TOMMUNO DI UNA | MARATHI MINUTI
`
`US010003553B2
`
`( 12 ) United States Patent
`Konda
`
`( 10 ) Patent No . : US 10 , 003 , 553 B2
`( 45 ) Date of Patent :
`* Jun . 19 , 2018
`
`( * ) Notice :
`
`( 51 )
`
`( 52 )
`
`( 54 ) OPTIMIZATION OF MULTI - STAGE
`HIERARCHICAL NETWORKS FOR
`PRACTICAL ROUTING APPLICATIONS
`( 71 ) Applicant : Venkat Konda , San Jose , CA ( US )
`( 72 ) Inventor : Venkat Konda , San Jose , CA ( US )
`( 73 ) Assignee : Konda Technologies Inc . , San Jose ,
`CA ( US )
`Subject to any disclaimer , the term of this
`patent is extended or adjusted under 35
`U . S . C . 154 ( b ) by 107 days .
`This patent is subject to a terminal dis
`claimer .
`( 21 ) Appl . No . : 15 / 140 , 470
`( 22 ) Filed :
`Apr . 28 , 2016
`Prior Publication Data
`( 65 )
`US 2016 / 0261525 A1 Sep . 8 , 2016
`Int . Cl .
`H04L 12 / 933
`( 2013 . 01 )
`H04L 29 / 06
`( 2006 . 01 )
`U . S . CI .
`CPC . . . . H04L 49 / 1515 ( 2013 . 01 ) ; H04L 29 / 06081
`( 2013 . 01 ) ; H04L 49 / 109 ( 2013 . 01 ) ; H04L
`65 / 4076 ( 2013 . 01 )
`( 58 ) Field of Classification Search
`CPC . . . . . . . . . . . HO4L 49 / 1515 ; H04L 65 / 4076 ; HO4L
`29 / 06081
`See application file for complete search history .
`References Cited
`U . S . PATENT DOCUMENTS
`5 , 153 , 843 A
`10 / 1992 Batcher
`5 , 345 , 444 A
`9 / 1994 Cloonan . . . . . . . . . . . . . H04L 12 / 5601
`370 / 381
`
`5 , 451 , 936 A
`5 , 541 , 914 A *
`5 , 654 , 695 A *
`6 , 018 , 523 A
`*
`6 , 091 , 723 A
`6 , 185 , 220 B1
`
`9 / 1995 Yang et al .
`7 / 1996 Krishnamoorthy . . . HO4L 49 / 254
`370 / 427
`8 / 1997 Olnowich . . . . . . . . . . . G06F 13 / 4022
`340 / 2 . 23
`1 / 2000 Even
`7 / 2000 Even . . . . . . . . . . . . . . . . . . . H04L 49 / 1507
`340 / 2 . 21
`2 / 2001 Muthukrishnan et al .
`( Continued )
`OTHER PUBLICATIONS
`Ronald I . Greenberg , “ The Fat - Pyramid and Universal Parallel
`Computation Independent of wire delay ” IEEE Trans . Computers ,
`43 ( 12 ) : 1358 - 1364 , Dec . 1994 .
`( Continued )
`
`Primary Examiner — Rasheed Gidado
`
`( 57 )
`ABSTRACT
`Significantly optimized multi - stage networks , useful in wide
`target applications , with VLSI layouts using only horizontal
`and vertical links to route large scale sub - integrated circuit
`blocks having inlet and outlet links , and laid out in an
`integrated circuit device in a two - dimensional grid arrange
`ment of blocks are presented . The optimized multi - stage
`networks in each block employ several rings of stages of
`switches with inlet and outlet links of sub - integrated circuit
`blocks connecting to rings from either left - hand side only , or
`from right - hand side only , or from both left - hand side and
`right - hand side ; and employ shuffle exchange links where
`outlet links of cross links from switches in a stage of a ring
`in one sub - integrated circuit block are connected to either
`inlet links of switches in the another stage of a ring in the
`same or another sub - integrated circuit block .
`
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`Page 1 of 47
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`FLEX LOGIX EXHIBIT 1001
`
`

