[PPT] - Capacity and Beyond Erozan M. Kurtas Acknowledgement M. Fatih PowerPoint Presentation

SLIDE 1

Capacity and Beyond

Erozan M. Kurtas

SLIDE 2

March/15/2004 Erozan Kurtas

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Acknowledgement

M. Fatih Erden

Sami Iren Dieter Arnold Raman Venkataramani Inci Ozgunes

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Conventional system

M H

r

M

c

H

c r

H S M Slope ) 1 ( − =

] [ ] [ ] [ 1 ] / [

2

inch w inch a bit inch bits ty ArealDensi =

Store bit by

Applying external H > Hc (magnetize up)
Applying external H < -Hc (magnetize down)

O

w a

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In reality there are tiny grains

Tiny grains with finite volume V and anisotropy coefficient Ku Minimum grain number fixed to preserve SNR

M T k V K

B u

≥

Boltzmann Constant Temperature Large number, like 60

Super paramagnetic limit : Maximum value limited by maximum writer field

Maximum Attainable Areal Density is Limited

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Dibit Responses Compared

10
8
6
4
2

2 4 6 8 10

0.8
0.6
0.4
0.2

0.2 0.4 0.6 0.8 Dibit response (Longitudinal model) t/T Amplitude ND=1.5 ND=2 ND=2.5 ND=3

5
4
3
2
1

1 2 3 4 5 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Dibit responses (Perpendicular model) t/T Amplitude ND=1.5 ND=2 ND=2.5 ND=3

Perpendicular model Longitudinal model

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Frequency Responses of Dibit responses

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.2 0.4 0.6 0.8 1 Frequency responses for a Longitudinal model Normalized frequency Normalized amplitude ND=1.5 ND=2 ND=2.5 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.2 0.4 0.6 0.8 1 Frequency responses of a Perpendicular model Normalized frequency Normalized amplitude ND=1.5 ND=2 ND=2.5

Longitudinal model Perpendicular model

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Reality is Quite Different

Signal suffers from nonlinearities

NLTS MR Asymmetry Base Line Wanders TAs Other distortions

Noise is Non-Gaussian Noise is Signal Dependent

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Noise Free Real Signals with Nonlinearities

9851 PRBS ND=2.1

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Extracted Dibit Response

extracted dibit

provides

information about systems linear response.

is a convenient

means for identifying nonlinearities present in system that show up as echoes around the main pulse.

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Volterra Model of a Readback Signal

VM can be characterized by 2L-1 kernels, For magnetic recording, only a few of the kernels are significant.

A rule of thumb: L ~ the extent of the dipulse (in units of bit interval, T)

L l t C l L , 2 ), (

) (

=

( ) ( ) ( ) ( ) ( )

L L + − + − + + − + − + − =

∑ ∑ ∑ ∑ ∑

− − − − − −

) ( ) ( ) ( ) ( ) ( ) (

3 3 , 1 3 1 3 2 , 1 2 1 2 2 2 2 1 1 1

kT t C a a a kT t C a a a kT t C a a kT t C a a kT t C a t y

k k k k k k k k k k k k k k k k

Second Order Kernels Third Order Kernels

Memory Length

Third Order Non- linear Response

First Order Kernel

Linear Response Second Order Non- linear Response

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VM Kernels can be conveniently identified from measured PRBS signals

50 100 150 200 250 300

0.04
0.02

0.02 0.04 0.06 0.08 0.1

Sample Number Amplitude (Volts)

15-Apr-2003 Research Channels

a-4 a-3 a-2 a-1 a0 a1 a2 a3 a4

1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1

1

3 1 1 1 1 1 1 1

1

1 4 1 1 1 1 1 1

1

1

1

5 1 1 1 1 1

1

1

1

1 6 1 1 1 1

1

1

1

1

1

7 1 1 1

1

1

1

1

1
1

506

1

1 1

1

1

1

1 1 1 507 1 1

1

1

1

1 1 1 1 508 1

1

1

1

1 1 1 1 1 509

1

1

1

1 1 1 1 1 1 510 1

1

1 1 1 1 1 1 1 511

1

1 1 1 1 1 1 1 1 512

1
1
1
1
1
1
1
1
1

All Patterns of Length L=9

M M M M

Signal Chips No signal chip

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Identification of Kernels

Distorted (1) There are only three kernels above the threshold We declare them as significant and include in the Reduced Complexity Volterra Model.

