available under
`Document made
`Patent Cooperation Treaty (PCT)
`
`the
`
`International application number: PCT/US2008/056064
`
`International filing date:
`
`06 March 2008 (06.03.2008)
`
`Document type:
`
`Certified copy of priority document
`
`Document details:
`
`Country/Office: US
`Number:
`60/940,383
`Filing date:
`25 May 2007 (25.05.2007)
`
`Date of receipt at the International Bureau:
`
`29 March 2008 (29.03.2008)
`
`Remark:
`
`Priority document submitted or transmitted to the International Bureau in
`compliance with Rule 17.1(a) or (b)
`
`
`
`World Intellectual Property Organization (WIPO) - Geneva, Switzerland
`Organisation Mondiale de la Propriété Intellectuelle (OMPI) - Genéve, Suisse
`
`Page 1 of 98
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`FLEX LOGIX EXHIBIT 1014
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`FLEX LOGIX EXHIBIT 1014
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`SRR=SNwin.
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`a eeeees~reserceWOee
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`SL v
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`:
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`SSS
`
`.
`
`ee
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`DEPARTMENT OF COMMERCE
`
`United States Patent anc Trademark Ofvice
`
`March 29, 2008
`
`Patent and Trademark Office
`
`THIS IS TO CERTIFY THAT ANNEXED HERETOIS A TRUE COPY FROM
`THE RECORDSOF THE UNITED STATES PATENT AND TRADEMARK
`OFFICE OF THOSE PAPERS OF THE BELOW IDENTIFIED PATENT
`APPLICATION THAT MET THE REQUIREMENTSTO BE GRANTED A
`FILING DATE.
`
`APPLICATION NUMBER: 60/940,383
`FILING DATE: May 25, 2007
`RELATED PCT APPLICATION NUMBER: PCT/US08/56064
`
`THE COUNTRY CODE AND NUMBER OF YOUR PRIORITY
`APPLICATION, TO BE USED FOR FILING ABROAD UNDER THE PARIS
`CONVENTION,IS US60/940,383
`
`Certified by
`NR
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`Na
`%
`
`:
`
`Under Secretary of Commerce
`for InteHectual Property
`aad Director af the Lnited States
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`Page 2 of 98
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`€
`

`

`M-0037 US
`
`FULLY CONNECTED GENERALIZED MULTI-STAGE NETWORKS
`
`Venkat Konda
`
`5
`
`CROSS REFERENCE TO RELATED APPLICATIONS
`
`This application is related to and incorporates by reference in its entirety the U.S.
`
`Provisional Patent Application Docket No. M-0038USentitled "FULLY CONNECTED
`
`GENERALIZED BUTTERFLY FAT TREE NETWORKS" by Venkat Kondaassigned
`
`to the same assignee as the current application, filed concurrently.
`
`10
`
`This application is related to and incorporates by reference in its entirety the U.S.
`
`Provisional Patent Application Docket No. M-0039USentitled "FULLY CONNECTED
`GENERALIZED REARRANGEABLY NONBLOCKING MULTI-LINK MULTI-
`
`STAGE NETWORKS" by Venkat Kondaassigned to the same assignee as the current
`
`application, filed concurrently.
`
`15
`
`This application is related to and incorporates by reference in its entirety the U.S.
`
`Provisional Patent Application Docket No. M-0040USentitled "FULLY CONNECTED
`
`GENERALIZED MULTI-LINK BUTTERILY FAT TREE NETWORKS" by Venkat
`
`Konda assigned to the same assignee as the current application, filed concurrently.
`
`This application is related to and incorporates by reference in its entirety the U.S.
`
`20
`
`‘Provisional Patent Application Docket No. M-0041US entitled "FULLY CONNECTED
`
`GENERALIZED FOLDED MULTI-STAGE NETWORKS" by Venkat Konda assigned
`
`to the same assignee as the current application, filed concurrently.
`
`This application is related to and incorporates by reference in its entirety the U.S.
`
`Provisional Patent Application Docket No. M-0042USentitled "FULLY CONNECTED
`
`25.
`
`GENERALIZED STRICTLY NONBLOCKING MULTI-LINK MULTL-STAGE
`
`NETWORKS" by Venkat Konda assigned to the sameassignee as the current application,
`
`filed concurrently.
`
`-|-
`
`Page 3 of 98
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`Page 3 of 98
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`