`

`US 10 , 003 , 553 B2
`Page 2
`
`( 56 )
`
`References Cited
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`326 / 38
`6 , 940 , 308 B2
`9 / 2005 Wong
`GO6T 7 / 20
`7 , 440 , 449 B2 *
`10 / 2008 Carson
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`
`5 / 2012 Konda
`8 , 170 , 040 B2
`9 / 2012 Konda
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`9 / 2012 Konda
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`1 / 2013 Konda
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`11 / 2014 Konda
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`6 / 2016 Konda
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`. . . . . . . . . . . .
`370 / 216
`2011 / 0037498 A1 *
`2 / 2011 Konda . . . . . . . . . . . . . . . . G06F 17 / 5077
`326 / 41
`2012 / 0269190 A1 *
`10 / 2012 Konda . . . . . . . . . . . . . . . G06F 17 / 5054
`370 / 388
`
`OTHER PUBLICATIONS
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`R . Goodman and Carlo H Sequin , Computer Science Technical
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`Chang , Generic universal switch blocks . IEEE Transactions on
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`a
`Reconfigurable Computing Array ( or , why you don ' t really want
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`for interconnection networks . In : Proc . Intl . Conf . on Parallel
`Processing , 2000 .
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`graph layout problems . J . Comput . Syst . Sci . 28 , 300 - 343 .
`* cited by examiner
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`U . S . Patent
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`Jun . 19 , 2018
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`Sheet 1 of 19
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`US 10 , 003 , 553 B2
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`Page 3 of 47
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`Jun . 19 , 2018
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`Sheet 2 of 19
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`US 10 , 003 , 553 B2
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`B ( 2 , 2n + 2 )
`
`100B
`
`
`
` Fo ( 1 . 2m - 1 )
`
`+ 2 )
`
`
`
` Bo ( 1 , 2m
`
`- 1 )
`
`
`
` Ui ( 1 , 2m
`
`
`
` Wi ( 1 , 2m )
`
`
`
` - Fo ( 1 , 2m )
`
`
`
`
`
` R ( 2 , 2n + 2 )
`
`
`
` Ri ( 2 , 2n + 1 )
`
`
`
`
`
` Ri ( 2 , 2n + 2 )
`
`Ring 1 , Stage " m - 1 "
`
`- 1 ) /
`
`F ( 1 . 2m
`
`Ring 1 , Stage mut
`
`)
`
`F ( 1 , 2m
`
`( 1 . 2m - 1 AU ( 1 . 2m )
`U ( 1 , 2m )
`
`Uo ( 1 , 2m )
`
`Vo ( 1 , 2m - 1 )
`
`
`
` F0 ( 2 , 2n - 1 )
`
`
`
`Fi ( 1 , 2m - 1 )
`
`Fi ( 1 , 2m )
`
`Bo ( 1 , 2m - 1 )
`
`B ( 1 , 2m - 1
`
`B ( 1 , 2m )
`
`Ring 2 , Stage “ n - 1 " )
`
`
`
` F ( 2 , 2n - 1 ) ,
`
`
`
` F ( 2 . 2n )
`
`U ( 2 , 2n - 1 ) ,
`
`U0 ( 2 , 2n )
`
`
`
`( uz?zin
`
`Bo ( 1 , 2m )
`
`Ro ( 2 , 2n - 1 )
`
`1 - 7 )
`
`Ro ( 2 , 2n )
`
`Uo ( 2 , 2n - 1
`
`B ( 2 , 2n - 1 )
`
`B ( 2 , 2n )
`
` B0 ( 2 , 2n + 1 )
`
`
`
`
` Ui ( 2 , 2n - 1 )
`
`
`
` Bo ( 2 , 2n + 2 ) T
`
` Ui ( 2 , 2n )
`
`
`
` - Fo ( 2 , 2n )
`
`
`
`
`
`
`
`-
`
`
`
` Fo ( 1 , 3 )
`
`.
`
`
`
` Fo ( 1 . 4 )
`
`Ui ( 1 , 3 )
`
`Vi ( 1 , 4 )
`
`Ri ( 2 , 2n - 1 )
`
`
`
` RI ( 2 , 2n )
`
`K
`
`110
`FIG . 1B
`_ _ 110
`
`- -
`
`-
`
`
`
`- 1 ) B0 ( 2 , 2n
`
`
`
`
`
`
`
` ( 2 , 2n )
`
`R
`
`- - - -
`
`-
`
`120 120
`
`-
`
`T
`
`
`
` - B0 ( 2 , 2n )
`
`
`
`F ( 1 , 3 )
`Ring 1 . Stage 1
`Ring 1 , Stage 1
`
`Ro ( 1 , 3 )
`
`F ( 1 . 4 )
`
`U ( 1 , 3 )
`
`U ( 1 , 4 )
`
`Vo ( 1 , 4 )
`
`Uo ( 1 , 3 )
`
`
`
` FO ( 2 , 3 )
`
`
`
` Fo ( 2 , 4 )
`
`Wi ( 2 , 3 )
`
`
`
` Ui ( 2 , 4 )
`
`Ro ( 1 , 4 )
`
`R ( 1 . 3 )
`
`( 1 , 4 )
`
`R
`
`B ( 1 , 3 )
`
`B ( 1 , 4 )
`
`Ring 2 , Stage 1
`
`Ri ( 1 , 3 )
`
`Ri ( 1 , 4 )
`
`a
`
` Bo ( 1 , 3 )
`
`F ( 2 , 3 )
`
`F ( 2 , 4 )
`
`( 2 , 3 )
`
`( 2 , 4 )
`
`Vo ( 2 , 4 )
`
`U0 ( 2 , 3 )
`
`B0 ( 2 , 3 )
`
`
`
`Bo ( 1 . 4 )
`
`
`
` Fo ( 1 , 2 )
`
`
`
` - Ui ( 1 , 1 )
`
`Ui ( 1 , 2 )
`
`
`
` - Fo ( 1 , 1 )
`
`
`
`F ( 1 , 1 )
`
`F ( 1 , 2 )
`
`( 1 , 1 )
`
`Vo ( 1 , 2 ) U ( 1 , 2 )
`
`Ring 1 , Stage 1 )
`
`Ro ( 1 , 1 )
`
`Uo ( 1 , 1 )
`
`Ro ( 1 , 2 )
`
`R ( 1 . 1 )
`
`( 1 , 2 )
`
`R
`
`B ( 1 , 1 )
`
`B ( 1 , 2 )
`
`Ri ( 1 , 1 )
`
`
`
` Ivi Ri ( 1 , 2 )
`
`
`
` Bo ( 1 , 1 )
`
`N
`
`
`
` Bo ( 1 , 2 )
`
`-
`
`Fi ( 2 , 3 )
`
`Fi ( 2 , 4 )
`
`B ( 2 , 3 )
`
`B ( 2 , 4 )
`
`Fo ( 2 , 1 )
`
`It
`
`
`
` - Fo ( 22 )
`
`Ui ( 2 , 1 }
`
`.
`
`J
`
`B0 ( 2 , 4 )
`li
`li ( 2 , 2 )
`
`F ( 2 , 1 )
`
`F ( 2 , 2 )
`
`U ( 2 . 1 )
`
`U ( 2 , 2 )
`
`Vo ( 2 , 2 )
`
`UO ( 2 , 1 )
`
`Ring 2 , Stage
`
`Fi ( 2 , 1 )
`
`Fi ( 2 , 2 )
`
`B0 ( 2 , 1 )
`
`B ( 2 , 1 )
`
`B ( 2 , 2 )
`
`-
`B0 ( 2 , 2 )
`
`-
`
`-
`
`Computational
`Block
`
`Ñ
`T12
`
`Page 4 of 47
`
`