10 20 30 40 50 1 2 3 4 5 6 7 x 10

3

Amplitude (Volts) Sample Number C(2)

1

C(2)

2

C(2)

3

C(3)

1,2

C(3)

1,3

C(3)

2,3

15-Apr-2003 Research Channels THRESHOLD

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Volterra Model Block Diagram

C(1)(t)

+

Linear Part NonLinear Distortion ak={-1,1}

ynl(t)

y(1)(t)

y(t)

) (

) 2 ( 1

t C ) (

) 3 ( 2 , 1

t C ) (

) 2 ( 2

t C

+ ak T T

X X X

ak-1 ak-2 + y(2)(t) y(3)(t) y(0)(t)

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How Good is VM?

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Longitudinal Media Noise and Signal

50 100 150 200 250 300 350 400

0.25
0.2
0.15
0.1
0.05

0.05 0.1 0.15 0.2 0.25

Sample Number (1Gsample/Sec) Volts (V) Synchronous Noise Samples and Noise Free Signal

29-Oct-2002

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Longitudinal: Media Noise Voltage

0.1

0.1 500 1000 1500 2000 2500

Noise Voltage Occurances Synchronous Noise Voltage

0.05

0.05 0.001 0.003 0.01 0.02 0.05 0.10 0.25 0.50 0.75 0.90 0.95 0.98 0.99 0.997 0.999

Noise Voltage

Probability

Normal Probability Plot

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Data Dependent AR Model (AR)

Noise Filter

Filter Lookup Signal Lookup

+

∑

D

L

zk wk

D

nk

L

nk-1 nk-L nk-L+1 ak y(α)

α β

σ(β) bL(β) b1(β)

{ {

N(0,1)~

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Perpendicular Signal and Media Noise

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Media Noise 400 MHz

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As ND Increases Noise Variance vs. Pattern

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AR noise generation

not a great fit

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Perpendicular: Media Noise Voltage

0.04 -0.02

0.02 0.001 0.003 0.01 0.02 0.05 0.10 0.25 0.50 0.75 0.90 0.95 0.98 0.99 0.997 0.999

Noise Voltage (V) Probability Normal Probability Plot

0.05

0.05 1000 2000 3000 4000 5000 6000

Noise Voltage (V) Occurances Synchronous Noise Voltage

Noise

distribution does not fit Gaussian!

Noise

distribution looks more like a laplacian.

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Generic Storage Channel

bits

adds redundancy to make signal robust

encoder modulator write head medium read head

demodulator & equalizer

decoder

uses redundancy to recover the data

bits bits

n k R = k n

Channel capacity

T 1

SNR PW50

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Brief Survey of the Literature

) 2 / N , ( ~ N Zk

– Bounds

Shamai at al. 1991, McLaughlin and Neuhoff 1993, and many others

– Direct Computation

Hirt 1988

– Markov-Chain Monte-Carlo Method

Arnold and Loeliger, Pfister et al., Sharma and Singh, Vontobel, all in 2001

– Shamai-Laroia conjecture

Shamai-Laroia 1996, Dholakia et al. 2000, Arnold and Eleftheriou 2002

FIR

k

Y

{ }

1 , 1 + − ∈

k

X

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Brief Survey of the Literature (cont.)

Kavcic 2001: Zhang, Duman, and Kurtas 2002: Modeling signal- dependent noise

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Set-up for Mismatch Lower Bounds

k

Y

) | ( ⋅ ⋅ W

[ ]

) )( log( Y QM EQW

[ ]

) | ( log X Y M EQW − ≡ ) , ( M Q I

) (⋅ Q ) | ( ⋅ ⋅ M

k

X

Mismatch lower bound:

) , ( ) , ( M Q I W Q I ≥

A. Ganti, A. Lapidoth, and I. E. Telatar, “Mismatched Decoding Revisited: General Alphabets, Channels with Memory, and

the Wide-Band Limit, “ IEEE Trans. on Inform. Theory, pp. 2315-2328, Nov. 2000.

