Systems for adaptively determining read threshold voltage using meta information
Embodiments adaptively determine a read retry threshold voltage for a next read operation using meta information collected from previous failed read data. A controller obtains meta information associated with a read operation on a select page, the meta information including a read threshold voltage set. The controller determines a mathematical model for estimating a checksum value for data associated with a next read operation, using a set function of the read threshold voltage set and a set checksum value. The controller determines a set of parameters by performing polynomial regression on the mathematical model. The controller estimates a next read threshold voltage for the next read operation based on the set of parameters.
1. A memory system comprising:
a memory device including a plurality of pages; and
a controller configured to:
obtain meta information associated with a read operation on a select page among the plurality of pages, the meta information including a read threshold voltage set;
determine a mathematical model for estimating a checksum value for data associated with a next read operation, using a set function of the read threshold voltage set and a set checksum value;
determine a set of parameters by performing polynomial regression on the mathematical model; and
estimate a next read threshold voltage for the next read operation based on the set of parameters.
2. The memory system of claim 1 , wherein the set function includes a sigmoid function, and
wherein the select page includes a least significant bit (LSB) page of a triple-level cell (TLC).
3. The memory system of claim 2 , wherein the mathematical model is a quadratic model, which is expressed as:
= cs max ×S (θ 0 +θ 1 v 2 +θ 2 v 2 2 +θ 3 v 6 +θ 4 v 6 2 ),
wherein S(⋅) denotes the sigmoid function, (v 2 , v 6 ) represents the read threshold voltage set for an LSB page, represents the estimated checksum value for the data associated with the next read operation, cs max represents the set checksum value and θ={θ 0 , θ 1 , . . . , θ 4 } represents the set of parameters.
4. The memory system of claim 3 , wherein the set checksum value is determined based on the number of rows of a parity check matrix used for decoding data associated with the read operation.
5. The memory system of claim 3 , wherein the controller determines the set of parameters by performing the polynomial regression on an inverse sigmoid function of the mathematical model according to the following equation:
θ
0
+
θ
1
v
2
+
θ
2
v
2
2
+
θ
3
v
6
+
θ
4
v
6
2
=
S
-
1
(
cs
cs
max
)
.
6. A memory system comprising:
a memory device including a plurality of pages; and
a controller configured to:
obtain meta information associated with read operations on a select page among the plurality of pages, the meta information including multiple read threshold voltage sets, multiple checksum values and percentages of bits of a specific value in data;
determine a mathematical model for estimating a percentage of bits of a specific value in data for a next read operation, using a set function of the read threshold voltage set used for a current read operation;
determine a set of parameters by performing linear regression on the mathematical model;
determine a surface, which is formed by each set of the multiple read threshold voltage sets; determine a line of the surface based on the set of parameters;
determine a best previous read threshold voltage set among the multiple read threshold voltage sets, based on the multiple checksum values;
determine a point corresponding to the best previous read threshold voltage set in the surface; and
estimate a next read threshold voltage for the next read operation by projecting the point onto the line.
7. The memory system of claim 6 , wherein the set function includes a sigmoid function, and
wherein the select page includes a least significant bit (LSB) page of a triple-level cell (TLC).
8. The memory system of claim 7 , wherein the mathematical model is a quadratic model represented by the following equation:
{circumflex over (P)} 1 =S (ϕ 0 +ϕ 1 v 2 +ϕ 2 v 6 )
wherein S(⋅) denotes the sigmoid function, (v 2 , v 6 ) represents a read threshold voltage set for LSB page, {circumflex over (P)} 1 represents a percentage of bits of a specific value and ϕ={ϕ 0 , ϕ 1 , ϕ 2 } represents the set of parameters.
9. The memory system of claim 8 , wherein the controller determines the set of parameters by performing the linear regression on an inverse sigmoid function of the mathematical model according to the following equation:
ϕ 0 +ϕ 1 v 2 +ϕ 2 v 6 =S −1 ( {circumflex over (P)} 1 ).