`

`M-0037 US
`
`This application is related to and incorporates by reference in its entirety the U.S.
`
`Provisional Patent Application Docket No. M-0045USentitled "VLSI LAYOUTS OF
`
`FULLY CONNECTED GENERALIZED NETWORKS" by Venkat Konda assigned to
`
`the sameassignee as the current application, filed concurrently.
`
`BRIEF DESCRIPTION OF DRAWINGS
`
`FIG. 1A is a diagram 100A of an exemplary symmetrical multi-stage network
`
`V(N,d,s) having inverse Benes connection topology of five stages with N = 8, d= 2 and
`
`s=2 with exemplary multicast connections, strictly nonblocking network for unicast
`
`connections and rearrangeably nonblocking network for arbitrary fan-out multicast
`
`10
`
`connections, in accordance with the invention.
`
`FIG. 1B is a diagram 100B of a general symmetrical multi-stage network
`V(N,d,2) with (2xlog, N)-1.
`stages
`strictly nonblocking network for unicast
`
`connections and rearrangeably nonblocking network for arbitrary fan-out multicast
`
`connections in accordance with the invention.
`
`15
`
`FIG. 1C is a diagram 100C of an exemplary asymmetrical multi-stage network
`
`V(N,,N,,d,2) having inverse Benes connection topology of five stages with N; = 8, N2
`
`= p* N; = 24 where p = 3, and d = 2 with exemplary multicast connections, strictly
`
`nonblocking network for unicast connections and rearrangeably nonblocking network for
`
`arbitrary fan-out multicast connections, in accordance with the invention.
`
`FIG. 1D is a diagram 100D of a general asymmetrical multi-stage network
`V(N,,N,,d,2) with No = p* N; and with (2xlog, N)-—1
`stages strictly nonblocking
`
`network for unicast connections and rearrangeably nonblocking networkfor arbitrary fan-
`
`out multicast connections in accordance with the invention.
`
`FIG. 1E is a diagram 100E of an exemplary asymmetrical multi-stage network
`
`V(N,,N,.d,2) having inverse Benes connection topology of five stages with No = 8, Ni
`
`= p* No = 24, where p = 3, and d = 2 with exemplary multicast connections, strictly
`
`nonblocking network for unicast connections and rearrangeably nonblocking network for
`
`arbitrary fan-out multicast connections, in accordance with the invention.
`-2-
`
`Page 4 of 98
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`

`

`M-0037 US
`
`FIG. 1F is a diagram 100F of a general asymmetrical multi-stage network
`V(N,,N,,d,2) with N; = p* No and with (2xlog, N)-1 stages strictly nonblocking
`
`network for unicast connections and rearrangeably nonblocking network for arbitrary fan-
`
`out multicast connections in accordance with the invention.
`
`FIG. 1A1 is a diagram 100A1 of an exemplary symmetrical multi-stage network
`
`V(N,d,2) having Omega connection topology of five stages with N = 8, d = 2 and s=2
`
`with exemplary multicast connections,
`
`strictly nonblocking network for unicast
`
`connections and rearrangeably nonblocking network for arbitrary fan-out multicast
`
`connections, in accordance with the invention.
`
`10
`
`FIG, 1C1 is a diagram 100C1 of an exemplary asymmetrical multi-stage network
`
`V(N,,N,,d,2) having Omega connection topology of five stages with Ni = 8, No = p*
`
`N: = 24 where p = 3, and d = 2 with exemplary multicast connections, strictly
`
`nonblocking network for unicast connections and rearrangeably nonblocking network for
`
`arbitrary fan-out multicast connections, in accordance with the invention.
`
`FIG. 1E1 is a diagram 100E1 of an exemplary asymmetrical multi-stage network
`
`V(N,,N,,d,2) having Omega connection topology of five stages with N2 = 8, Ni = p*
`
`Nz = 24, where p = 3, and d = 2 with exemplary multicast connections, strictly
`
`nonblocking network for unicast connections and rearrangeably nonblocking network for
`
`arbitrary fan-out multicast connections, in accordance with the invention.
`
`FIG. 1A2 is a diagram 100A2 of an exemplary symmetrical multi-stage network
`
`V(N,d,2) having nearest neighbor connection topology of five stages with N = 8, d= 2
`
`and s=2 with exemplary multicast connections, strictly nonblocking network for unicast
`
`connections and rearrangeably nonblocking network for arbitrary fan-out multicast
`
`connections, in accordance with the invention.
`
`FIG. 1C2 is a diagram 100C2 of an exemplary asymmetrical multi-stage network
`
`VWN,,N,,d,2) having nearest neighbor connection topology of five stages with N; = 8.
`
`No = p* N; = 24 where p = 3, and d = 2 with exemplary multicast connections, strictly
`
`Page 5 of 98
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`