`

`U . S . Patent
`
`Jun . 19 , 2018
`
`Sheet 3 of 19
`
`US 10 , 003 , 553 B2
`
`FIG . 2A
`
`FIG . 2A
`
`( k 2m + 1 ) /
`
`F ( K , 2m + 2 ) /
`
`Uo ( k , 2m + 1 )
`
`B ( k , 2m + 1 ) /
`
`U ( k , 2m + 1 )
`
`Fi { k . 2m + 1 )
`
`Fi ( k . 2m + 2 )
`
`Bo ( k . 2m + 1 )
`
`200A
`
`2002
`
`Foík , 2m + 1 )
`
`Ri ( k , 2m + 1 )
`
`Fo ( k , 2m + 2 )
`
`Ri ( k , 2m + 2 )
`
`Hi R ( k , 2m + 1 )
`
`Ui ( k , 2m + 1 )
`
`Bork , 2m + 1 )
`
`Uo ( k , 2m + 1 )
`
`B ( k , 2m + 1 )
`
`U ( k , 2m + 1 )
`
`FIG . 2B
`
`FIG . 2B
`
`Rock , 2m + 1 )
`
`F ( k , 2m + 1 ) /
`
`F ( k . 2m + 2 ) /
`
`Ro?k , 2m +
`
`R ( k , 2m + 2 )
`
`200B
`
`2008
`
`Fo { k , 2m + 1 )
`
`folk . 2013
`
`Fo { k , 2m + 2 )
`
`Ui?k , 2m + 1 )
`
`Bo ( k 2m + 2 )
`
`( k , 2m + 2
`
`Vi?k , 2m + 2 )
`
`Bo { k . 2m + 2 )
`
`Uok . 2m + 2
`
`Ui { k , 2m + 2 )
`
`B ( k , 2m + 2 ) /
`
`U ( k , 2m + 2 ) /
`
`B ( k , 2m + 2 )
`
`U ( k , 2m + 2 ) /
`
`FIG . 2D
`
`2000
`200D
`
`Fi ( k . 2m + 1 )
`
`Fi ( k . 2m + 2 )
`
`Fo { k , 2m + 1 )
`
`Fo { k , 2m + 2 )
`
`F ( k , 2m + 1 ) /
`
`F ( k , 2m + 2 ) /
`
`FIG . 2C
`
`2000
`
`Fo { k . 2m + 1 )
`
`F ( k , 2m + 1 )
`
`F ( k , 2m + 2 ) /
`
`B ( k , 2m + 1 )
`
`B ( k . 2m + 2 )
`
`Fo { k . 2m + 2 )
`
`Bi ( k . 2m + 1 )
`
`Bi ( k , 2m + 2 )
`
`Fi { k , 2m + 1 )
`
`Fi?k , 2m + 2 )
`
`Bo { k . 2m + 1 )
`
`Bo { k . 2m + 2 )
`
`.
`
`Page 5 of 47
`
`

`

`U . S . Patent
`
`Jun . 19 , 2018
`
`Sheet 4 of 19
`
`US 10 , 003 , 553 B2
`
`FIG . 2E
`
`200E
`
`Ri?k , 2m + 1 )
`
`Ri ( k , 2m + 2 )
`
`Boík , 2m + 1 )
`
`Bo?k , 2m + 2 )
`
`Ro ( k , 2m + 1 )
`
`( k , 2m + 1 )
`
`F ( k , 2m + 1 ) /
`
`k ( k , 2m + 2 )
`
`F ( k , 2m + 2 )
`
`Uo ( k , 2m + 1
`
`# U ( k , 2m + 1 )
`
`B ( k , 2m + 1 )
`
`Fo ( k , 2m + 1 )
`
`no
`
`Ui ( k , 2m + 1 )
`
`44 Fo ( k , 2m + 2 )
`44 B ( k , 2m + 2 )
`
`Uo ( k , 2m + 2 )
`
`Ui?k , 2m + 2 )
`
`U ( k , 2m + 2 )
`
`Page 6 of 47
`
`

`

`atent
`
`Jun . 19 , 2018
`
`Sheet 5 of 19
`
`US 10 , 003 , 553 B2
`
`FIG . 3A
`
`300A
`
`Rix , 2p + 1 )
`
`Ring " x " , Stage " p "
`
`Ro ( x - 2p + 1 )
`
`R ( x , 2p + 1 ) /
`
`F ( x , 2p + 1 )
`
`Rocx , 2p + 2
`
`R ( x , 2p + 2 )
`
`F ( x , 2p + 2 )
`
`Fo ( x , 2p + 1 )
`
`Rix , 2p + 3 )
`
`Fo ( x , 2p + 2 )
`
`Ri ( x , 4p + 4 )
`
`Ri ( x . 2p + 21 BERITA
`
`Ring " x " , Stage “ p + 1 " )
`
`Ro ( x , 2p + 3 )
`
`Fo ( x , 2p + 3 )
`
`R ( x , 2p + 3 )
`
`F ( x , 2p + 3 )
`
`RO ( x , 2p + 4 )
`
`R ( x , 2p + 4 )
`
`F ( x , 2p + 4 )
`
`Uo ( x , 2p + 3 )
`
`B ( x , 2p + 3 )
`
`U ( x . 2p + 3 )
`
`Uo ( x , 2p + 4 )
`
`Fo ( x , 2p + 4 )
`
`, 2p + 3 )
`
`2p + 4 )
`
`Bo ( x , 2p + 1 )
`
`Uo ( x , 2p + 1 )
`
`Uix , 2p + 1 )
`
`Bo ( x , 2p + 3 )
`
`B ( x , 2p + 1 )
`
`U ( x , 2p + 1 )
`
`Bo ( x , 2p + 2 )
`
`Uo ( x , 2p + 2 )
`
`Li ( x2n + 2 )
`
`Bo ( x , 2p + 4 )
`
`B ( x , 2p + 2 ) /
`
`U ( x , 2p + 2 )
`
`B ( x , 2p + 4 )
`
`U ( x , 2p + 4 )
`
`Hop ( 1 , 1 )
`Hop ( 2 , 1 )
`
`Hop ( 1 , 2 )
`Hop ( 2 . 2 )
`
`Ring “ y ” , Stage " q "
`
`( Ring " y " , Stage " q + 1 " )
`
`Ricy , 2q + 1 )
`
`Focy , 29 + 1 )
`
`Ricy . 2q + 3 )
`
`Ro?y , 2q + 1 )
`
`R ( y , 29 + 1 ) /
`
`F ( y , 2q + 1 ) /
`
`Ri ( y , 2q + 2 )
`
`Rody , 29 + 2 )
`
`Focy , 2q + 2 )
`
`. Ricy , 2q + 4 )
`
`Ry , 2q + 3 )
`
`Fly , 2q + 3 )
`
`Ro ( y , 2q + 4
`
`Roy , 2q + 3 )
`
`Fo ( y , 2q + 3 )
`
`R ( y , 2q + 2 ) /
`
`F ( y , 2q + 2 )
`
`R ( y , 2q + 4 )
`
`F ( y , 2q + 4 )
`
`Bofy , 2q + 1 )
`
`Uo ( y , 29 + 1 )
`
`Bo ( y , 2q + 2 )
`
`B ( y , 2q + 1 )
`
`V ( y , 2q + 1 ) A
`
`Uo ( y , 29 + 2 )
`
`B ( y , 29 + 2 )
`
`U ( y , 29 + 2 )
`
`Jily . 29 + 1
`
`Bofy , 29 + 3 )
`
`Vily , 2q + 2 )
`
`Boly , 29 + 4 )
`
`Uo ( y , 29 + 3 )
`
`By , 29 + 3 )
`
`U ( y , 29 + 3 )
`
`( y , 2q + 4 )
`
`Uily , 2q + 4 )
`
`By , 2q + 4 )
`
`U ( y , 29 + 4 )
`
`Fo ( y , 2q + 4 )
`
`Ui ( ) , 2 ( + 3 )
`
`Page 7 of 47
`
`

