University of Hawaii, College of Engineering

September 2013

COCONETS

Optimal Detectorsfor Flash Memory Channels

with Intercell Interference

Alek Kavčić

Department of Electrical Engineerig

University of Hawaii

collaborators:

Meysam Asadi

Xiujie Huang

Narayana (Prasad) Santhanam

slide 2University of Hawaii, College of EngineeringCOCONETS

Kavčić – September 2013 – Detectors… Flash Channels with ICI

Outline

• Flash memories: outlook and basics

• Chanel model

• Detectors

• Results and Conclusion

• Comments on Information Theoretic problems

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Kavčić – September 2013 – Detectors… Flash Channels with ICI

Flash memories

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Kavčić – September 2013 – Detectors… Flash Channels with ICI

Near-term challenge

• In an effort to scale down prices and increase capacities, manufacturers have scaled down their manufacturing process– Exceeded the rate predicted by Moores law– Price reduction: >$100/GB in 2008 to <$1/GB in 2013

• Scaling down features acts to exacerbate many noise sources

• Reliably mitigating noise requires understanding the channel

© Bellordo 2013

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Kavčić – September 2013 – Detectors… Flash Channels with ICI

Trends

© Bellordo 2013

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Kavčić – September 2013 – Detectors… Flash Channels with ICI

Architecture

Signal processing and coding

© Bellordo 2013

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Kavčić – September 2013 – Detectors… Flash Channels with ICI

NAND Flash Block

© Bellordo 2013

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Kavčić – September 2013 – Detectors… Flash Channels with ICI

NAND Flash Block

Data block

© Bellordo 2013

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Kavčić – September 2013 – Detectors… Flash Channels with ICI

NAND Flash Block

Bit line © Bellordo 2013

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Kavčić – September 2013 – Detectors… Flash Channels with ICI

NAND Flash Block

Word line

© Bellordo 2013

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Kavčić – September 2013 – Detectors… Flash Channels with ICI

NAND Flash Block

Even page

© Bellordo 2013

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Kavčić – September 2013 – Detectors… Flash Channels with ICI

NAND Flash Block

Odd page

© Bellordo 2013

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Kavčić – September 2013 – Detectors… Flash Channels with ICI

Intercell Interference – capacitive coupling

© Bellordo 2013

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Kavčić – September 2013 – Detectors… Flash Channels with ICI

Intercell interference – capacitive coupling

© Bellordo 2013

slide 15University of Hawaii, College of EngineeringCOCONETS

Kavčić – September 2013 – Detectors… Flash Channels with ICI

Intercell interference – capacitive coupling

© Bellordo 2013

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Kavčić – September 2013 – Detectors… Flash Channels with ICI

Chanel model – one dimensional

k k+1 k+2

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Kavčić – September 2013 – Detectors… Flash Channels with ICI

1) Erase memory

k k+1 k+2

Voltage

Ek+1Ek Ek+2

slide 18University of Hawaii, College of EngineeringCOCONETS

Kavčić – September 2013 – Detectors… Flash Channels with ICI

2) Decide what to write (one of 4 levels)

k k+1 k+2Voltage

Ek Ek+2

Xk=1

Xk+1=3

Xk+2=2

Ek+1

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Kavčić – September 2013 – Detectors… Flash Channels with ICI

3) Write k-th cell (using incremental -filling)

k k+1 k+2Voltage

Ek Ek+2

Xk=1

Xk+1=3

Xk+2=2

Xk+Uk+Wkunifr

omG

auss

ian

Ek+1

slide 20University of Hawaii, College of EngineeringCOCONETS

Kavčić – September 2013 – Detectors… Flash Channels with ICI

4) Write (k+1)-st cell (incremental -filling)

k k+1 k+2Voltage

Ek Ek+1 Ek+2

Xk=1

Xk+1=3

Xk+2=2

Xk+Uk+Wk

Xk+Uk+Wk+1(k+1)

capcitive coupling

k+1

coup

ling

coeff

.

slide 21University of Hawaii, College of EngineeringCOCONETS

Kavčić – September 2013 – Detectors… Flash Channels with ICI

5) Write (k+2)-nd cell (incremental -filling)

k k+1 k+2Voltage

Ek Ek+1 Ek+2

Xk=1

Xk+1=3

Xk+2=2

k+2

capacitive coupling

capacitive coupling

k+1

slide 22University of Hawaii, College of EngineeringCOCONETS

Kavčić – September 2013 – Detectors… Flash Channels with ICI

So we have an M-level channel model

Yk = Xk+Uk+Wk+1(Yk+1 – Ek+1)+2(Yk+2 – Ek+2)

unifr

omG

auss

ian

chan

nel o

utpu

tch

anne

l in

put

(

M-

leve

ls)

Gau

ssia

n

Gau

ssia

n

1-st

nei

ghbo

r co

uplin

g

2-n

d ne

ighb

or c

oupl

ing

Anti-causal difference equation

slide 23University of Hawaii, College of EngineeringCOCONETS

Kavčić – September 2013 – Detectors… Flash Channels with ICI

Equivalent causal M-level channel model

Yk = Xk+Uk+Wk+1(Yk–1 – Ek–1)+2(Yk–2 – Ek–2)

causal difference equation

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Kavčić – September 2013 – Detectors… Flash Channels with ICI

Let’s generalize further

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Kavčić – September 2013 – Detectors… Flash Channels with ICI

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Kavčić – September 2013 – Detectors… Flash Channels with ICI

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Kavčić – September 2013 – Detectors… Flash Channels with ICI

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Kavčić – September 2013 – Detectors… Flash Channels with ICI

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Kavčić – September 2013 – Detectors… Flash Channels with ICI

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Kavčić – September 2013 – Detectors… Flash Channels with ICI

Insight into suboptimal detectors

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Kavčić – September 2013 – Detectors… Flash Channels with ICI

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Kavčić – September 2013 – Detectors… Flash Channels with ICI

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Kavčić – September 2013 – Detectors… Flash Channels with ICI

Branch metric equation

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Kavčić – September 2013 – Detectors… Flash Channels with ICI

Sub-MAP detector for iid inputs

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Kavčić – September 2013 – Detectors… Flash Channels with ICI

Other detectors – prior art

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Kavčić – September 2013 – Detectors… Flash Channels with ICI

Simulation parameters and results

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Kavčić – September 2013 – Detectors… Flash Channels with ICI

BER for Varying Coupling Factor s

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Kavčić – September 2013 – Detectors… Flash Channels with ICI

BER for Varying SNR

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Kavčić – September 2013 – Detectors… Flash Channels with ICI

Soft Information Quality (SIQ) of a Detector

Xk – channel input symbol

Sk – soft-output of a detector (vector quantity)

Define SIQ as:q = I ( Xk ; Sk )|Xk is iud

SIQ is the capacity of random linear block codes [Kavcic, Ma, Mitzenmacher 2003]

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Kavčić – September 2013 – Detectors… Flash Channels with ICI

SIQ for Varying Coupling Factor s

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Kavčić – September 2013 – Detectors… Flash Channels with ICI

SIQ for Varying SNR

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Kavčić – September 2013 – Detectors… Flash Channels with ICI

Some Open Information-Theoretic Problems

Yk = f ( Xk–M , Yk–L ) + Wkk k–1

Finite Output Memory and State Channel (FOMASC)

Not a finite state channelViterbi/BCJR detector is optimalWhat is the “indecomposability condition”?Is information rate independent od starting state?Do Markov processes asymptotically achieve capacity?