`

`10
`
`15
`
`M-0037 US
`
`nonblocking network for unicast connections and rearrangeably nonblocking network for
`
`arbitrary fan-out multicast connections, in accordance with the invention.
`
`FIG. 1E2 is a diagram 100E2 of an exemplary asymmetrical multi-stage network
`
`V(N,,N,,d,2) having nearest neighbor connection topology of five stages with No = 8.
`
`Ni = p* No= 24, where p = 3, and d = 2 with exemplary multicast connections, strictly
`
`nonblocking network for unicast connections and rearrangeably nonblocking network for
`
`arbitrary fan-out multicast connections, in accordance with the invention.
`
`FIG. 2A is a diagram 200A of an exemplary symmetrical multi-stage network
`
`V(N,d,3) having inverse Benes connection topology of five stages with N = 8, d= 2 and
`
`s=3 with exemplary multicast connectionsstrictly nonblocking network for arbitrary fan-
`
`out multicast connections, in accordance with the invention.
`
`FIG. 2B1 & FIG. 2B2 is a diagram 200B of a general symmetrical multi-stage
`network V(N,d,3) with (2xlog, N)—1 stagesstrictly nonblocking network for arbitrary
`
`fan-out multicast connections in accordance with the invention.
`
`FIG. 2C is a diagram 200C of an exemplary asymmetrical multi-stage network
`
`V(N,,N,,d,3) having inverse Benes connection topology of five stages with N; = 8, N2
`
`= p* N; = 24 where p = 3, and d = 2 with exemplary multicast connections strictly
`
`nonblocking network for arbitrary fan-out multicast connections, in accordance with the
`
`invention.
`
`FIG. 2D1 & FIG. 2D2 is a diagram 200D of a general asymmetrical multi-stage
`network V(N,,N,,d,3) with No = p* N; and with (2xlog, N)-1.
`stages strictly
`
`nonblocking network for arbitrary fan-out multicast connections in accordance with the
`
`invention.
`
`FIG, 2E is a diagram 200E of an exemplary asymmetrical multi-stage network
`
`V(N,.N,.d,3) having inverse Benes connection topology of five stages with No = 8, Ni
`
`= p* No = 24, where p = 3, and d = 2 with exemplary multicast connectionsstrictly
`
`nonblocking network for arbitrary fan-out multicast connections, in accordance with the
`
`invention.
`
`-4-
`
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`

`

`M-0037 US
`
`FIG, 2F1 & FIG. 2F2 is a diagram 200F of a general asymmetrical multi-stage
`network V(N,,N,,d,3) with N; = p* No and with (2xlog, N)—1_
`stages strictly
`
`nonblocking network for arbitrary fan-out multicast connections in accordance with the
`
`invention.
`
`FIG. 2A1 is a diagram 200A1 of an exemplary symmetrical multi-stage network
`
`V(N,d,3) having Omega connection topology of five stages with N = 8, d = 2 and s=3
`
`with exemplary multicast connections, strictly nonblocking network for arbitrary fan-out
`
`multicast connections, in accordance with the invention.
`
`FIG. 2C1 is a diagram 200C1 of an exemplary asymmetrical multi-stage network
`
`10
`
`V(N,,N,.,d,3) having Omega connection topology of five stages with N; = 8, No = p*
`
`N, = 24 where p = 3, and d = 2 with exemplary multicast connections, strictly
`
`nonblocking network for arbitrary fan-out multicast connections, in accordance with the
`
`invention.
`
`FIG. 2E1 is a diagram 200E1 of an exemplary asymmetrical multi-stage network
`
`15
`
`V(N,,N,,d,3) having Omega connection topology of five stages with No = 8, Ni = p*
`
`Nz = 24, where p = 3, and d = 2 with exemplary multicast connections, strictly
`
`nonblocking network for arbitrary fan-out multicast connections, in accordance with the
`
`invention.
`
`FIG. 2A2 is a diagram 200A2 of an exemplary symmetrical multi-stage network
`
`V(N,d,3) having nearest neighbor connection topology of five stages with N = 8,d =2
`
`and s=3 with exemplary multicast connections, strictly nonblocking network for arbitrary
`
`fan-out multicast connections, in accordance with the invention.
`
`FIG. 2C2 is a diagram 200C2 of an exemplary asymmetrical multi-stage network
`
`V(N,,N,,d,3) having nearest neighbor connection topology of five stages with N; = 8,
`
`No = p* N; = 24 where p = 3, and d = 2 with exemplary multicast connections, strictly
`
`nonblocking network for arbitrary fan-out multicast connections, in accordance with the
`
`invention.
`
`Page 7 of 98
`
`Page 7 of 98
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`

