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University of Hawaii, College of Engineering September 2013 COCONETS Optimal Detectors for Flash Memory Channels with Intercell Interference Alek Kavčić Department of Electrical Engineerig University of Hawaii collaborators: Meysam Asadi Xiujie Huang Narayana (Prasad) Santhanam
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slide 2 University of Hawaii, College of Engineering COCONETS 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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slide 3 University of Hawaii, College of Engineering COCONETS Kavčić – September 2013 – Detectors … Flash Channels with ICI Flash memories
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slide 4 University of Hawaii, College of Engineering COCONETS 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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slide 5 University of Hawaii, College of Engineering COCONETS Kavčić – September 2013 – Detectors … Flash Channels with ICI Trends © Bellordo 2013
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slide 6 University of Hawaii, College of Engineering COCONETS Kavčić – September 2013 – Detectors … Flash Channels with ICI Architecture Signal processing and coding © Bellordo 2013
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slide 7 University of Hawaii, College of Engineering COCONETS Kavčić – September 2013 – Detectors … Flash Channels with ICI NAND Flash Block © Bellordo 2013
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slide 8 University of Hawaii, College of Engineering COCONETS Kavčić – September 2013 – Detectors … Flash Channels with ICI NAND Flash Block Data block © Bellordo 2013
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slide 9 University of Hawaii, College of Engineering COCONETS Kavčić – September 2013 – Detectors … Flash Channels with ICI NAND Flash Block Bit line © Bellordo 2013
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slide 10 University of Hawaii, College of Engineering COCONETS Kavčić – September 2013 – Detectors … Flash Channels with ICI NAND Flash Block Word line © Bellordo 2013
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slide 11 University of Hawaii, College of Engineering COCONETS Kavčić – September 2013 – Detectors … Flash Channels with ICI NAND Flash Block Even page © Bellordo 2013
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slide 12 University of Hawaii, College of Engineering COCONETS Kavčić – September 2013 – Detectors … Flash Channels with ICI NAND Flash Block Odd page © Bellordo 2013
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slide 13 University of Hawaii, College of Engineering COCONETS Kavčić – September 2013 – Detectors … Flash Channels with ICI Intercell Interference – capacitive coupling © Bellordo 2013
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slide 14 University of Hawaii, College of Engineering COCONETS Kavčić – September 2013 – Detectors … Flash Channels with ICI Intercell interference – capacitive coupling © Bellordo 2013
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slide 15 University of Hawaii, College of Engineering COCONETS Kavčić – September 2013 – Detectors … Flash Channels with ICI Intercell interference – capacitive coupling © Bellordo 2013
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slide 16 University of Hawaii, College of Engineering COCONETS Kavčić – September 2013 – Detectors … Flash Channels with ICI Chanel model – one dimensional k k+1k+2
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slide 17 University of Hawaii, College of Engineering COCONETS Kavčić – September 2013 – Detectors … Flash Channels with ICI 1) Erase memory k k+1k+2 Voltage E k+1 EkEk E k+2
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slide 18 University of Hawaii, College of Engineering COCONETS Kavčić – September 2013 – Detectors … Flash Channels with ICI 2) Decide what to write (one of 4 levels) k k+1k+2 Voltage EkEk E k+2 Xk=1Xk=1 X k+1 =3 X k+2 =2 E k+1
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slide 19 University of Hawaii, College of Engineering COCONETS Kavčić – September 2013 – Detectors … Flash Channels with ICI 3) Write k-th cell (using incremental -filling) k k+1k+2 Voltage EkEk E k+2 Xk=1Xk=1 X k+1 =3 X k+2 =2 X k +U k +W k unifrom Gaussian E k+1
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slide 20 University of Hawaii, College of Engineering COCONETS Kavčić – September 2013 – Detectors … Flash Channels with ICI 4) Write (k+1)-st cell (incremental -filling) k k+1k+2 Voltage EkEk E k+1 E k+2 Xk=1Xk=1 X k+1 =3 X k+2 =2 X k +U k +W k X k +U k +W k + 1 ( k+1 ) capcitive coupling k+1 coupling coeff.