`

`U . S . Patent
`
`Jun . 19 , 2018
`
`Sheet 6 of 19
`
`US 10 , 003 , 553 B2
`
`FIG . 3B
`
`300B
`
`Ring “ x ” , Stage “ p + 1 "
`
`Fo ( x , 2p + 1 )
`
`Ri ( x , 2n + 3
`
`Ro ( x - 2p + 3 )
`
`Fo ( x , 2p + 3 )
`
`Ring " x " , Stage " p " )
`
`Rix , 2p + 1 )
`
`Ro ( x , 2p + 1 )
`
`Ri ( x2p + 2 )
`
`Bo ( x , 2p + 1 )
`
`Bo ( x , 2p + 2 )
`
`R ( x , 2p + 1 )
`
`RO ( x 2p + 2 )
`
`R ( x , 2p + 2 ) ,
`
`B ( x , 2p + 1 )
`
`B ( x , 2p + 2 )
`
`F ( x , 2p + 1 )
`
`F ( x , 2p + 2 ) /
`
`R ( x , 2p + 3 )
`
`F ( x , 2p + 3
`
`Fo ( x , 2p + 2 )
`
`Ri ( x , 2p + 4 }
`
`Ro ( x - 2p + 4 )
`
`R ( x , 2p + 4 )
`
`F ( x , 2p + 4 )
`
`Vo ( x , 2p +
`
`Mix 2p + 1 }
`
`Bo ( x , 2p + 3 )
`
`FU ( x , 2p + 1 )
`
`B ( x , 2p + 3 )
`
`( x . 2p +
`
`xny
`
`, 2p + 3 )
`
`Voix , 2p + 2 )
`
`lix , 2p + 2 )
`
`Bo ( x , 2p + 4 )
`
`U ( x , 2p + 2 ) /
`
`B ( x , 2p + 4
`
`U ( x , 2p + 4 )
`
`Fo ( x , 2p + 4 )
`
`Li ( 1 , 2p + 3 )
`
`Mix , 2p + 4 )
`
`Hop ( 1 , 1 )
`Hop ( 2 . 1 )
`
`Hop ( 1 , 2 )
`Hop ( 2 , 2 )
`
`ITT
`U44
`
`Ring " y " , Stage " q "
`
`Ricy , 29 + 1 )
`
`Foly , 29 + 1 )
`
`Ricy , 2q + 3 )
`
`Ro?y , 2q + 1 )
`
`R ( y , 2q + 1 ) /
`
`Fly , 2q + 1 )
`
`Ri ( y , 29 + 2 )
`
`Roly , 2q + 2 )
`
`Foly , 2q + 2 )
`
`1 . Ricy , 20 + 4 )
`
`Rly . 24 + 4 ) DRY , 2q + 3 )
`Ro?y , 2q + 4 )
`
`R ( y , 2q + 2 )
`
`Fly , 2q + 2 ) /
`
`Bofy 2q + 1 )
`
`Uocy ( v . 20
`
`B ( y , 29 + 1 )
`
`Uly . 29 + 1 )
`
`Body . 2q + 2 )
`1 B ( 4 , 29 + 2 ) /
`
`Vocy ,
`
`Uly , 29 + 2 )
`
`viry , 29 + 1 )
`
`Uily , 2q + 2 )
`
`Bo { y , 29 + 3 )
`
`B0 ( , 2q + 4 )
`
`Ring " y " , Stage “ q + 1 "
`
`Rody , 2q + 3 )
`
`Foly , 2q + 3 )
`
`Fly , 2q + 3 )
`
`Fy , 2q + 4 )
`
`20 +
`
`Fo ( y , 2q + 4 )
`
`Jiky , 2x + 3 )
`
`Bly , 29 + 3 ) /
`
`Bly , 2q + 4 )
`
`Uo ( y , 2q + 4 ) AUy , 2x + 3 ) = Uy , 2x + 4 )
`
`Ji ( ) , 2 ( 14 )
`
`Page 8 of 47
`
`

