university of hawaii, college of engineering september 2013 coconets optimal detectors for flash...
TRANSCRIPT
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?