10. The memory system of claim 8 , wherein the specific value is 1.
11. The memory system of claim 8 , wherein the controller estimates the next read threshold voltage according to ϕ 0 +ϕ 1 v 2 +ϕ 2 v 6 =0.
12. A memory system comprising:
a memory device including a plurality of pages; and
a controller configured to:
obtain meta information associated with read operations on a select page among the plurality of pages, the meta information including multiple read threshold voltage sets, multiple checksum values and a percentage of bits of a specific value in data;
determine a first mathematical model for estimating a checksum value data associated with for a next read operation, using a set function of the read threshold voltage set and a set checksum value;
determine a first set of parameters by performing polynomial regression on the first mathematical model;
estimate a first next read threshold voltage for the next read operation based on the first set of parameters;
determine a second mathematical model for estimating a percentage of bits of specific value in data for the next read operation, using a set function of the read threshold voltage set used for a current read operation;
determine a second set of parameters by performing linear regression on the second mathematical model;
determine a surface, which is formed by each set of the multiple read threshold voltage sets;
determine a line of the surface based on the second set of parameters;
determine a best previous read threshold voltage set among the multiple read threshold voltage sets, based on the multiple checksum values;
determine a point corresponding to the best previous read threshold voltage set in the surface; and
estimate a second next read threshold voltage for the next read operation by projecting the point onto the line.
13. The memory system of claim 12 , wherein the set function includes a sigmoid function, and
wherein the select page includes a least significant bit (LSB) page of a triple-level cell (TLC).
14. The memory system of claim 13 , wherein the first mathematical model is a quadratic model, which is expressed as:
= cs max ×S (θ 0 +θ 1 v 2 +θ 2 v 2 2 +θ 3 v 6 +θ 4 v 6 2 )
wherein S(⋅) denotes the sigmoid function, (v 2 , v 6 ) represents a read threshold voltage set for LSB page, represents the estimated checksum value for the next read operation, cs max represents the set checksum value and θ={θ 0 , θ 1 , . . . , θ 4 } represents the first set of parameters.
15. The memory system of claim 14 , wherein the set checksum value is determined based on the number of rows of a parity check matrix used for decoding data associated with the read operation.
16. The memory system of claim 14 , wherein the controller determines the first set of parameters by performing the polynomial regression on an inverse sigmoid function of the first mathematical model according to the following equation:
θ
0
+
θ
1
v
2
+
θ
2
v
2
2
+
θ
3
v
6
+
θ
4
v
6
2
=
S
-
1
(
cs
cs
max
)
.
17. The memory system of claim 13 , wherein the second mathematical model is a quadratic model represented by the following equation:
{circumflex over (P)} 1 =S (ϕ 0 +ϕ 1 v 2 +ϕ 2 v 6 )
wherein S(⋅) denotes the sigmoid function, (v 2 , v 6 ) represents a read threshold voltage set for LSB page, {circumflex over (P)} 1 represents a percentage of bits of a specific value and ϕ={ϕ 0 , ϕ 1 , ϕ 2 } represents the second set of parameters.
18. The memory system of claim 17 , wherein the controller determines the second set of parameters by performing the linear regression on an inverse sigmoid function of the mathematical model according to the following equation:
ϕ 0 +ϕ 1 v 2 +ϕ 2 v 6 =S −1 ( {circumflex over (P)} 1 ).
19. The memory system of claim 17 , wherein the specific value is 1, and
wherein the controller estimates the second next read threshold voltage according to ϕ 0 +ϕ 1 v 2 +ϕ 2 v 6 =0.
20. The memory system of claim 13 , wherein the controller further determines whether the first and second next read threshold voltages are within a set threshold range;
when it is determined that both of the first and second next read threshold voltages are not within the set threshold range, the controller:
divides the set threshold range into multiple zones,
finds a zone corresponding to the lowest number of read operations, among the multiple zones, and
randomly determines, as a next read threshold voltage, any read threshold voltage in the zone.