`

`U . S . Patent
`
`Jun . 19 , 2018
`
`Sheet 7 of 19
`
`US 10 , 003 , 553 B2
`
`FIG . 4
`
`400
`
`Ring x , Stage " + 1 )
`
`Ring " x " , Stage " p + 1 "
`
`Fo ( x , 2p + 1 )
`
`Fi ( x , 2p + 3 )
`
`Fo ( x , 2p + 3 )
`
`Fi ( x , 2p + 4 )
`
`F ( x , 2p + 3 )
`
`F ( x , 2p + 4 )
`
`Bo ( x , 2p + 3 )
`Uo ( x , 2p + 3 )
`
`Fo ( x , 2p + 2 )
`
`Wi ( x , 2p + 2 ) hui ( x , 2p + 1 ) / 27
`
`Ring “ x ” , Stage " p "
`
`Fi ( x , 2p + 1 )
`
`Fi ( x , 2p + 2 )
`
`F ( x , 2p + 1 )
`
`Bo ( x , 2p + 1 )
`
`Jo ( x 2p + 1 )
`
`Fo ( x , 2p + 4 )
`
`Ui ( x , 2p + 3 )
`
`Ui ( x , 4p + 4 )
`
`Fo ( y , 2q + 3 )
`
`Fo ( y , 29 + 4 )
`
`Ui ( y , 29 + 3 )
`
`Uify , 2x + 4 )
`
`B ( x , 2p + 1 )
`
`U ( x , 2p + 1 )
`
`B ( x , 2p + 3 )
`
`U ( x , 2p + 3 )
`
`Jo ( x , 2p + 2 )
`
`B0 ( x , 2p + 4 )
`
`Jo ( x , 2p
`
`B ( x , 2p + 2 )
`
`U ( x , 2p + 2 )
`
`B ( x , 2p + 4 )
`
`U ( x , 2p + 4 )
`
`Bo ( x , 2p + 2 )
`
`Hop ( 1 , 1 )
`Hop ( 2 , 1 )
`
`Hop ( 1 , 2 )
`Hop ( 2 , 2 )
`HI
`
`Ring " y " , Stage " q "
`
`Ring " y " , Stage " q + 1 "
`
`Fi ( y , 2q + 1 )
`
`Fi ( y , 2q + 2 )
`
`Bo ( y , 2q + 1 )
`
`Foly , 2q + 1 )
`
`Fo ( y , 2q + 2 )
`
`F ( y , 2q + 1 )
`
`F ( y , 2q + 2 )
`
`29 + 1 )
`
`y , 2q + 1 )
`
`Bly , 29 + 1 )
`
`U ( y , 29 + 1 )
`
`Fi ( y , 2q + 3 )
`
`Fi ( y , 2q + 4 )
`
`Fly , 29 + 3 )
`
`F ( y , 2q + 4 )
`
`Bo ( y , 2q + 3 )
`Uo ( y , 29 + 3 )
`
`B ( y , 2q + 3 )
`
`U ( y , 29 + 3 )
`
`Uo ( y , 29
`
`Ui ( y , 2x + 2 )
`
`Boty , 2q + 4 )
`
`Vo ( y , 297
`
`B ( y , 29 + 2 )
`
`U ( y , 29 + 2 )
`
`B ( y , 2q + 4 )
`
`U ( y , 29 + 4 )
`
`Bo ( y , 2q + 2 )
`
`Page 9 of 47
`
`

`

`U . S . Patent
`
`Jun . 19 , 2018
`
`Sheet 8 of 19
`
`US 10 , 003 , 553 B2
`
`FIG . 5
`
`500
`
`( Ring " x " , Stage “ p ”
`
`Ring " x " , Stage " p + 1 "
`
`Fo ( x , 2p + 1 )
`
`Fi ( x , 2p + 3 )
`
`Fo ( x , 2p + 3 )
`
`Fi ( x , 2p + 4 )
`
`F ( x , 2p + 3 )
`
`F ( x , 2p + 4 )
`
`Fo ( x , 2p + 4 )
`
`Fo ( x , 2p + 2 )
`
`LUi ( x2p + 2 ) Jui ( 1 , 2p + 1 )
`
`Fi ( x , 2p + 1 )
`
`Fi ( x , 2p + 2 )
`
`F ( x , 2p + 1 )
`
`F ( x , 2p + 2 )
`
`Bo ( x , 2p + 1 )
`Uo ( x , 2p + 1 )
`
`B ( x , 2p + 1 ) /
`
`U ( x , 2p + 1 )
`
`B ( x , 2p + 2 )
`
`U ( x , 2p + 2 )
`
`Bo ( x , 2p + 2 )
`
`Hop ( 1 , 1 )
`Hop ( 2 , 1 )
`
`Hop ( 1 , 2 )
`Hop ( 2 , 2 )
`
`Ring " y " , Stage " q "
`
`Ring " y " , Stage “ q + 1 "
`
`Foly , 29 + 2 ) LFo { y , 2q + 1 )
`
`Fi ( y , 29 + 1 )
`
`Fi ( y , 2q + 2 )
`
`F ( y , 2q + 1 ) /
`
`Fly , 2q + 2 )
`
`Bo?y , 29 + 1 )
`Uo ( y , 29 + 1 )
`
`B ( y , 2q + 1 )
`
`U ( y , 29 + 1 ) /
`
`Jily , 2q + 1 )
`
`UOC
`
`Ui ( y , 29 + 2 )
`
`Fi ( y , 2q + 3 )
`
`Fi ( y , 2q + 3 )
`
`Fly , 2q + 3 )
`
`Fly , 2q + 4 )
`
`Bo ( y , 2q + 3 )
`Uo ( y , 2q + 3 )
`va
`
`1 , 29 + 3 )
`
`Vly , 29 + 3 )
`
`Bo ( y , 2q + 4 )
`
`Joly , 2q + 4 )
`
`Foly , 2q + 3 )
`
`Foy , 2q + 4 )
`
`Uify , 2x + 3 )
`
`Uity , 24 + 4 )
`
`B ( y , 29 + 2 )
`
`( y , 29 + 2 ) /
`
`By , 29 + 4 )
`
`Vly , 2q + 4 )
`
`Boly , 2q + 2 )
`
`Page 10 of 47
`
`