`

`M-0037 US
`
`FIG, 2E2 is a diagram 200E2 of an exemplary asymmetrical multi-stage network
`
`V(N,,N,,d,3) having nearest neighbor connection topology of five stages with No = 8,
`
`N, = p* No= 24, where p = 3, and d = 2 with exemplary multicast connections, strictly
`
`nonblocking network for arbitrary fan-out multicast connections, in accordance with the
`invention.
`
`FIG. 3A is high-level flowchart of a scheduling method according to the
`
`invention, used to set up the multicast connections in all the networks disclosed in this
`
`invention.
`
`DETAILED DESCRIPTION OF THE INVENTION
`
`10
`
`15
`
`The present invention is concerned with the design and operation of large scale
`
`crosspoint reduction using arbitrarily large multi-stage switching networks for broadcast,
`
`unicast and multicast connections. Particularly multi-stage networks with stages more
`
`than three and radices greater than or equal to two offer large scale crosspoint reduction
`
`whenconfigured with optimallinks as disclosed in this invention.
`
`Whena transmitting device simultaneously sends information to more than one
`
`receiving device, the one-to-many connection required between the transmitting device
`
`and the receiving devices is called a multicast connection. A set of multicast connections
`
`is referred to as a multicast assignment. Whena transmitting device sends information to
`
`one receiving device, the one-to-one connection required between the transmitting device
`
`and the receiving device is called unicast connection. Whena transinitting device
`
`simultaneously sends information to all the available receiving devices, the one-to-all
`
`connection required between the transmitting device and the receiving devices is called a
`
`broadcast connection.
`
`In general, a multicast connection is meant to be one-to-many connection, which
`
`includes unicast and broadcast connections. A multicast assignment in a switching
`
`network is nonblocking if any of the available inlet links can always be connected to any
`
`of the available outlet links.
`
`Page 8 of 98
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`

`

`10
`
`15
`
`M-0037 US
`
`In certain multi-stage networks of the type described herein, any connection
`
`request of arbitrary fan-out, i.e. from an inlet link to an outlet link or to a set of outlet
`
`links of the network, can be satisfied without blocking if necessary by rearranging some
`
`of the previous connection requests. In certain other multi-stage networks of the type
`
`described herein, any connection request of arbitrary fan-out, i.e. from an inlet link to an
`
`outlet link or to a set of outlet links of the network, can be satisfied without blocking with
`
`never needing to rearrange any of the previous connection requests.
`
`In certain multi-stage networks of the type described herein, any connection
`
`request of unicast fromaninlet link Lo an outlet link of the network, can be satisfied
`
`without blocking if necessary by rearranging some of the previous connection requests. In
`
`certain other multi-stage networks of the type described herein, any connection request of
`
`unicast from an inlet link to an outlet link of the network can be satisfied without
`
`blocking with never needing to rearrange any of the previous connection requests.
`
`Nonblocking configurations for other types of networks with numerous
`
`conncction topologics and scheduling mcthods are disclosed as follows:
`
`1) Strictly and rearrangeably nonblocking for arbitrary fan-out multicast and
`
`unicast for generalized butterfly fat tree networks Vor (N,,N,,d,s) with numerous
`
`connection topologies and the scheduling methods are described in detail in U.S.
`
`Provisional Patent Application, Attorney Docket No. M-0038 USthat is incorporated by
`
`reference above.
`
`2) Rearrangeably nonblocking for arbitrary fan-out multicast and unicast, and
`
`strictly nonblocking for unicast for generalized multi-link multi-stage networks
`
`Viwinae ON, N>,d,8) and generalized folded multi-link multi-stage networks
`
`Vout—mtinn (N,,N>,d@,5) with numerous connection topologies and the scheduling methods
`
`are described in detail in U.S. Provisional Patent Application, Attorney Docket No. M-
`
`0039 USthatis incorporated by reference above.
`
`3) Strictly and rearrangeably nonblocking for arbitrary fan-out multicast and
`
`unicast for generalized multi-link butterfly fat tree networks V,i.5; (N,,N2,.d,5) with
`
`-7-
`
`Page 9 of 98
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`

