Determining optimal read reference and programming voltages for non-volatile memory using mutual information
Approaches for operating a memory device comprising memory cells are disclosed. Optimal values for one or more of programming voltages used to program memory cells of the memory device and read reference voltages used to read the memory cells are determined using a mutual information function, I(X; Y), where X represents data values programmed to the memory cells and Y represents data values read from the memory cells. The read reference and/or programming voltages used for reading and/or programming the memory cells are adjusted using the optimal values.
1. A method of operating a memory device, comprising:
jointly determining, using a mutual information function, I(X; Y), optimal values that provide predetermined bit error rate criteria for one or more of programming voltages used to program memory cells of the memory device and read reference voltages used to read the memory cells, where X represents data values programmed to the memory cells and Y represents data values read from the memory cells in the function I(X; Y), wherein the optimal values for one of the read reference voltages and programming voltages are determined while holding the other of the read reference voltages and programming voltages fixed; and
adjusting at least one of the read reference voltages and the programming voltages using the optimal values.
2. The method of claim 1 , wherein determining optimal values comprises determining optimal values for the programming voltages.
3. The method of claim 2 , wherein determining optimal values comprises determining the mutual information for each of a plurality of input/output channels, wherein each of the channels are constrained to have the same mutual information value.
4. The method of claim 2 , wherein determining optimal values comprises determining the mutual information for each of a plurality of input/output channels, wherein the channels are not constrained to have the same mutual information value.
5. The method of claim 2 , wherein determining the optimal programming voltages comprises determining mutual information for a channel that has M levels, wherein M is a number of possible voltage levels that can be stored in the memory cells and M is greater than 2.
6. The method of claim 1 , wherein determining optimal values comprises determining optimal values of the read reference voltages.
7. The method of claim 6 , wherein determining the optimal read reference voltages comprises determining mutual information for a channel that has M levels, wherein M is a number of possible voltage levels that can be stored in the memory cells and M is greater than 2.
8. The method of claim 1 , wherein jointly determining the read reference voltages and the programming voltages comprises determining optimal values for the read reference voltages while holding the programming voltages fixed.
9. The method of claim 1 , wherein jointly determining the read reference voltages and the programming voltages comprises determining optimal values for the programming voltages while holding the read reference voltages fixed.
10. The method of claim 1 , wherein determining the optimal values comprises maximizing I(X; Y).
11. The method of claim 1 , wherein determining the optimal values comprises determining if a sum of mutual information values for all programming voltages is maximum.
12. An apparatus, comprising:
a controller configured to control a memory, the controller configured to
jointly determine, using a mutual information function, I(X; Y), optimal values that achieve predetermined bit error rate criteria for one or more of programming voltages used to program memory cells of the memory and read reference voltages used to read the memory cells, where X represents data values programmed to the memory cells and Y represents data values read from the memory cells in the function I(X; Y), wherein the optimal values for one of the read reference voltages and programming voltages are determined while holding the other of the read reference voltages and programming voltages fixed, and
generate signals to control adjustment of at least one of the read reference voltages and the programming voltages to the optimal values.
13. The apparatus of claim 12 , wherein the controller is configured to determine the optimal values for multipage memory architecture.
14. The apparatus of claim 12 , wherein the controller is configured to determine the optimal values for full sequence memory architecture.
15. The apparatus of claim 12 , wherein the controller is configured to determine the optimal values by maximizing I(X; Y).
16. The apparatus of claim 12 , wherein the controller is configured to determine if a sum of mutual information values for all programming voltages is maximum without constraint that the mutual information values for all programming voltages are equal.
17. The apparatus of claim 12 , wherein the controller is configured to estimate noise used in determining the mutual information using asymmetrical noise distributions.