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How to model the noise?

0.04 -0.02

0.02 0.001 0.003 0.01 0.02 0.05 0.10 0.25 0.50 0.75 0.90 0.95 0.98 0.99 0.997 0.999

Noise Voltage (V) Probability Normal Probability Plot

0.05

0.05 1000 2000 3000 4000 5000 6000

Noise Voltage (V) Occurances Synchronous Noise Voltage

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Just use histograms

) | ( ⋅ ⋅ W ) | ( ⋅ ⋅ M

k

X ) (⋅ Q

k

Y

k

Z

) , ( ) 1 , (

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Validation on the ideal (1-D)-Channel

k

N

k

Y

k

V (1-D) channel AWGN L=1 b=1,3,5

k

X 1-D

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(1-D)-Channel – Histograms

(dotted for low SNR, solid for high)

Low SNR High SNR

L=1 b=3 +1

1

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Model the channel as a GPR or FSM

1. Capturing the influence of the neighbor bits by means of a state

Dc=2.0 ) ,..., , ,..., , (

1 ) 1 ( m k k k m k m k k

x x x x x s

+ + − − −

≡

2. Sorting over time by means of a trellis of size |

L m

2 2 | S

1 2

= =

+ 1 + k

x

k

S

1 + k

S

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Use Quantized Histograms per Branch for Noise

3. Representation of the noise pdfs per branch:

k

z

4 + k

z

5 + k

z

1 + k

z

2 + k

z

3 + k

z

1 − k

z

6 + k

z ... ... Pr

Amplitude

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Big Picture

modulator write head medium read head demodulator & equalizer

bits

n

x1

n

y1

n n

z y

1 Q(b) 1 a

1. Measurement step

bits encoder bits decoder

2. Quantization step
3. Computation step

) )( ( ) | ( log 1

1 1 1 LB n n n

Z QM X Z M n I C ← ≥

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How complex is it?

Memory # of multiplications per branch n ⋅ 2 2 b # of comparisons per trellis section Example: 6 , 32 | S | , 106 = = = b n

On a P4, 2.5 GHz, 512 MB

< 20 s

Orders of magnitude faster than performance evaluation of Turbo-Codes.

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Results with Real Waveforms

Waveform: perpendicular n=44276 Model: L=4, b=6

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Compare with Turbo Codes

Dc=2.4 [k=256,n=289] . = σ Dc=2.0 [k=4096,n=4624] 05 . = σ

SLIDE 37

Heat Assisted Magnetic Recording

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Conventional system

M H

r

M

c

H

c r

H S M Slope ) 1 ( − =

] [ ] [ ] [ 1 ] / [

2

inch w inch a bit inch bits ty ArealDensi =

Store bit by

Applying external H > Hc (magnetize up)
Applying external H < -Hc (magnetize down)

O

w a

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In reality there are tiny grains

Tiny grains with finite volume V and anisotropy coefficient Ku Minimum grain number fixed to preserve SNR

M T k V K

B u

≥

Boltzmann Constant Temperature Large number, like 60

Super paramagnetic limit : Maximum value limited by maximum writer field

Maximum Attainable Areal Density is Limited A solution : HAMR

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Heat Assisted Magnetic Recording

CENTRAL CONCEPT: CENTRAL CONCEPT: Use interplay of Use interplay of temperature and field gradients to perform temperature and field gradients to perform high density high density thermomagnetic thermomagnetic recording on recording on very very high high coercivity coercivity (thermally stable) media. (thermally stable) media.

x y z

Medium P

l

e H e a d v

Light Spot Isotherms

Hpole(x,y,z) T(x,y,z,t) Ring Head Hring(x,y,z)

Image courtesy of T. McDaniel, Seagate Technology

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Idea behind HAMR

M

r

M

c

H

c

H

r

M

After heating Enables writability

H

Before heating Enables thermal stability

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An illustrative example

6
4
2

2 4 6 x 10

7

300 400 500 600 700

6
4
2

2 4 6 x 10

7

0.5 1 1.5 2 2.5 x 10

5

6
4
2

2 4 6 x 10

7

0.5 1 1.5 2 2.5 x 10

5

D own-Track Position Temperature in C Hc Magnitude Mr Magnitude

(a) (b) (c)

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Why should we have any issue?