`

`M-0037 US
`
`numerous connection topologies and the scheduling methods are described in detail in
`
`U.S. Provisional Patent Application, Attorney Docket No. M-0040 USthatis
`
`incorporated by reference above.
`
`4) Strictly and rearrangeably nonblocking for arbitrary fan-out multicast and
`
`unicast for generalized folded multi-stage networks V,,,,(N,,N,,d,5) with numerous
`
`connection topologies and the scheduling methods are described in detail in US.
`
`Provisional Patent Application, Attorney Docket No. M-0041 USthatis incorporated by
`reference above.
`
`10
`
`15
`
`5) Strictly nonblocking for arbitrary fan-out multicast for generalized multi-link
`
`multi-stage networksV,,,,,,(NV,,N,,d,s5) and generalized folded multi-link multi-stage
`
`networks Vowad min (N,,N,,d,s) with numerous connection topologies and the scheduling
`
`methodsare described in detail in U.S. Provisional Patent Application, Attorney Docket
`
`No. M-0042 US thatis incorporated by reference above.
`
`6) VLSI layouts of generalized multi-stage networks V(N,,N,,d,5), generalized
`
`folded multi-stage networks V,,,,(N,,N,,d,s), generalized butterfly fat tree networks
`
`Vin (Ni N,.d,5), generalized multi-link multi-stage networks V,,,,,,(N,,N.,d.5),
`
`generalized folded multi-link multi-stage networks Vpod—mtinkN,»N>,d,5), generalized
`multi-link butterfly fat tree networks Vm‘int N,,N,.d,5), and generalized hypercube
`
`networksV,_,. (N,,N,,d,s) fors = 1,2,3 or any numberin general, are described in
`
`20
`
`detail in U.S. Provisional Patent Application, Attorney Docket No. M-0045 USthatis
`
`incorporated by reference above.
`
`Symmetric RNB Embodiments:
`
`Referring to FIG. 1A, in one embodiment, an exemplary symmetrical multi-stage
`
`network 100A with five stages of thirty two switches for satisfying communication
`
`iwa
`
`requests, such as setting up a telephonecall or a data call, or a connection between
`
`configurable logic blocks, between an input stage 110 and output stage 120 via middle
`
`stages 130, 140, and 150 is shown where input stage 110 consists of four, two by four
`
`-8-
`
`Page 10 of 98
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`Page 10 of 98
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`

`

`M-0037 US
`
`switches IS1-IS4 and output stage 120 consists of four, four by two switches OS1-OS4.
`
`Andall the middle stages namely middle stage 130 consists of eight, two by two switches
`
`MS(1,1) - MS(1,8), middle stage 140 consists of eight, two by two switches MS(2,1) -
`
`MS(2,8), and middle stage 150 consists of eight, two by two switches MS(3,1) - MS@,8).
`
`Such a network can be operated in strictly non-blocking mannerfor unicast
`
`connections, because the switches in the input stage 110 are of size two by four, the
`
`switches in output stage 120 are of size four by two, and there are eight switches in each
`
`of middle stage 130, middle stage 140 and middle stage 150. Such a network can be
`
`operated in rearrangeably non-blocking manner for multicast connections, because the
`
`10
`
`switchesin the input stage 110 are of size two by four, the switches in output stage 120
`
`are of size four by two, and there are eight switches in each of middle stage 130, middle
`
`stage 140 and middle stage 150.
`
`In one embodimentof this network each of the input switches IS1-IS4 and output
`
`switches OS1-OS4are crossbar switches. The numberof switches of input stage 110 and
`
`of output stage 120 can be denoted in general with the variable = , WhereWNisthe total
`
`15
`
`numberof inlet links or outlet links. The number of middle switches in each middle stage
`
`is denoted by axe . The size of each input switch IS1-IS4 can be denoted in general
`
`with the notation d *2d and each output switch OS1-OS4 can be denoted in general with
`
`the notation 2d *d. Likewise, the size of each switch in any of the middle stages can be
`
`denoted as d*d. A switch as used herein can be either a crossbar switch, or a network
`
`of switches each of which in turn may be a crossbar switch or a network of switches. A
`
`symmetric multi-stage network can be represented with the notation V(NV,d,s), where
`
`N represents the total numberofinlet links of all input switches (for example the links
`
`IL1-IL8), d represents the inlet links of each input switch or outlet links of each output
`
`switch, and s is the ratio of number of outgoing links from each input switch to the inlet
`
`links of each input switch. Althoughit is not necessary that there be the same numberof
`
`inlet links IL1-IL8 as there are outlet links OL1-OL8, in a symmetrical network they are
`
`the same.
`
`Page 11 of 98
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`