`

`U . S . Patent
`
`Jun . 19 , 2018
`
`Sheet 9 of 19
`
`US 10 , 003 , 553 B2
`
`600
`
`FIG . 6
`
`( Ring “ x ” , Stage “ p ”
`
`Fi ( x , 2p + 1 )
`
`Fi ( x , 2p + 2 )
`
`F ( x , 2p + 1 )
`
`F ( x , 2p + 2 )
`
`Wi ( x , 2p + 2 ) hui ( x , 2p + 1 . Fo ( x , 2p + 2 ) 10 ( x , 2p + 1 )
`
`Bo ( x , 2p + 1 )
`Uo ( x , 2p + 1 )
`
`p + 1 )
`
`V ( x , 2p + 1 )
`
`B ( x , 2p + 2 )
`
`( x , 2p + 2 )
`
`Bo ( x , 2p + 2 )
`
`Hop ( 1 , 1 )
`Hop ( 2 , 1 )
`
`Hop ( 1 , 2 )
`Hop ( 2 , 2 )
`
`Ring " y " , Stage " q "
`
`Ring " y " , Stage " q + 1 "
`
`Fi ( y , 29 + 1 )
`
`Fi ( y , 29 + 2 )
`
`F ( y , 2q + 1 ) /
`
`F ( y , 2q + 2 )
`
`Fo ( y , 2q + 1 )
`
`Fo ( y , 2q + 2 )
`
`Fi ( y , 29 + 3 )
`
`Fi ( y , 2q + 4 )
`
`F ( y , 2q + 3 )
`
`F ( y , 2q + 4 )
`
`Bo ( y , 29 + 1 )
`Uo ( y , 2q + 1 )
`
`Ui ( y , 29 + 1 )
`
`Bo ( y , 2q + 3 )
`Uo ( y , 29 + 3 )
`
`By , 29 + 1 )
`
`U ( y , 29 + 1 )
`
`Bly , 2q + 3 )
`
`U ( y , 2q + 3 )
`
`Uity , 2q + 2 )
`
`Bofy , 2q + 4 )
`
`Uo ( y , 29
`
`By , 2q + 2 )
`
`U ( y , 2q + 2 ) /
`
`B ( y , 2q + 4 )
`
`U ( y , 2q + 4 )
`
`Fo ( y , 2q + 3 )
`
`Fo ( y , 29 + 4 )
`
`Ui ( y , 29 + 3 )
`
`Ji ( y , 2q + 4 )
`
`Bo ( y , 2q + 2 )
`
`Page 11 of 47
`
`

`

`U . S . Patent
`
`Jun . 19 , 2018
`
`Sheet 10 of 19
`
`US 10 , 003 , 553 B2
`
`FIG . 7
`
`700
`
`XXXNNN
`
`5 6
`2 3 4
`> ?
`41 V3 U3 L2 H3 K3 V5
`?
`1 2 3 4 5 6 Y
`
`Stages in 1st Ring
`
`Stages in 2nd Ring — >
`
`Page 12 of 47
`
`

`

`U . S . Patent
`
`Jun . 19 , 2018
`
`Sheet 11 of 19
`
`US 10 , 003 , 553 B2
`
`800
`
`( 1 , 10 )
`
`( 2 , 10 )
`
`( 3 , 10 )
`
`( 4 , 10 )
`
`( 5 , 10 )
`
`( 6 , 10 )
`
`( 7 , 10 )
`
`( 8 , 10 )
`
`( 9 , 10 )
`
`( 10 , 10 )
`
`( 1 , 9 )
`
`( 2 , 9 )
`
`( 3 , 9 )
`
`( 4 , 9 )
`
`( 5 , 9 )
`
`( 6 , 9 )
`
`( 7 , 9 )
`
`( 8 , 9 )
`
`( 9 , 9 )
`
`( 10 , 9 )
`
`( 1 , 8 )
`
`( 2 , 8 )
`
`( 3 , 8 )
`
`( 4 , 8 )
`
`( 5 , 8 )
`
`( 6 , 8 )
`
`( 7 , 8 )
`
`( 8 , 8 )
`
`( 9 , 8 )
`
`( 10 , 8 ) ( 10 , 8 )
`
`1
`
`( 1 , 7 )
`
`( 2 , 7 )
`
`( 3 , 7 )
`
`( 4 , 7 )
`
`( 5 , 7 )
`
`( 6 , 7 )
`
`( 8 , 7 )
`
`( 9 , 7 )
`
`( 10 , 7 ) ( 10 , 7 )
`
`( 1 , 6 )
`
`( 2 , 6 )
`
`( 3 , 6 )
`
`( 4 , 6 )
`
`( 5 , 6 )
`
`( 8 , 6 )
`
`( 10 . 6 ) ( 10 , 6 )
`( 9 , 6 )
`
`FIG . 8
`
`( 1 , 5 )
`
`( 2 , 5 )
`
`( 3 , 5 )
`
`( 4 , 5 )
`
`( 5 , 5 )
`
`( 6 , 5 )
`
`( 7 , 5 )
`
`( 8 , 5 )
`
`40 . 5 ) ( 10 , 5 )
`( 9 , 5 )
`
`( 6 , 6 )
`
`( 7 , 6 )
`
`( 1 , 4 )
`
`( 2 , 4 )
`
`( 3 , 4 )
`
`( 4 , 4 )
`
`( 5 , 4 )
`
`( 6 , 4 )
`
`( 7 , 4 )
`
`( 8 , 4 )
`
`( 9 , 4 )
`
`( 10 , 4 )
`
`( 1 , 3 )
`
`( 2 , 3 )
`
`( 3 , 3 )
`
`( 4 , 3 )
`
`( 5 , 3 )
`
`( 6 , 3 )
`
`( 7 , 3 )
`( 8 , 3 )
`
`( 9 , 3 )
`
`( 10 , 3 )
`
`( 1 , 2 )
`
`( 2 , 2 )
`
`( 3 , 2 )
`
`( 4 , 2 )
`
`( 5 , 2 )
`
`( 6 , 2 )
`
`( 7 , 2 )
`( 8 , 2 )
`
`( 9 , 2 )
`
`( 10 . 2 )
`
`( 1 , 1 )
`
`l
`
`( 2 , 1 )
`
`( 3 , 1 )
`
`( 4 , 1 )
`
`( 5 , 1 )
`
`( 6 , 1 )
`
`( 7 , 1 )
`( 8 , 1 )
`
`( 9 , 1 )
`
`( 10 , 1 )
`
`Block
`
`Page 13 of 47
`
`