Assume speed to be 25m/s 25 nm equivalent to 1ns

Increase the heat of the medium by 300K – 400K
Write the bit of information
Cool the medium

!!! Complete everything in 1ns !!!

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Major issues in HAMR

Magnetic issues
Availability of desirable Ku(T) for particles
Controllability of the spatial orientation of Ku(T)

to minimize the temperature difference

Thermal issues
Lubricant and overcoat stability
Air bearing flying stability
Media-Head air bearing surface smoothness
Optical issues -- Confining light in a very small spot. Some methods
Solid Immersion Lenses (SIL)
Apertures
Antennas
Waveguides

Each have their own advantages and disadvantages (*)

(*) Challener et al,

Jpn. J. Appl. Phys. 42, (2003 ) 981

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Solid Immersion Lenses (SIL)

Theoretical spot size

*Q. Wu et al., Appl. Phys.

Lett. 75 (1999) 4064.

n d λ ⋅ ≥ 51 .

FWHM diameter:

Image courtesy of T. McDaniel, Seagate Technology

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Circular Aperture in Ideal Conductor

4 2

27 64       ⋅         = λ π d T

wave plane hole

area power incident area power d transmitte       ≡

Hans Bethe,

Phys. Rev.

(1944) 163.

0.6%

1 µm 50 nm

5

10 5 . 1 A A

−

× = ⋅

spot hole

T

Image courtesy of T. McDaniel, Seagate Technology

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How can we get a useful channel model?

) (

a loop H

F M =

d h a

H H H + =

              − −         + =

− −

y g x y g x H H x 2 / tan 2 / tan

1 1

π

) ( * x H x M H

step x d

∂ ∂ =

2 2 2 2

) 2 / ( ) 2 / ( ln 2 y g x y g x H H y + − + + − = π

Function of M

Karlqvist Head Field Approximation

Very difficult to solve loop equation

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Approximation – Thermal Williams Comstock Model

Williams Comstock equation

      ∂ ∂ + ∂ ∂ ∂ ∂ = ∂ ∂ x H x H H M x M

d h

Temperature profile

Thermal Williams Comstock equation

      ∂ ∂ ∂ ∂ + − ∂ ∂ + ∂ ∂ ∂ ∂ = ∂ ∂ x T T H H H H x H x H H M x M

c c d h d h

Temperature dependent

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Using the equations

Find transition location x_0 which satisfies

) ( ) ( ) ( x H x H x H

c d h

= +

Find a-parameter as a function of x_0

..) ,...,...,. ( x Function a =

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Isolated transition response

Readback voltage from isolated transition

        + − − + + =

− −

d x a g x d x a g x x CM x V

r GMR

) ( 2 / tan ) ( 2 / tan ) ( ) (

1 1 0 δ

Temperature dependent Requires iterations to find a_parameter and x_0 for given temperature profile

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Temperature profile as a function of position

Down track position Temperature in C

6
4
2

2 4 6 x 10

7

300 350 400 450 500 550 600 650 700

Peak Temp = 700 Temp sigma = 150 nm

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Longitudinal Component of Karlqvist Head Field as a function of position

6
4
2

2 4 6 x 10

7

1 2 3 4 5 6 7 x 10

5

Magnitude

              − −         + =

− −

y g x y g x H H x 2 / tan 2 / tan

1 1

π

Ho = 800000 A/m g = 300nm y = 50 nm Down track position

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Normalized isolated transition response as a function of position

1
0.5

0.5 1 x 10

6

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Down track position Magnitude

a_parameter = 22.8nm x_0 = -200nm

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Another Head Field as a function of position

Magnitude

              − −         + =

− −

y g x y g x H H x 2 / tan 2 / tan

1 1

π

6
4
2

2 4 6 x 10

7

2 4 6 8 10 12 14 16 18 x 10

4

Ho = 500000 A/m g = 50 nm y = 40 nm Down track position

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Normalized isolated transition response as a function of position

