Determination of memory read reference and programming voltages

1. A method of operating a memory device, comprising:

using symmetrical or asymmetrical noise distributions for voltages corresponding to symbols that can be stored in multi-level memory cells (MLCs) of the memory device;

determining at least one of read reference voltages and programming voltages for the MLCs including:

jointly determining the read reference voltages and programming voltages using the symmetrical distributions and a maximum likelihood estimation (MLE); and

determining at least one of the read reference voltages and the programming voltages using the asymmetrical distributions; and

performing at least one of programming the MLCs using the programming voltages and reading the MLCs using the read reference voltages.

2. The method of claim 1 , wherein jointly determining the noise distributions comprises determining at least one noise distribution comprising a first noise distribution for voltages above target signal level and a second noise distribution, different from the first noise distribution, for voltages below the target signal level.

3. The method of claim 1 , wherein:

the MLCs are arranged as a physical page of the memory device and the MLCs are configured to store a least significant bit (LSB) page and most significant bit (MSB) page in the physical page, the LSB page comprising LSBs of the MLCs and a the MSB page comprising MSBs of the MLCs page; and

jointly determining the read reference voltages and programming voltages for the MLCs using the noise distributions comprises determining the read reference and programming voltages so that a bit error rate of the MSB page and a bit error rate of the LSB page are about equal.

4. The method of claim 1 , wherein:

the MLCs are arranged as a physical page of the memory device; and

jointly determining the read reference and programming voltages for the MLCs using the noise distributions comprises determining the read reference voltages to achieve a minimal average bit error rate.

5. The method of claim 4 , wherein the memory device is configured to store a single page of data in the physical page.

6. The method of claim 4 , wherein the memory device is configured to store a least significant bit (LSB) page comprising LSBs of the MLCs and a most significant bit (MSB) page comprising MSBs of the MLCs in the physical page.

7. A method of operating a memory device, comprising:

using noise distributions for voltages corresponding to symbols that can be stored in multi-level memory cells (MLCs) of the memory device, each noise distribution comprising a first noise distribution for voltages above a target signal value and a second noise distribution, different from the first noise distribution, for voltages below the target signal value;

determining at least one of read reference voltages and programming voltages for the MLCs using the first and second noise distributions; and

performing at least one of programming the MLCs using the programming voltages and reading the MLCs using the read reference voltages ,

wherein the first and second noise distributions comprise at least one of:

1) the first noise distribution comprises a first Gaussian noise distribution having a first standard deviation, σ 1 , and the second noise distribution comprises a second Gaussian noise distribution having a second standard deviation, σ 2 , where σ 1 ≠σ 2 ,

2) the first noise distribution comprises a first triangular noise distribution having a first base, b 1 , and the second noise distribution comprises a second triangular noise distribution having a second base, b 2 , where b 1 ≠b 2 ,and

3) the first noise distribution comprises a first exponential noise distribution having a first rate of change, al and the second noise distribution comprises a second exponential noise distribution having a second rate of change, α 2 , where α 1 ≠α 2 .

8. The method of claim 7 , wherein:

the MLCs are arranged as a physical page of the memory device and the memory device is configured to store a least significant bit (LSB) page comprising LSBs of the MLCs and a most significant bit (MSB) page comprising MSBs of the MLCs in the physical page; and

determining at least one of read reference voltages and programming voltages for the MLCs using the first and second noise distributions comprises determining at least one of read reference voltages and programming voltages so that a bit error rate of the MSB page and a bit error rate of the LSB page are about equal.

9. The method of claim 7 , wherein:

the MLCs are arranged as a physical page of the memory device; and

determining at least one of read reference voltages and programming voltages for the MLCs using the first and second noise distributions comprises at least one of read reference voltages and programming voltages to achieve a minimal average bit error rate.

10. The method of claim 7 , wherein the first noise distribution comprises a first type of distribution function and the second noise distribution comprises a second type of distribution function, different from the first type of distribution function.

11. An apparatus, comprising:

a controller capable of being coupled to a memory device, the controller configured to

use symmetrical or asymmetrical noise distributions for symbols corresponding to voltage levels capable of being stored in multi-level memory cells (MLCs) of the memory device; and

jointly determine read reference voltages and programming voltages for the MLCs using the symmetrical noise distributions and a maximum likelihood estimation or determine at least one of the read reference voltages and the programming voltages using the symmetrical or the asymmetrical distributions.

12. The apparatus of claim 11 , wherein each of the asymmetrical noise distributions includes first and second noise distributions comprising at least one of:

a first Gaussian noise distribution having a first standard deviation, σ 1 , and a second the second Gaussian noise distribution having a second standard deviation, σ 2 , where σ 1 ≠σ 2 ;

a first triangular noise distribution having a first base, b 1 , and a second triangular noise distribution having a second base, b 2 , where b 1 ≠b 2 ; and

a first exponential noise distribution having a first rate of change, α1 and second exponential noise distribution having a second rate of change, α 2 , where α 1 ≠α 2 .

13. The apparatus of claim 11 , wherein:

the MLCs are arranged as a physical page of the memory device, the physical page configured to store a least significant bit (LSB) page comprising LSBs of the MLCs and a most significant bit (MSB) page comprising MSBs of the MLCs in the physical page; and

the controller is configured to determine at least one of the read reference voltages and programming voltages for the MLCs using the first and second noise distribution functions so that a bit error rate of the MSB page and a bit error rate of the LSB page are about equal.

14. The apparatus of claim 13 , wherein the MLCs are arranged as a physical page of the memory device, the physical page is configured to store a single data page.

15. The apparatus of claim 13 , wherein the controller is configured to determine at least one of the read reference voltages and programming voltages to achieve a minimal average bit error rate.

16. The apparatus of claim 13 , wherein the MLCs are arranged as a physical page of the memory device, the physical page is configured to store more than one data page.

17. The apparatus of claim 13 , wherein the more than one data page comprises a most significant bit (MSB) page and a least significant bit (LSB) page and the controller is configured to determine at least one of the read reference voltages and programming voltages to achieve equal or about equal bit error rate of the MSB page and the LSB page.