`

`U . S . Patent
`
`Jun . 19 , 2018
`
`Sheet 12 of 19
`
`US 10 , 003 , 553 B2
`
`Fi ( k . 2m + 1 )
`YFI ( K , 2m + 1 )
`Fi ( k . 2m + 2 )
`
`Bo { k , 2m + 1 )
`
`Bo { k , 2m + 2 )
`
`FIG . 9A
`
`900A
`
`NYFo { k , 2m + 1 )
`
`YF ( k , 2m + 1
`
`F ( k , 2m + 1 ) /
`
`Fík , 2m + 2 )
`
`Uo ( k , 2m + 1 )
`
`B ( k , 2m + 1 )
`
`U ( K , 2m + 1 )
`
`Uo ( k , 2m + 2
`
`B ( k , 2m + 2 )
`
`m + 2 ) /
`
`Fo { k , 2m + 1 )
`
`Fo ( k . 2m + 2 )
`
`Ui ( k . 2m + 1 )
`
`i ( k . 2m + 2 )
`
`Fi?k , 2m + 1 )
`
`Fi ( k , 2m + 2 )
`
`Boík , 2m + 1 )
`
`Bo ( k . 2m + 2 )
`
`FIG . 9B
`
`900B
`
`Fo ( k , 2m + 1 )
`
`Fi { k , 2m + 1 )
`
`Fo { k , 2m + 2 )
`
`Fi?k , 2m + 2 )
`
`F { k , 2m + 1 )
`
`F ( k , 2m + 2 )
`
`FIG . 9C
`
`9000
`
`F ( k , 2m + 1 ) /
`
`F { k , 2m + 2 )
`
`Uo ( k , 2m + 1 )
`
`YUo ( k , 2m + 1 ) Ui ( k , 2m + 1 )
`
`B ( k , 2m + 1
`
`( k , 2m + 1 ) A
`
`YU ( k , 2m + 1
`
`Bock , 2m + 1 )
`
`UYo { k , 2m + 1 )
`
`B { k , 2m + 1 )
`
`VY ( K , 2m +
`
`Uo ( k , 2m + 2 )
`
`U
`
`B ( k , 2m + 2 )
`
`( k , 2m + 2 )
`
`YUi?k , 2m + 1 )
`Bo { k , 2m + 2 )
`
`Ui?k , 2m + 2 )
`
`Uo ( k , 2m + 2 )
`
`B ( k , 2m + 2 )
`
`uk , 2m + 27
`
`Fo ( k , 2m + 1 )
`
`Fo ( k . 2m + 2 )
`
`Vi?k , 2m + 1 )
`
`UYi?k , 2m + 1 )
`
`Ui { k , 2m + 2 )
`
`900E
`
`Fo ( k . 2m + 1 )
`
`Fo ( k , 2m + 2 )
`
`Ui?k , 2m + 1 )
`
`UYi { k , 2m + 1 )
`
`Ui ( k 2m + 2 )
`
`FIG . 9D
`
`900D
`
`FIG . 9E
`Fi ( k . 2m + ?
`Fi ( k 2m + 1 ) .
`F YFo ( k , 2m + 1 )
`YFik . 2001 ) VF { k , 2m + 18
`YFi { k , 2m + 1 )
`YUok , 2m + 1 ) Tout me Fikret
`Fi ( k . 2m + 2 )
`
`Foík , 2m + 1 )
`
`Fo ( k . 2m + 2 )
`
`F { k , 2m + 1 )
`
`F ( k , 2m + 2 ) /
`
`K . 2m + 1 )
`
`Bo ( k , 2m + 1 )
`
`UYO ( K , 2m +
`
`YFo { k , 2m + 1 )
`
`YF { k , 2m + 17
`
`F { k , 2m + 1 ) /
`
`Fi?k , 2m + 1 )
`YFi ( k . 2m + 1 )
`
`N
`
`Fi ( k , 2m + 2 )
`
`Bo { k , 2m + 1 ) .
`
`Uo { k , 2m + 1 )
`
`F { k , 2m + 2 )
`
`Bo { k , 2m + 2 ) .
`
`B ( k , 2m + 1
`
`U ( k , 2m1 + 1 )
`
`YU ( k , 2m + 1 )
`
`Uo ( k , 2m + 2 )
`
`Yuick , 2m + 1 ) Bock , 2m + 2 )
`
`B ( k , 2m + 2 )
`
`U ( k , 2m + 2 )
`
`Di?k , 2m + 2 )
`
`B ( k , 2m + 1
`
`kB ( k , 2m + 2 )
`
`Uo ( k , 2m + 2 ) VY ( 2m + 1 AU ( k , 2m + 2 )
`
`Page 14 of 47
`
`

