Optical Multistage Interconnection Networks: New challenges And Approaches

1
Optical Multistage Interconnection Networks New
challenges And Approaches

• ?? t??ep????????e? ?pt???? ???? µe f?t???????
  d?a??pte? e??a? t? µ????? st?? t??ep????????e?.
• ?? d?a??pte? ?d????µe??? ??µat?? (guided wave)
  ???????ta? se
• ?ß??d???? d?a??pte? , st??? ?p????? ta s?µata
  e??a? ?pt??? a??? t? ??e???? t?? d?a??pt? ?a? ??
  ap?f?se?? d?ad??µ?s?? ?aµß????ta? ??e?t?????? .
• ?pt???? d?a??pte?, ?p?? ??e? ?? d?ad??as?e?
  ?????ta? µe ?pt??? t??p?

2
???ß??µata t?? ?pt???? MINs

• ?? ßas??? d?a??pt??? st???e?? (Switching
  Element SE ) e??a? ??a? ?ate????t?????
  s??e??t?? µe d?? e?e???? e?s?d??? ?a? d?? e?e????
  e??d???
• ?a p??ß??µata t?? ?pt???? MINs e??a? ta e???
• ? e?a?t?µe?? ap? t? µ???p?t? ap??e?a , ? ?p??a
  sta µe???a d??t?a e??a? e????? a?????? t??
  a???µ?? t?? s??e??t???? p?? ???s?µ?p?????ta?,
• ?? ?pt???? pa?eµß???? a??µesa sta ?a??d?a, p??
  s?µßa????? ?ta? d?? ?a????a µe s?µata
  a????ep?d???? se ??a d?a??pt??? d??t??

3
???ß??µata t?? ?pt???? MINs (s????e?a)

• ?? pa?eµß???? e??a? d?? e?d??
• ?ta? ta ?a????a d?asta??????ta? µeta?? t??? ??a
  t?? d?µ??????a µ?a? t?p?????a?
• ?ta? d?? µ???p?t?a µ???????ta? ??a SE µp??e? ?a
  ?p???e? a?ep???µ?t? s??e??? ap? t? ??a ?a???? st?
  ????.
• ?? p??ß??µa t?? pa?eµß???? e??a? p?? s?µa?t???
  ap? t? p??ß??µa t?? ap??e?a? sta µ???p?t?a.

4
???ta?e?se? ??se??

• St?? ?????? p??s????s? , pe??ss?te??? d?a??pte?
  ?a? s??d?se?? ???s?µ?p?????ta? µe s??p? ?a
  e?asfa??ste? ?t? t?? ???e st??µ? µ??? µ?a e?s?d??
  ?a? µ?a ???d?? ?a e??a? e?e???? se ???e ded?µ???
  st??µ?.
• St?? ??????? p??s????s?, ?? pa?eµß????
  a?t?µet?p????ta? ?? s??????se?? , ?p?te d??
  s??d?se?? p?? ???s?µ?p????? t? ?d?? SE, ?????ta?
  se d?af??et??? ??????? st??µ?.

5
?????? ??e????s?

• ???s? t?? ??e???µ???? ???t??? Benes (Dilated
  Benes Network -DBN) .
• ??a NxN DBN ??e? 2N e?s?d??? ?a? e??d???,
  ap? t?? ?p??e? µ??? ?? ? e??a? d?a??s?µe?.
• ?atas?e?? ap? d?? ?/2x?/2 ?p?d??t?a, t? ??a p???
  st? ????.
• ? a???µ?? t?? stad??? e??a? M(N) 2logN.
• ???? µ?a ap? t?? d?? e?s?d??? t?? SEs t?? p??t??
  ?a? t?? te?e?ta??? stad??? e??a? ???e f???
  e?e???, ? ap?f??? t?? pa?eµß???? e??a? e????µ???.
  
• ?p?????? d?? pa?a??a??? t?? ????ta????
  d?e???µ???? eµp?d?st???? d??t???. ???t??, t?
  dilated slipped Banyan ?a? de?te??? t? two-plane
  Banyan.