6
4
2

2 4 6 x 10

7

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Magnitude

A_parameter = 20.6nm X_0 = -63nm

Down track position

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System should be considered as a whole

Joint optimization of
Tribological system
Medium magnetics
Near field optical system

Necessary to solve the issues

Success in optimization will determine the attainable areal density

SLIDE 57

Object Based Storage Devices

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Storage Architectures Today

Pros: Simple, Physically secure
Cons: Not scalable, no data

sharing, limited capacity sharing

Pros: Secure data and

capacity sharing

Cons: Limited scalability
Pros: Scalable capacity

sharing

Cons: No data sharing

Goal: Scalability, Security, Data Sharing

Storage Area Network (SAN) Network Attached Storage (NAS) Direct Attached Storage (DAS)

I/O Application I/O Application Network Storage System I/O Application Network Storage System Storage System Storage Device Storage Device Storage Device (Blocks) (Blocks) (Files)

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Today’s File Server

NAS Clients NAS Clients

Block Block-

Based Storage

Based Storage

SAN NAS

Block I/O

Performance Bottleneck (Not scalable!) NAS Servers NAS Servers

Clients need direct access to storage to remove bottleneck

File I/O

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Block-Based Storage

MANAGEMENT

Eth switch

Trusted SAN

DATA

METADATA

Security is poor
High virtualization
verhead

Scalable, but poor security!

2nd Generation File Server

SAN/FS Clients

SAN/FS Servers

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The Problem – expand endpoint function

Endpoints (users at top, disks at bottom)

not very sophisticated today
disks don’t understand users/apps
users/apps don’t understand disks
need many intermediaries to translate

Intermediary functions

some add value (e.g. data sharing)
others simply cover limitations

(e.g. reliability via RAID)

today – many layers of hardware and software between users and disks

users disks

understand what is really going on, disambiguate functions

users disks

move appropriate functions to the endpoints

disks users

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OSD Interface

File System User Component File System Storage Component

Applications

System Call Interface

Storage Device

Block I/O Manager

Storage Device

Block I/O Manager File System Storage Component

CPU

Applications

File System User Component System Call Interface

CPU

OSD Interface Sector/LBA Interface

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OSD Functions

Basic Protocol

READ
WRITE
CREATE
REMOVE
GET ATTR
SET ATTR

Specialized

APPEND – write w/o offset
CREATE & WRITE – save msg
FLUSH OBJ – force to media
LIST – recovery of objects

Security

Authorization – on each request
Integrity – for args & data
SET KEY
SET MASTER KEY

Groups

CREATE COLLECTION
REMOVE COLLECTION
LIST COLLECTION

Management

FORMAT OSD
CREATE PARTITION
REMOVE PARTITION

Very Basic shared secrets Space Mgmt Attributes

timestamps
vendor-specific
shared, opaque

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File Server with OSD

Clients Access Request

Object-Based Storage Device

MANAGEMENT

Eth switch

SAN

SECRET SECRET KEY KEY SECRET SECRET KEY KEY SECRET SECRET KEY KEY

D A T A

Check permissions Check permissions Check permissions Validate Capability Validate Capability Validate Capability

Problem solved!

Servers

Space Management Backup/Recovery QoS via attributes Security etc. Intelligent Device

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Quality of Service on the Disk

What Applications want What disks can do

OSD Traditional

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Example OSD Drive Uses

–Enterprise

Data sharing
Scalability
Security
Improved reliability
Self-managed, self-configured

drives

– Desktops/Notebooks

Automatic de-fragmentation
Object semantics
Free space management
QoS

–Consumer Electronics

Video streams
Video can tolerate occasional bit

loss

Drive takes advantage of this to

improve performance (e.g., skipping ECC on a read)

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Summary

–OSD enables scalable and secure data sharing

Highly desirable in the enterprise market

–Pushes intelligence down to disks

Self-aware, self-managed, self-configured drives
Better communication between applications and drives

(QoS)

Increased system performance
Disk level computations (searches, etc.)