`

`U . S . Patent
`
`Jun . 19 , 2018
`
`Sheet 13 of 19
`
`US 10 , 003 , 553 B2
`
`Ri?k , 2m + 1 )
`
`vac zner
`
`YRI ( k , 2m + 1 )
`
`Ri ( k , 2m + 2 ) )
`
`Bo { k , 2m + 1 )
`
`Bo ( k , 2m + 2 )
`
`Ri { k . 2m + 1 )
`
`FIG . 10A
`D F { k , 2m + 17
`
`YRock , 2m + 1
`
`VR ( k . 2m + 1 .
`
`R ( k , 2m + 1
`
`Rock , 2m + 1 )
`
`Rock . 2m + 2 )
`
`R ( k , 2m + 2
`
`F ( k . 2m + 2 )
`
`Uo { k , 2m + 1 )
`
`B ( k , 2m + 1
`
`Vik , 2m + 17
`
`1000A
`rammen er og
`
`Fo { k , 2m + 1 )
`
`Fo ( k . 2m + 2 )
`
`Ri ( k , 2m + 1 )
`
`RYi ( k , 2m + 1 )
`Ri ( k , 2m + 2 )
`
`Ui ( k . 2m + 1 )
`
`Bo ( k , 2m + 1 )
`
`FIG . 10B
`
`1000B
`
`Yolk , 2m + 1 )
`RYO ( k , 2m + 1 )
`
`Rik , 2m + 2X RY { k , 2m +
`Ro ( k , 2m + 2 )
`
`F ( k , 2m + 1 )
`
`F { k , 2m + 2 )
`
`Uo ( k , 2m + 1 )
`
`B ( k , 2m + 1 )
`
`Wik , 2m + 1 )
`
`Fo { k , 2m + 1 )
`
`Fo k , 2m + 2 )
`
`Ui ( k , 2m + 1 )
`
`Uo ( k 2m + 2 )
`
`Ui ( k . 2m + 2 )
`
`Bo k , 2m + 2 )
`
`Uo { k , 2m + 2 )
`
`Ui ( k , 2m + 2 )
`
`B ( k , 2m + 2y
`
`Uk , 2m + 2 )
`
`B ( k , 2m + 2 )
`
`Vik , 2m + 2 )
`
`FIG . 10C
`
`1000C
`
`Rock { m + 1 )
`
`Rik , 2m + 1 )
`
`Rok 2m + 2 )
`
`F ( k , 2m + 1
`
`Fo ( k , 2m + 1 )
`
`Ri ( k , 2m + 1 )
`
`FIG . 10D
`
`1000D
`
`Rock , 2m + 1 )
`
`R ( k , 2m + 1 )
`
`F ( k , 2m + 1 ) /
`
`Rock , 2m + 2 )
`
`Fo { k , 2m + 1 )
`
`Fork , 2m + 2 )
`
`Ri ( k . 2m + 2 )
`
`Bo?k , 2m + 1 )
`
`Bo ( k . 2m + 2 )
`
`R ( k , 2m + 2 )
`
`B ( k , 2m + 1
`
`B ( k _ 2m + 2y
`
`tui?k . 2m + 1 )
`YUo { k , 2m + 1 Ui ( k , 2m + 1 )
`i
`rujck . 2m + 13
`YUj ( k . 2m + 1 )
`Ui ( k , 2m + 2 )
`
`Uo ( k , 2m + 1 )
`
`m
`
`U ( k . 2m + 1 )
`
`Vo { k , 2m + 2 )
`
`U ( k , 2m + 2
`
`FIG . 10E
`
`GOLV F ( k , 2m + 2 )
`
`Fo { k . 2m + 2 )
`
`Ri?k , 2m + 2 )
`
`YU ( k , 2m
`
`Bo ( k , 2m + 1 )
`
`Bo ( k , 2m + 2 )
`
`Rík , 2m + 2 )
`
`Fík , 2m + 2 ) /
`
`UY0 ( k , 2m + 1 )
`
`B ( k , 2m + 1
`
`VYK , 2m + 1
`
`Uo ( k , 2m + 2 )
`
`B ( k , 2m + 2
`
`U ( k , 2m + 2
`
`1000E
`
`Ri { k , 2m + 1 )
`Fo { k , 2m + 1 )
`
`FIG . 10F
`
`RYO ( k , m + 1 )
`
`RYi?k , 2m + 1 )
`Fo { k . 2m + 2 )
`
`Rik 2m + 2YRY { k , 2m + 1
`Rock , 2m + 2 )
`
`F ( k , 2m + 17
`
`Fík , 2m + 2 )
`
`YUO ( K , 2m + 1 ) Ui ( k . 2m + 1 , Ri?k , 2m + 2 )
`Bo?k , 2m + 1 )
`YUi ( k . 2m + 1 )
`Ui { k , 2m + 2 ) Bo { k . 2m + 2 )
`
`YU ( k , 2m +
`
`UYo { k , 2m + 1 )
`
`Uo ( k , 2m + 2 ) VYK , 2m + T TUK , Zm + 2T
`
`B [ k , 2m + 1
`
`B ( k , 2m + 27
`
`Vi ( k , 2m + 1 )
`
`UYi ( k . 2m + 1 )
`
`Ui?k , 2m + 2 )
`
`uick . 2m + 2 )
`1000F
`
`Fo ( k , 2m + 1 )
`
`Fo { k , 2m + 2 )
`
`Ui ( k , 2m + 1 )
`E
`ÙYi ( k , 2m + 1 )
`
`Ui ( k . 2m + 2 )
`
`Ri?k , 2m + 1 ) .
`YRI ( k . 2m + 1 )
`Ri ( k , 2m + 2 )
`
`Boík 2m + 1 ) ,
`
`Bock , 2m + 2 ) .
`
`NYFork , 2m + 1 )
`
`Ro?k , 2m + 1 )
`
`VR ( k , 2m + 12
`
`R ( k , 2m + 1 )
`
`Fík , 2m + 1 )
`
`Rock , 2m + 2 )
`
`Rík , 2m + 2 )
`
`F { k , 2m + 2 )
`
`Uo ( k 2m + 1 ) .
`
`B ( k , 2m + 1
`
`U { K 2m + 1
`
`Uo ( k , 2m + 2 )
`
`B { k , 2m + 2y
`
`U ( k , 2m + 2y
`
`Page 15 o