Adaptive read and write systems and methods for memory cells

An apparatus, comprising:

• multi-level memory cells including at least one M level memory cell having M levels;
• and
• a computation block configured to compute optimal or near optimal mean values of level distributions of the multi-level memory cells based, at least in part, on (i) estimated mean values of level distributions of the multi-level memory cells and (ii) estimated standard deviation values of level distributions of the multi-level memory cells,
• wherein an ith level optimal or near optimal mean value ({tilde over (m)}i) of the M level memory cell is computed according to the equation
• m
• ~
• i
• =
• m
• 0
• +
• σ
• 0
• +
• 2
• ⁢
• ∑
• k
• =
• 1
• i
• -
• 1
• ⁢
• ⁢
• σ
• k
• +
• σ
• i
• σ
• 0
• +
• 2
• ⁢
• ∑
• k
• =
• 1
• M
• -
• 2
• ⁢
• ⁢
• σ
• k
• +
• σ
• M
• -
• 1
• ⁢
• L
• wherein mi is the estimated mean value of the ith level of the M level memory cell, σi is the estimated standard deviation value of the ith level of the M level memory cell, and L is equal to mM-1−m0, and wherein at least one of the estimated standard deviation values σ0, . . . , σM-1 is non-zero.

A method, comprising:

• estimating (i) mean values of level distributions of a multi-level memory cells and (ii) standard deviation values of level distributions of the multi-level memory cells;
• and
• computing optimal or near optimal mean values of level distributions of the multi-level memory cells based, at least in part, on (i) the estimated mean values and (ii) the estimated standard deviation values, the optimal or near optimal mean values to be used to facilitate writing of data to the multi-level memory cells,
• wherein the multi-level memory cells include at least one M level memory cell having M levels, and said computing comprises computing an ith level near optimal mean value ({tilde over (m)}) of the M level memory cell according to the equation
• m
• ~
• i
• =
• m
• 0
• +
• σ
• 0
• +
• 2
• ⁢
• ∑
• k
• =
• 1
• i
• -
• 1
• ⁢
• ⁢
• σ
• k
• +
• σ
• i
• σ
• 0
• +
• 2
• ⁢
• ∑
• k
• =
• 1
• M
• -
• 2
• ⁢
• ⁢
• σ
• k
• +
• σ
• M
• -
• 1
• ⁢
• L
• wherein mi is the estimated mean value of the ith level of the M level memory cell, σi is the estimated standard deviation value of the ith level of the M level memory cell, and L is equal to mM-1−m0, and wherein at least one of the estimated standard deviation values σ0, . . . , σM-1 is non-zero.