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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
slide 3University of Hawaii, College of EngineeringCOCONETS
Kavčić – September 2013 – Detectors… Flash Channels with ICI
Flash memories
slide 4University of Hawaii, College of EngineeringCOCONETS
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
slide 5University of Hawaii, College of EngineeringCOCONETS
Kavčić – September 2013 – Detectors… Flash Channels with ICI
Trends
© Bellordo 2013
slide 6University of Hawaii, College of EngineeringCOCONETS
Kavčić – September 2013 – Detectors… Flash Channels with ICI
Architecture
Signal processing and coding
© Bellordo 2013
slide 7University of Hawaii, College of EngineeringCOCONETS
Kavčić – September 2013 – Detectors… Flash Channels with ICI
NAND Flash Block
© Bellordo 2013
slide 8University of Hawaii, College of EngineeringCOCONETS
Kavčić – September 2013 – Detectors… Flash Channels with ICI
NAND Flash Block
Data block
© Bellordo 2013
slide 9University of Hawaii, College of EngineeringCOCONETS
Kavčić – September 2013 – Detectors… Flash Channels with ICI
NAND Flash Block
Bit line © Bellordo 2013
slide 10University of Hawaii, College of EngineeringCOCONETS
Kavčić – September 2013 – Detectors… Flash Channels with ICI
NAND Flash Block
Word line
© Bellordo 2013
slide 11University of Hawaii, College of EngineeringCOCONETS
Kavčić – September 2013 – Detectors… Flash Channels with ICI
NAND Flash Block
Even page
© Bellordo 2013
slide 12University of Hawaii, College of EngineeringCOCONETS
Kavčić – September 2013 – Detectors… Flash Channels with ICI
NAND Flash Block
Odd page
© Bellordo 2013
slide 13University of Hawaii, College of EngineeringCOCONETS
Kavčić – September 2013 – Detectors… Flash Channels with ICI
Intercell Interference – capacitive coupling
© Bellordo 2013
slide 14University of Hawaii, College of EngineeringCOCONETS
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
slide 16University of Hawaii, College of EngineeringCOCONETS
Kavčić – September 2013 – Detectors… Flash Channels with ICI
Chanel model – one dimensional
k k+1 k+2
slide 17University of Hawaii, College of EngineeringCOCONETS
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
slide 19University of Hawaii, College of EngineeringCOCONETS
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
slide 24University of Hawaii, College of EngineeringCOCONETS
Kavčić – September 2013 – Detectors… Flash Channels with ICI
Let’s generalize further
slide 25University of Hawaii, College of EngineeringCOCONETS
Kavčić – September 2013 – Detectors… Flash Channels with ICI
slide 26University of Hawaii, College of EngineeringCOCONETS
Kavčić – September 2013 – Detectors… Flash Channels with ICI
slide 27University of Hawaii, College of EngineeringCOCONETS
Kavčić – September 2013 – Detectors… Flash Channels with ICI
slide 28University of Hawaii, College of EngineeringCOCONETS
Kavčić – September 2013 – Detectors… Flash Channels with ICI
slide 29University of Hawaii, College of EngineeringCOCONETS
Kavčić – September 2013 – Detectors… Flash Channels with ICI
slide 30University of Hawaii, College of EngineeringCOCONETS
Kavčić – September 2013 – Detectors… Flash Channels with ICI
Insight into suboptimal detectors
slide 31University of Hawaii, College of EngineeringCOCONETS
Kavčić – September 2013 – Detectors… Flash Channels with ICI
slide 32University of Hawaii, College of EngineeringCOCONETS
Kavčić – September 2013 – Detectors… Flash Channels with ICI
slide 33University of Hawaii, College of EngineeringCOCONETS
Kavčić – September 2013 – Detectors… Flash Channels with ICI
Branch metric equation
slide 34University of Hawaii, College of EngineeringCOCONETS
Kavčić – September 2013 – Detectors… Flash Channels with ICI
Sub-MAP detector for iid inputs
slide 35University of Hawaii, College of EngineeringCOCONETS
Kavčić – September 2013 – Detectors… Flash Channels with ICI
Other detectors – prior art
slide 36University of Hawaii, College of EngineeringCOCONETS
Kavčić – September 2013 – Detectors… Flash Channels with ICI
Simulation parameters and results
slide 37University of Hawaii, College of EngineeringCOCONETS
Kavčić – September 2013 – Detectors… Flash Channels with ICI
BER for Varying Coupling Factor s
slide 38University of Hawaii, College of EngineeringCOCONETS
Kavčić – September 2013 – Detectors… Flash Channels with ICI
BER for Varying SNR
slide 39University of Hawaii, College of EngineeringCOCONETS
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]
slide 40University of Hawaii, College of EngineeringCOCONETS
Kavčić – September 2013 – Detectors… Flash Channels with ICI
SIQ for Varying Coupling Factor s
slide 41University of Hawaii, College of EngineeringCOCONETS
Kavčić – September 2013 – Detectors… Flash Channels with ICI
SIQ for Varying SNR
slide 42University of Hawaii, College of EngineeringCOCONETS
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?