6
??????? ??e????s?

• ?pa?a???µ?s? µe p???p?e??a ??????
  (reconfiguration with time-division multiplexing
  - RTDM).
• ??a µet??es? ?????eta? se d?? ? pe??ss?te?e?
  ?p?-a?t?µeta??se?? , t?t??e? ?ste ?aµ?a ap? a?t??
  ?a µ?? ??e? pa?eµß????.
• ??a µet??es? ???ete se ??a MIN se a??et???
  ?????? , ??a? ??a ???e ?p?-µet??es? , µ?a
  te????? p?? ???eta? crosstalk-and-conflict-free
  CF ?a?t????f?s?.

7
Ge????

• ?? t? ??st?? se ?????(a?a?????? µe t?? a???µ? t??
  ????? p?? ??e?????ta?) ?a? t? ??st?? se
  ????(a?a?????? µe t?? a???µ? t?? SE p??
  ??e?????ta?) ?ta? a?ta?????µa , ? ???????
  d?e????s? e??a? p??? p?? ap?d?t???

8
???p?? e?????? t?? ?????? MINs

• ? d?a??pt???? ??e????(switching control) , ????
  ?? d?a??pte? t?? d??t??? e??????ta? a?e???t?ta ?
  ??a? ap? t?? ???? ?a? µp????? ?a e??a? se
  ?e????st?? ?atast?se?? se ???e ??????? st??µ?.
• ? ??e???? st???? (column control) , ?? d?a??pte?
  p?? t?? ?d?a? st???? e??????ta? ap? ??a ?????
  s?µa ?a? e??a? st?? ?d?a ?at?stas? t?? ???e
  ??????? st??µ?.
• G?a t? d??t?? DSB e??e p??ta?e? ?a
  ???s?µ?p??e?ta? ??a bit e?????? , µe t? 0 ?a
  s?µa??e? e??e?a s??des? ?a? t? 1 d?a????a
  s??des?.

9
?a?t????f?s?

• Se ??a NxN DSB , ?? ?(?-1) s??d?se?? µp?????
  µp??? se ? CFs ?? e???
• ? kth CF , , pe????e? s??d?se??
  t?? i ?a? j ef?s??
• ??a p????? d?as??dedeµ??? d??t?? ??e???eta? 2? CF
  ?a?t???af?se??, ??a ?????? µ??? d?? CF
  ?a?t???af?se??, ??a? ??ß??? s??dedeµ???? ??????
  (CCC) t?e?? CF ?a?t???af?se?? ?a? ? ?pe???ß??
  logN CF ?a?t???af?se??.

10
?µ?-µet??es? (semi-permutation)

• ???a? µ?a µe???? µet??es? ? ?p??a e?asfa???e? ?t?
  µ??? µ?a e?e??? s??des? pe???e? ap? ???e e?s?d?
  ?a? ???d? t?? d?a??pt?.
• ???e µet??es? µp??e? ?a ap?s??te?e? se
  ?µ?-a?t?µeta??se?? , ?a? ? a???µ?? a?t?? t??
  ?µ?-a?t?µeta??se?? ??a ??a? pe??tt? a???a??
  a???µ? ? e??a?

11
?µ?-µet??es? (s????e?a)

• ???e µet??es? µp??e? ?a ????ste? se d??
  ?µ?-µeta??se??, ?a? µ?a ?µ?-µet??es? µp??e? ?a
  p?a?µat?p????e? se ??a p??asµa se ??a d??t??
  Benes.
• S??ep?? , ???e µet??es? µp??e? ?a p?a?µat?p????e?
  ????? pa?eµß???? se d?? ?????? se ??a d??t??
  Benes, t? ?p??? e??a? ?a? t? ??t? ???? ??a ???e
  ?pt??? d??t?? ????? pa?eµß????

12
? a??????µ?? Odd - Even (????- ????)