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slide 21 University of Hawaii, College of Engineering COCONETS Kavčić – September 2013 – Detectors … Flash Channels with ICI 5) Write (k+2)-nd cell (incremental -filling) k k+1k+2 Voltage EkEk E k+1 E k+2 Xk=1Xk=1 X k+1 =3 X k+2 =2 k+2 capacitive coupling capacitive coupling k+1
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slide 22 University of Hawaii, College of Engineering COCONETS Kavčić – September 2013 – Detectors … Flash Channels with ICI So we have an M-level channel model Y k = X k +U k +W k + 1 (Y k+1 – E k+1 )+ 2 (Y k+2 – E k+2 ) unifrom Gaussian channel output channel input (M- levels) Gaussian 1-st neighbor coupling 2-nd neighbor coupling Anti-causal difference equation
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slide 23 University of Hawaii, College of Engineering COCONETS Kavčić – September 2013 – Detectors … Flash Channels with ICI Equivalent causal M-level channel model Y k = X k +U k +W k + 1 (Y k–1 – E k–1 )+ 2 (Y k–2 – E k–2 ) causal difference equation
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slide 24 University of Hawaii, College of Engineering COCONETS Kavčić – September 2013 – Detectors … Flash Channels with ICI Let’s generalize further
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slide 25 University of Hawaii, College of Engineering COCONETS Kavčić – September 2013 – Detectors … Flash Channels with ICI
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slide 26 University of Hawaii, College of Engineering COCONETS Kavčić – September 2013 – Detectors … Flash Channels with ICI
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slide 27 University of Hawaii, College of Engineering COCONETS Kavčić – September 2013 – Detectors … Flash Channels with ICI
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slide 28 University of Hawaii, College of Engineering COCONETS Kavčić – September 2013 – Detectors … Flash Channels with ICI
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slide 29 University of Hawaii, College of Engineering COCONETS Kavčić – September 2013 – Detectors … Flash Channels with ICI
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slide 30 University of Hawaii, College of Engineering COCONETS Kavčić – September 2013 – Detectors … Flash Channels with ICI Insight into suboptimal detectors
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slide 31 University of Hawaii, College of Engineering COCONETS Kavčić – September 2013 – Detectors … Flash Channels with ICI
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slide 32 University of Hawaii, College of Engineering COCONETS Kavčić – September 2013 – Detectors … Flash Channels with ICI
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slide 33 University of Hawaii, College of Engineering COCONETS Kavčić – September 2013 – Detectors … Flash Channels with ICI Branch metric equation
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slide 34 University of Hawaii, College of Engineering COCONETS Kavčić – September 2013 – Detectors … Flash Channels with ICI Sub-MAP detector for iid inputs
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slide 35 University of Hawaii, College of Engineering COCONETS Kavčić – September 2013 – Detectors … Flash Channels with ICI Other detectors – prior art
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slide 36 University of Hawaii, College of Engineering COCONETS Kavčić – September 2013 – Detectors … Flash Channels with ICI Simulation parameters and results
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slide 37 University of Hawaii, College of Engineering COCONETS Kavčić – September 2013 – Detectors … Flash Channels with ICI BER for Varying Coupling Factor s
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slide 38 University of Hawaii, College of Engineering COCONETS Kavčić – September 2013 – Detectors … Flash Channels with ICI BER for Varying SNR
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slide 39 University of Hawaii, College of Engineering COCONETS Kavčić – September 2013 – Detectors … Flash Channels with ICI Soft Information Quality (SIQ) of a Detector X k – channel input symbol S k – soft-output of a detector (vector quantity) Define SIQ as: q = I ( X k ; S k ) | X k is iud SIQ is the capacity of random linear block codes [Kavcic, Ma, Mitzenmacher 2003]
![slide 39 University of Hawaii, College of Engineering COCONETS Kavčić – September 2013 – Detectors … Flash Channels with ICI Soft Information Quality (SIQ) of a Detector X k – channel input symbol S k – soft-output of a detector (vector quantity) Define SIQ as: q = I ( X k ; S k ) | X k is iud SIQ is the capacity of random linear block codes [Kavcic, Ma, Mitzenmacher 2003]](http://images.slideplayer.com./25/7705655/slides/slide_39.jpg "slide 39 University of Hawaii, College of Engineering COCONETS Kavčić – September 2013 – Detectors … Flash Channels with ICI Soft Information Quality (SIQ) of a Detector X k – channel input symbol S k – soft-output of a detector (vector quantity) Define SIQ as: q = I ( X k ; S k ) | X k is iud SIQ is the capacity of random linear block codes [Kavcic, Ma, Mitzenmacher 2003]")
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slide 40 University of Hawaii, College of Engineering COCONETS Kavčić – September 2013 – Detectors … Flash Channels with ICI SIQ for Varying Coupling Factor s
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slide 41 University of Hawaii, College of Engineering COCONETS Kavčić – September 2013 – Detectors … Flash Channels with ICI SIQ for Varying SNR
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slide 42 University of Hawaii, College of Engineering COCONETS Kavčić – September 2013 – Detectors … Flash Channels with ICI Some Open Information-Theoretic Problems Y k = f ( X k–M, Y k–L ) + W k k k–1 Finite Output Memory and State Channel (FOMASC) Not a finite state channel Viterbi/BCJR detector is optimal What is the “indecomposability condition”? Is information rate independent od starting state? Do Markov processes asymptotically achieve capacity?
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