`

`M-0037 US
`
`Each of the - input switches IS] —IS4 are connected to exactly 2xd switches
`
`a
`
`in middle stage 130 through 2d links (for example input switch IS1 is connected to
`
`middle switches MS(1,1), MS(1,2), MS(1,5) and MS(1,6) through the links ML(1,1),
`
`ML(1,2), ML(1,3) and ML(1,4) respectively).
`
`Each of the 2x0 middle switches MS(1,1) - MS(1,8) in the middle stage 130
`
`are connected from exactly d input switches through d links (for examplethe links
`
`ML(1,1) and ML(1,5) are connected to the middle switch MS(1,1) from input switch IS1
`
`and IS2 respectively) and also are connected to exactly d switches in middle stage 140
`
`through d links (for example the links ML(2,1) and ML(2,2) are connected from middle
`
`10
`
`switch MS(1,1) to middle switch MS(2,1) and MS(,3) respectively).
`
`Similarly each of the 2x= middle switches MS(2,1) — MS(2,8) in the middle
`
`stage 140 are connected from exactly d switches in middle stage 130 through d links
`
`(for example the links ML(2,1) and ML(2,6) are connected to the middle switch MS(2,1)
`
`from middle switches MS(1,1) and MS(1,3) respectively) and also are connected to
`
`15
`
`exactly d switches in middle stage 150 through d links (for example the links ML(3,1)
`
`and ML(3,2) are connected from middle switch MS(2,1) to middle switch MS(3,1) and
`
`MS(3,3) respectively).
`
`Similarly each of the 2x middle switches MS(3,1) — MS(3,8) in the middle
`
`stage 150 are connected from exactly d switches in middle stage 140 through d links
`
`(for example the links ML(3,1) and ML(3,6) are connected to the middle switch MS(3,1)
`
`from middle switches MS@,1) and MS(@,3) respectively) and also are connected to
`
`exactly d output switches in output stage 120 through d links (for example the links
`
`ML(4,1) and ML(4,2) are connected to output switches OS1 and OS2 respectively from
`
`middle switches MS(3,1)).
`
`-10-
`
`Page 12 of 98
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`