• ???s?µ?p??e?ta? ??a t?? d?µ??????a e??? s??????
  d??µ?????s?? se ??a a?? st??? e?e???µe?? Banyan
  d??t??.
• ? ???? e?????? pa???eta? µe t?? ???s? t?? p?????
  XOR a??µesa st?? d?ad??? a?apa??stas? t?? e?s?d??
  µe t?? d?ad??? a?apa??stas? t?? e??d??.
• Se ???e st???, ? d?ad??? a?apa??stas? t??
  e?s?d?? d?af??e? µe t?? d?ad??? a?apa??stas? t??
  e??d?? ,st? st?d?? k, µ??? st? bit n k.
• ?? s??d?se?? ???????ta? s?µf??a µe t?? a?a??a?e?
  ???e?? e?????? ?a? t?? ?s?t?µ?a t?? e?s?d?? t???.
  
• Oi ?a? Ei ,µe , a?apa??st??? t?? ?µ?da t??
  s??d?se?? ?? ?p??e? apa?t??? t?? ???? ??e???? i
  , a??? t?? ?p???? ? ?s?t?µ?a t?? e?s?d?? e??a?
  µ??? ?a? ???? a?t?st???a.

13
? a??????µ?? Odd - Even 2

• ? a???µ?? t?? s??d?se?? ,t?? ?µ?da? Oi ?a
  ??µa??eta? ap? 0 µ???? ?/2 ?a de???eta? ??
  Oi, ?p?? ?a? st?? Ei ?a de???eta? ??
  Ei.
• Se ??a ???? ? a??????µ?? a?t?? e??a??d??e? µ?a
  s??des? t?? s??d?se?? ?? ?p??e? ??e?????ta? t??
  ?d?a ???? e?????? , ef?s?? a?t?? ????? t?? ?d?a
  ?s?t?µ?a e?s?d??.
• ?f?? ?? d?ad???? a?apa?ast?se?? t?? d?? e?s?d??
  ????? t?? ?d?a ?s?t?µ?a , a?t? s?µa??e? ?t?
  d?af????? se t??????st?? 2 bits , ????ta?
  ap?stas? Hamming t??????st?? 2. ?? Oi gt 0 (?
  Ei gt 0) ,t?te ? p????aµµat?sµ?? st? Oi(?
  st? Ei ) e?asfa???e? ?t? ?? s??d?se?? a?t??
  de? ?a s??a?t????ta? se ?a???a d?a??pt?.
• Se ??a Banyan , t?? ?p???? ???? ?? d?a??pte?
  e??a? ?d? ??t? ap? t?? ??e??? st???? , ?p??????
  a???ß?? N/2 s??d?se?? p?? ????? ???? (? µ???)
  ?s?t?µ?a e?s?d??.
• ??a s?µf??a µe t?? a??????µ? ??e? ?? N/2
  s??d?se?? µp????? ?a p?a?µat?p??????? se ??a
  ????. ? ??????? p???p????t?ta t?? a??????µ??
  e??a? p??????µ??? s????t?s? t?? a???µ?? t?? ?p?
  e??a??d??s? s??d?se??.

14
? a??????µ?? Odd - Even 3

• ??a? ß??t?st?? a??????µ?? p??spa?e? ?a µe??se?
  t?? a???µ? t?? ????? µe t? ?a e???e? t?? ?µ?de?
  Oi ?a? Ei se ??a ????.
• G?a a???µ? s??d?se?? lt 100
• ? a??????µ?? Odd Even de? ?e?t????e? ?a?? e??
  ,
• ? a??????µ?? Greedy e??a? s?ed?? t?s? ?a??? ?s?
  ?a? ? ß??t?st??.
• G?a a???µ? s??d?se?? µeta?? 100 ?a? 1000 , ?
  a??????µ?? Odd Even ?e?t????e? sa? t??
  ß??t?st? , af?? ?? e??se?? e??a? sp???e? .
• S??????? t? Banyan p??sf??e? ?a??te??
  e??s????p?s? ap? ??a DSB ?d??? µe??????.