-ИИИИИ"ИИИИИИИИИ 2017.

Transcription

1 -.. -ИИИИИ"ИИИИИИИИИ Ы :,. : ,..,

2 .. " " : «, -.» 2. : ( ): ( ) Э (, ). : ИИИИИИИИИИИИИИИИ. : ИИИИИИИИИИИИИИИИИИ..,.. : ИИИИИИИИИИИИИ

3 45, ,. : (MDS codes),,,.

4 Abstact Pages 45, 3 tables and 5 pictures. The thesis is devoted to Study of efficiency of the Guruswami Wooters method for data recovery in storage systems. A description of the Guruswami Wooters method is presented, its software implementation is described, and simulation results are presented. Key words: Maximum Distance Separating (MDS codes), Guruswamy- Wooters algorithm, encoding, decoding of repairing information.

5 Э , MDS MDS А = F

6 4. Ч З

7 BCH (Bose Chaudhuri Hocquenghem codes), RS MDS (maximum distance separating) ADSL xdsl CD - DVD RAID RAID5 ё 7

8 ( ).,, Д2]. ( ),., n.,. k, F. F. n 1,..., n. (, ). k..., и ющих, 8

9 ,. [1],., [1]..,...,. =.,.. 9

10 1 1.1.,..,..,,.,.,. : 10

11 -, ; - =, ; -.,. - ( ё ) -. =,. (parity check matrix),, =,., : = (1.1) 1.2. К. (Reed Solomon codes) (Irving S. Reed) (Gustave Solomon). 11

12 GF(2) ( ),. ( )., -,,, = =,,., =, =,, - ( ) =,, : = =,.. =, deg <.,., = +.,, ( ). - : - (, CD, DVD, -,..); - (,..); - ; - / DVB (digital video broadcast); 12

13 -, ADSL, xdsl К :. :,,.. =. =. Э : g0 g1 gd 2 gd g0 gd 3 gd 2 gd 1 0 G g0 g1 gd 1,.. k, k. 13

14 ,.,, /. Э,,,, ,.,.,.,,,,. 14

15 ,.. [1] -,.. ( ),,.,,... Э (, SIMD)...1., RAID- 5,. 15

16 RAID -., : ( ),

17 2 Э 2.1.,, ё,. -. : =, = {,.., : е е и е лее }, F, = {,., } а а. С. С,,,,..., С..,,, C. 17

18 ,.,,,.. - -,, F,. (MDS),,.,,, (MDS),,, min { : } = + MDS,,,,,., k f :,.. С,, А. : = { : : = } 18

19 MDS MDS :,,,., ( ),. MDS, f F, F. n,.,,.., Д1],,., = = ( ). : \{ }., = λ 19

20 ,, F В. : { ( ): } \ = b,, = max \{ } (2.2). 3. :.,.,,, 20

21 =. В,,.,, : = max \{ } = log -.,. [1] log, -,,. =,, =.,. 2.3.,,, log = log. Д4] MDS,, F,. 21

22 ., Д4] ( ) MDS. MDS =,, В. Э ё (5, 3) (6, 4) 1, (14, 10) -, ApКМСО HКНШШp, FКМОЛШШФ. Д5, 6, 7, 8, 9, 10] -. -,,,, -,.. ё [4] -.,, [1] Д4]. -, Д4] =,,. 22

23 , MDS, -. -, Д4]. ( ), ;., Ч. Д4],,. 1, RS MDS ё MDS ( - )...,, -, ( ) 23

24 ., -, -.., ( ), ё.,,,. Д1]. - =, = log. -.,. :., : = + (2.4) Д11, 12],. [13], (, ), (2.4).., Д14],,, (2.4) ; = 24

25 , exp [15]., (2.4) /, [16, 17]. :.,,, (2.4)., + MDS., <, = +.. = + ё, = Х MDS MDS., MDS, { : } =. 1:, ; - ; - 25

26 MDS. : -, -, { : } = { : } max \{ } : 1 [1],, MDS.,, 1. Д1], 4.,,,,. 4,,, -., F. 26

27

28 3 А = F А =,. 3.1 С { : }, { : } =. 28 [1], (1.1),, max \{ } : (3.1) Д1],, =,, ( )

29 = { ( ) } F B. =. = { : } = = 1: α = =, =. Э 2., α =, =, -,. В. = {, } = {, } - F : i = 1 : i = 2 : = ( ) = + = = = {,,, },, ( ) ( ) ( ) G 0 k 1 k 14 k ( ) ( ) ( ) 29

30 . = [,,, ] -. = = [,,, ] * [ ] {, }: = {,,,,,,,,,,,,,, } = {,,,,,,,,,,,,,, },,,. 2. (16, 8) = = (2).,. = 8, log =., Д1], =,, log =.,.,.. \{ },,, 30

31 =, \{ }. : =, \{ },,,,.,.,,,,,.,. [1]. 1: - =. - RS,, B,. 2:. =. RS, log. Э MDS ; +, 1. 31

32 MDS. B -. ( ) log, ( ) MDS log log \{ } : :., = \{ } \{ } 32 {, : } : -. : = {,,, }, :, = ( ) = {,

33 - {, : }, = : * q11 q 1, ( ) t1 v1 * q1 t q tt v t, ( ) t 3.. = {,,, },., Z , = ( ) = { =.,,, :

34 , = \{ } \{ } А,, : = {,,,,,,,,,,,,,, } = {,,,,,,,,,,,,,, } { ( ): }. = {,,, } - В, = {,,, }. = = 3.2 -,, CRSExtendedProcessor. 34

35 . 2. RAID,.,,. 1,. 1.,. Attach CheckCodeWord EncodeStrip IsCorrectable DecodeDataSymbols UpdateInformation 35

36 -, Attach.,,..,. ResetErasures.. FieldValue. FТОХНCШЧstruМtШr :,,,,.. «RSGenerator».,, «rs_misc.h». -,,.,,. ErasureID ( ). IsCorrectable,.,, :,... 36

37 ,,. RAID.. EncodeStripe -,.. RAID,..,.,,,..,.,,.,. 37

38 . DecodeDataSymbols. CheckCodeword,,.,,. UpdateInformationSymbols,.., ( ),,., -. 38

39 4 Ч 3., 16,. ё, ( ).. 5. ё,, ё.,, {,..., }., = 8, 2, = %, -. =,., = 30%. 39

40 Data read redundancy, times (16, K) RS B = GF(2) (16, K) RS B = GF(4) 16, К RS Code Dimension, K ( / ) 0 2,68435e e e e e e e e ,, 0,. 40

41 1 1 1 ; ; ,,.,,.,,., -,,,,! Э, RS.,, = ; 41

42 З -, -. - (.., ) 25%.,. 700,,, 87,5 700.,.,,,, (, ),,,,. RAID, RAID,. 42

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