Linear Programming based decoding for memory devices

1. A method to determine a value of a memory cell of a flash memory device, the method comprising:

detecting a cell threshold voltage level of the memory cell;

determining an interference voltage level of an interference cell that interferes with the memory cell; and

decoding the cell threshold voltage level in accordance with a set of probabilities to determine the value of the memory cell, the set of probabilities associated with a minimization of a linear program that represents inter-cell interference between the memory cell and the interference cell.

2. The method of claim 1 , wherein the set of probabilities comprises marginal probabilities that satisfy a constraint associated with the linear program.

3. The method of claim 1 , further comprising:

receiving a model representing inter-cell interferences associated with a plurality of cells of the flash memory device, wherein the model comprises the set of probabilities.

4. The method of claim 1 , wherein the set of probabilities is obtained by:

modeling the inter-cell interference between the memory cell and the interference cell as an integer programming problem;

relaxing the integer programming problem to obtain the linear program; and

solving the linear program to obtain the set of probabilities.

5. The method of claim 1 , further comprising:

identifying, for a plurality of signals written to a plurality of cells of the flash memory device, measured threshold voltage levels and resulting threshold voltage values; and

determining, based upon the resulting threshold values, a configuration used to write to the plurality of cells, wherein the configuration minimizes a Euclidean distance between the resulting threshold values and the measured threshold voltage levels.

6. The method of claim 5 , further comprising:

determining an integer programming problem that represents the Euclidean distance between the resulting threshold values and the measured threshold voltage levels;

relaxing the integer programming problem to obtain a linear programming problem; and

identifying the set of probabilities that correspond to marginal probabilities that minimizes the linear programming problem.

7. The method of claim 1 , wherein detecting the cell threshold voltage level comprises detecting the cell threshold voltage level in response to receipt of a request to read the value of the memory cell.

8. The method of claim 1 , wherein decoding the cell threshold voltage comprises:

compensating for the inter-cell interference between the memory cell and the interference cell by multiplication of the cell threshold voltage level by a marginal probability that corresponds to at least one of the set of probabilities; and

determining the value of the memory cell in accordance with a result of multiplication of the cell threshold voltage level by the marginal probability.

9. The method of claim 1 , wherein decoding the cell threshold voltage level comprises:

determining a probability that the value of the memory cell is equal to zero;

determining a further probability that the value of the memory cell is equal to one;

in response to a determination that the probability is greater than the further probability, determining the value of the memory cell is zero; and

in response to a determination that the further probability is greater than the probability, determining the value of the memory cell is one.

10. A computer readable medium comprising computer executable instructions that, when executed by a computer, cause the computer to:

detect a cell threshold voltage level of a memory cell of a flash memory device;

determine an interference voltage level of an interference cell that interferes with the memory cell; and

decode the cell threshold voltage level in accordance with a set of probabilities to determine a value of the memory cell, the set of probabilities comprising a minimization of a linear program that represents inter-cell interference between the memory cell and the interference cell.

11. The computer readable medium of claim 10 , further comprising computer executable instructions that, when executed by the computer, cause the computer to:

receive a model that represents inter-cell interferences between a plurality of cells of the flash memory device, wherein the model comprises the set of probabilities.

12. The computer readable medium of claim 10 , wherein the set of probabilities comprises marginal probabilities that satisfies a constraint associated with the linear program.

13. The computer readable medium of claim 10 , wherein to obtain the set of probabilities, the computer executable instructions, when executed by the computer, further cause the computer to:

model the inter-cell interference between the memory cell and the interference cell as an integer programming problem;

relax the integer programming problem to obtain the linear program; and

solve the linear program to obtain the set of probabilities.

14. The computer readable medium of claim 10 , further comprising computer executable instructions that, when executed by the computer, further cause the computer to:

identify, for a plurality of signals written to a plurality of cells of the flash memory device, measured threshold voltage levels and resulting threshold voltage values; and

determine, based upon the resulting threshold voltage values, a configuration used to write to the plurality of cells, wherein the configuration minimizes a Euclidean distance between the resulting threshold voltage values and the measured threshold voltage levels.

15. The computer readable medium of claim 14 , further comprising computer executable instructions that, when executed by the computer, further cause the computer to:

determine an integer programming problem that represents the Euclidean distance between the resulting threshold voltage values and the measured threshold voltage levels;

relax the integer programming problem to obtain a linear programming problem; and

identify the set of probabilities, wherein the set of probabilities corresponds to marginal probabilities that minimizes the linear programming problem.

16. The computer readable medium of claim 10 , wherein to detect the cell threshold voltage level, the computer executable instructions, when executed by the computer, further cause the computer to detect the cell threshold voltage level in response to a request to read the value of the memory cell.

17. The computer readable medium of claim 10 , wherein to decode the cell threshold voltage level, the computer executable instructions, when executed by the computer, further cause the computer to:

multiply the cell threshold voltage level by a marginal probability that corresponds to at least one of the set of probabilities to compensate for the inter-cell interference between the memory cell and the interference cell; and

determine the value of the memory cell in accordance with a result of multiplication of the cell threshold voltage level by the marginal probability.

18. The computer readable medium of claim 10 , wherein to decode the cell threshold voltage level, the computer executable instructions, when executed by the computer, further cause the computer to:

determine a probability that the value of the memory cell is equal to zero;

determine a further probability that the value of the memory cell is equal to one;

in response to a determination that the probability is greater than the further probability, determine the value of the memory cell is zero; and

in response to a determination that the further probability is greater than the probability, determine the value of the memory cell is one.

19. A computing device, comprising:

a flash memory device comprising a plurality of cells; and

a processor coupled to the flash memory device and configured to execute non-transitory computer executable instructions to

receive a request to read a value of a memory cell of the flash memory device,

obtain a mathematical model that represents inter-cell interferences of the plurality of cells, wherein the model comprises a set of marginal probabilities that satisfy constraints associated with the mathematical model,

detect a cell threshold voltage level of the memory cell,

determine, based upon the mathematical model, an interference voltage level of an interference cell that interferes with the memory cell, and

decode the cell threshold voltage level in accordance with the set of marginal probabilities to determine the value of the memory cell, wherein the set of marginal probabilities comprises a minimization of a linear program representing the inter-cell interferences.

20. The computing device of claim 19 , wherein the processor is further configured to execute the computer executable instructions to

generate the mathematical model as an integer programming problem,

relax the integer programming problem to obtain the linear program, and

solve the linear program to obtain the set of marginal probabilities that minimize the linear program.

21. The computing device of claim 19 , wherein the processor is further configured to execute the computer executable instructions to

identify, for a plurality of signals written to the plurality of cells of the flash memory device, measured threshold voltage levels and resulting threshold voltage values,

determine, based upon the resulting threshold values, a configuration used to write to the plurality of cells, wherein the configuration minimizes a Euclidean distance between the resulting threshold voltage values and the measured threshold voltage levels, and

generate the mathematical model based, at least partially, upon the Euclidean distance.

22. The computing device of claim 21 , wherein the processor is further configured to execute the computer executable instructions to

determine an integer programming problem that represents the Euclidean distance between the resulting threshold values and the measured threshold voltage levels,

relax the integer programming problem to obtain a linear programming problem, and

identify the set of marginal probabilities, wherein the set of marginal probabilities minimizes the linear programming problem.