1. Neighbor-Cell Assisted Error Correction for MLC NAND Flash Memories
SIGMETRICS’14

2. Summary
Problem: as P/E cycle increases, raw BER significantly increases beyond the fixed ECC capability
Goal: this paper tries to extend lifetime by reducing # of bit errors in a page (to the extent which ECC can fix)
How to reduce # of bit errors: when reading a page, they use multiple sets of reference voltages, instead of conventional single set of reference voltages
Rationale of multiple sets of reference voltages: they observed “the threshold voltage distributions based on the values in the neighboring cell”, and reading with “the new reference voltage from the threshold voltage distributions” brings less error data
Solution: When read page fails to pass ECC, Neighbor-cell Assisted Correction (NAC) mechanism reads a page several times using multiple reference voltages, which makes # of errors in the page drop by the degree ECC can correct

3. Background: Program Interference
Prior works characterized and modeled this error type
Threshold voltage of a cell (victim cell) can change when its neighbor cells (aggressor cells) are being programmed
Program interference from neighbor cells on the same WL is negligible
Program interference on a victim cell C(n, j) due to the aggressor cell on the WL that is immediately above the victim WL “C(n+1, j)” is dominant

4. Optimizing Read Reference Voltage
Neighboring states (Pi and Pi+1) are overlapped
By a reference voltage (Vref), blue is error due to “Pi misread as Pi+1” and read is error due to “Pi+1 misread as Pi”
F(x) and g(x) are probability density functions (PDF) of cells programmed into state Pi and Pi+1, respectively
Optimal read reference voltage to minimize above BER is at cross-point of neighbor distributions

5. Modeling Raw BER Algebraic manipulation with a set of assumptions
Threshold voltage distributions (f(x) and g(x)) follow Gaussian distribution
The Gaussian distribution has equal variance (σ1 = σ2 = σ)
Random data are programmed (P0 = P1)
Optimum read reference voltage is used, v= (μ1+μ2)/2 from previous slide
Q(x) is a function of raw BER
When x = (μ2-μ1)/2σ, Q(x) (or raw BER) can be minimum
As x increases, Q(x) (or raw BER) monotonically decreases
Higher value of (μ2-μ1)/2σ is desirable for minimizing raw BER
Larger threshold voltage distance (μ2-μ1) between neighboring distributions
Smaller variance (σ) of threshold voltage distribution, narrower distributions

6. Observations on Voltage Distribution
[After]
[Before Aggress WL is programmed]
We want to read “victim page” (WL) “with minimum raw bit error”
Before aggressor page (WL) is programmed, two neighboring distributions of victim page are easy to distinguish
After aggressor page is programmed, program interference cause the distributions to overlap, increasing raw BER
The threshold voltage distributions of all cells (overall distribution) can be further divided into four different threshold voltage distributions (conditional distribution) based on the values of aggressor cells

7. Overall vs Conditional Distribution
Overall distribution is the sum of all four conditional distributions
In perspective of minimizing raw BER
Threshold voltage distance between neighboring distributions
Variance of threshold voltage distribution
Distance: overall distribution ≈ conditional distribution
Variance: overall distribution > conditional distribution
Using conditional distribution to read a page, instead of overall distribution can minimize raw BER
Distance of conditional distribution pairs
Variance of overall distribution
Variance of conditional distribution

8. Multiple Sets of Reference Voltages
Optimal read reference voltage is (μ1+μ2)/2 from the previous model
REFx is the single read reference voltage for overall distribution
REFx11 is the read reference voltage for conditional distribution whose neighbor (aggressor) cell is programmed with value “11”
For 2-bit MLC flash, there can be additionally four different read voltages for conditional distributions
Due to the small variance (or narrower distribution), using the multiple sets of reference voltages (REFx11, REFx00, REFx10, REFx01), instead of single set of reference voltage (REFx), can minimize raw BER

9. Measurement Analysis Conditional distributions ≈ > < >
SNR (Signal to Noise Ratio): x = (μ2-μ1)/2σ, making Q(x) minimum
Due to small variance (narrower distribution), conditional distribution is more likely to generate less error when reading threshold voltage

10. Neighbor-cell Assisted Correction
(1) read target page using overall read reference (REFx)
(2) check ECC, if it fails, NAC works
(3) firstly read neighbor (aggressor) pages (MSB/LSB) using REFx
(4) then read target page using conditional read references (REF00,11,10,01)
(5) when partially corrected, try to run ECC again
(6) if it fails, try to use another read reference
(7) if ECC continuously fails until all conditional references, return error

11. NAC Implementation
Page-to-be-Corrected Buffer: to store final read data
Neighbor LSB/MSB Page Buffers: to store aggressor page data
Bit1/Bit2: to determine which conditional reference voltage is used
Local-Optimum-Read Buffer: to store temporary page read with one of four conditional references

12. Prioritized NAC
P/E cycle increases
NAC degrades latency due to the increased reads (up to +6)
The first read with overall read reference (1)
The read for neighbor MSB/LSB page (2)
The read with conditional read reference (4)
Observation reveals that specific errors are dominant
Pi+1(11)->Pi : the cell in state Pi+1 whose neighbor cell is 11 misread as Pi
Try to use REFx11 first among four conditional references
If ECC still fails, then use REFx10  REFx01  REFx00

13. Lifetime Extension
NAC with different strengths (different # of conditional references)
Lifetime can be largely increased by lowering raw BER (to be corrected by ECC)

14. Performance Analysis
Low P/E cycles: performance a little improved since neighbor MSB/LSB page read of NAC generates hits in SSD buffer due to good locality of some workloads
18K~24K P/E cycles: less than 5% degradation while providing 33% lifetime improvement
Over 25K P/E cycles: sharply increased latency because to one of every 3 reads requires NAC due to ECC failure