based on a type of solid state storage.
15. The system according to claim 9 , wherein the optimal read threshold estimator is further suitable for, before the determining the flip difference, searching a minimum bin to find optimal read threshold estimates for three read thresholds.
16. The system according to claim 9 , wherein the solid state storage comprises a Multi-Level Cell (MLC) NAND, and two bits (low significant bit (LSB) and most significant bit (MSB)) are programmed on the NAND.
17. A computer implemented process for estimating an optimal read threshold, comprising program instructions to:
determine a flip difference corresponding to an optimal step size Δ opt ;
estimate a first slope m 1 at a first read point and a second slope m 2 at a second read point, wherein the first read point is a read point to the left of an optimal read threshold X minbin opt , the second read point is a read point to the right of the optimal read threshold X minbin opt , the first slope m 1 and the second slope m 2 are slopes on the left side and right side of an estimated read threshold curve, respectively; and
obtain an optimal read threshold estimation (X LP opt ) as the intersection of a first line with the first slope m 1 and a second line with the second slope m 2 .
18. The computer implemented process according to claim 17 , wherein the flip difference is determined as 1 CD (R k −Δ opt /2, R k +Δ opt /2)/Δ opt at read points ((R k −Δ opt /2) and (R k +Δ opt /2)), where the R k denotes the read at Kth time, and 1 CD (R k−1 , R k ) is the function for ones count difference between R k−1 and R k .
19. The computer implemented process according to claim 17 , wherein the slopes m 1 and m 2 are estimated as:
m 1 =( F ( X minbin opt −L L +Δ m )− F ( X minbin opt −L L ))/Δ m
m 2 =( F ( X minbin opt +L R +Δ m )− F ( X minbin opt +L R ))/Δ m
where the values of L L , L R and Δ m are chosen depending upon a solid state storage, the L L denotes the shift on the left side of the estimated threshold X minbin opt , the L R is the shift on the right side of the estimated threshold X minbin opt , the Δm is the step size, and
F ( X minbin opt −L L +Δ m )=1 CD ( X minbin opt −L L +Δ m −Δ opt /2, X minbin opt −L L +Δ m +Δ opt /2)/Δ opt ,
F ( X minbin opt −L L )=1 CD ( X minbin opt −L L −Δ opt /2, X minbin opt −L L +Δ opt /2)/Δ opt,
F ( X minbin opt −L R +Δ m )=1 CD ( X minbin opt −L R +Δ m −Δ opt /2, X minbin opt −L R +Δ m +Δ opt /2)/Δ opt , and
F ( X minbin opt −L R )=1 CD ( X minbin opt −L R −Δ opt /2, X minbin opt −L R +Δ opt /2)/Δ opt .
20. The computer implemented process according to claim 17 , wherein the first read point is (x 1 , y 1 ) and the second read point is (x 2 , y 2 ); and the optimal read threshold is obtained as:
X LP opt =( x 2 m 2 −x 1 m 1 +y 1 −y 2 )/( m 2 −m 1 )
where x 1 =X minbin opt −L L , x 2 =X minbin opt +L R , y 1 =F(x 1 ) and y 2 =F(x 2 ), the L L denotes the shift on the left side of the estimated threshold X minbin opt , the L R is the shift on the right side of the estimated threshold X minbin opt , x 1 m 1 is product of x 1 and m 1 , and x 2 m 2 is product of x 2 and m 2 .
21. The computer implemented process according to claim 17 , wherein the step size Δ opt value is 12.
22. The computer implemented process according to claim 17 , wherein the step size Δ opt value is determined based on a type of solid state storage.
23. The computer program product according to claim 17 , wherein the program instructions further comprise searching a minimum bin to find optimal read threshold estimates for three read thresholds before the determining the flip difference.
24. The computer program product according to claim 17 , wherein the solid state storage comprises a Multi-Level Cell (MLC) NAND, and two bits (low significant bit (LSB) and most significant bit (MSB)) are programmed on the NAND.