Neighbor-Cell Assisted Error Correction for MLC NAND Flash - PowerPoint Presentation

Slide1

Neighbor-Cell Assisted Error Correction for MLC NAND Flash Memories

SIGMETRICS’14Slide2

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 voltagesRationale 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 dataSolution: 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 Slide3

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 dominantSlide4

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, respectivelyOptimal read reference voltage to minimize above BER is at cross-point of neighbor distributionsSlide5

Modeling Raw BER

Algebraic manipulation

with a set of assumptions

Threshold voltage distributions (

f(x) and g(x)) follow Gaussian distributionThe Gaussian distribution has equal variance (σ1 = σ2 = σ)Random data are programmed (P0 = P1)

Optimum read reference voltage is used

, v= (

μ

1+

μ

2)/2 from previous slideQ(x) is a function of raw BERWhen x = (μ2-μ1)/2σ, Q(x) (or raw BER) can be minimum

As x increases, Q(x) (or raw BER) monotonically decreasesHigher value of (μ2-μ1)/2σ is desirable for minimizing raw BERLarger threshold voltage distance (μ2-μ1) between neighboring distributions

Smaller variance (

σ

)

of threshold voltage distribution

, narrower

distributionsSlide6

Observations on Voltage Distribution

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

[

Before

Aggress WL is programmed]

[

After

]Slide7

Overall

vs Conditional Distribution

Overall distribution

is the sum of all four

conditional distributionsIn perspective of minimizing raw BERThreshold voltage distance between neighboring distributionsVariance of threshold voltage distributionDistance: overall distribution ≈ conditional distributionVariance

: overall distribution > conditional distribution

Using conditional distribution to read a page

, instead of overall distribution

can minimize raw BER

Variance of overall distribution

Variance of conditional distribution

Distance of conditional distribution pairsSlide8

Multiple Sets of Reference Voltages

Optimal read reference voltage

is

(

μ1+μ2)/2 from the previous modelREFx is the single read reference voltage for overall distributionREFx11 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 BERSlide9

Measurement Analysis

SNR (Signal to Noise Ratio

): x = (

μ2-μ1)/

2σ, making Q(x) minimumDue to small variance (narrower distribution), conditional distribution is more likely to generate less error when reading threshold voltage

≈

Conditional distributions

>

>

<Slide10

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 errorSlide11

NAC Implementation

Page-to-be-Corrected Buffer

: to store final read data

Neighbor LSB/MSB

Page Buffers: to store aggressor page dataBit1/Bit2: to determine which conditional reference voltage is usedLocal-Optimum-Read Buffer: to store temporary page read with one of four conditional referencesSlide12

Prioritized NAC

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 dominantPi+1(11)->Pi : the cell in state Pi+1 whose neighbor cell is 11 misread as PiTry to use REFx11 first among four conditional referencesIf ECC still fails, then use REFx10  REFx01  REFx00

P/E cycle increasesSlide13

Lifetime Extension

NAC with different strengths (different # of conditional references)

Lifetime can be largely increased by lowering raw BER (to be corrected by ECC)Slide14

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 improvementOver 25K P/E cycles: sharply increased latency because to one of every 3 reads requires NAC due to ECC failure