`

`M-0037 US
`
`Each of the - output switches OSI — OS4 are connected from exactly 2xd
`
`a
`
`switches in middle stage 150 through 2d links (for example output switch OS1 is
`
`connected from middle switches MS(3,1), MS(3,2), MS(3,5) and MS(3,6) through the
`
`links ML(4,1), ML(4,3), ML(4,9) and ML(4,11) respectively).
`
`Finally the connection topology of the network 1OOA shownin FIG. 1A is known
`
`to be back to back inverse Benes connection topology.
`
`Referring to FIG. 1A1, in another embodiment of network V(N,d, 5s), an
`
`exemplary symmetrical multi-stage network 100A1 with five stages of thirty two
`
`switches for satisfying communication requests, such as setting up a telephonecall or a
`
`10
`
`15
`
`data call, or a connection between configurable logic blocks, between an input stage 110
`
`and output stage 120 via middle stages 130, 140, and 150 is shown where inputstage 110
`
`consists of four, two by four switches IS1-I$4 and output stage 120 consists of four, four
`
`by two switches OS1-OS4. And all the middle stages namely middle stage 130 consists of
`
`eight, two by two switches MS(1,1) - MS(1,8), middle stage 140 consists of eight, two by
`
`two switches MS(2,1) - MS(2,8), and middle stage 150 consists of eight, two by two
`
`switches MS(3,1) - MS(3,8).
`
`Such a network can be operated in strictly non-blocking mannerfor unicast
`
`connections, because the switches in the input stage 110 are of size two by four, the
`
`switches in output stage 120 are of size four by two, and there are eight switches in each
`
`of middle stage 130, middle stage 140 and middle stage 150. Such a network can be
`
`operated in rearrangeably non-blocking mannerfor multicast connections, because the
`
`switches in the input stage 110 are of size two by four, the switches in output stage 120
`
`are of size four by two, and there are eight switches in each of middle stage 130, middle
`
`stage 140 and middle stage 150.
`
`25
`
`In one embodiment of this network each of the input switches IS1-IS4 and output
`
`switches OS1-OS4are crossbar switches. The numberof switches of input stage 110 and
`
`of output stage 120 can be denoted in general with the variable = , WhereWNisthe total
`
`numberof inlet links or outlet links. The number of middle switches in each middle stage
`
`-l1-
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`is denoted by 2x . The size of each input switch IS1-IS4 can be denoted in general
`
`with the notation d *2d and each output switch OS1-OS4 can be denoted in general with
`
`the notation 2d *d. Likewise, the size of each switch in any of the middle stages can be
`
`denoted as d *d. A switch as used herein can beeither a crossbar switch, or a network
`
`of switches each of which in turn may be a crossbar switch or a network of switches. The
`
`symmetric multi-stage network of FIG. 1A1 is also the network of the type V(NV,d,s),
`
`where N represents the total numberofinlet links of all input switches (for example the
`
`links IL1-IL8), d represents the inlet links of each input switch or outlet links of each
`
`output switch, and s is the ratio of number of outgoing links from each input switch to
`
`10
`
`the inlet links of each input switch. Althoughit is not necessary that there be the same
`
`numberof inlet links IL1-IL8 asthere are outlet links OL1-OL8, in a symmetrical
`
`networkthey are the same.
`
`Eachof the = input switches IS1 —IS4 are connected to exactly 2xd switches
`
`a
`
`in middle stage 130 through 2d links (for example input switch IS1 is connected to
`
`15
`
`middle switches MS(1,1), MS(1,2), MS(1,5) and MS(1,6) through the links ML(1,1),
`
`ML(1,2), ML(1,3) and ML(1,4) respectively).
`
`Each of the 2x middle switches MS(1,1) — MS(1,8) in the middle stage 130
`
`are connected from exactly d input switches through d links (for example the links
`
`ML(1,1) and ML(1,9) are connected to the middle switch MS(1,1) from input switch IS1
`
`20
`
`and IS3 respectively) and also are connected to exactly d switches in middle stage 140
`
`through d links (for example the links ML@,1) and ML(@,2) are connected from middle
`
`switch MS(1,1) to middle switch MS(2,1) and MS(2,2) respectively).
`
`Similarly each of the 2x= middle switches MS(2,1) — MS(@,8)in the middle
`
`stage 140 are connected from exactly d switches in middle stage 130 through d links
`
`(for example the links ML(2,1) and ML(2,5) are connected to the middle switch MS(2,1)
`
`from middle switches MS(1,1) and MS(1,3) respectively) and also are connected to
`
`exactly d switches in middle stage 150 through d links (for example the links ML(3,1)
`-12-
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`and ML(3,2) are connected from middle switch MS(2,1) to middle switch MS(3,1) and
`
`MS(3,2) respectively).
`
`Similarly each of the 2x2 middle switches MS(3,1) — MS(3,8) in the middle
`
`stage 150 are connected from exactly d switches in middle stage 140 through d links
`
`(for example the links ML(3,1) and ML(3,5) are connected to the middle switch MS(3,1)
`
`from middle switches MS(@,1) and MS(2,3) respectively) and also are connected to
`
`exactly d output switches in output stage 120 through d links (for example the links
`
`ML(4,1) and ML(4,2) are connected to output switches OS1 and OS2 respectively from
`
`middle switches MS(3,1)).
`
`10
`
`Each of the - output switches OS] — OS4 are connected from exactly 2xd
`
`a
`
`switches in middle stage 150 through 2d links (for example output switch OS1 is
`
`connected from middle switches MS(G,1), MS(3,3), MS(3,5) and MS(3,7) through the
`
`links ML(4,1), ML(4,5), ML(4,9) and ML(4,13) respectively).
`
`Finally the connection topology of the network 1OQAI shown in FIG. 1A1 is
`
`15
`
`known to be back to back Omega connection topology.
`
`Referring to FIG. 1A2, in another embodiment of network V(N, d,s), an
`
`exemplary symmetrical multi-stage network 100A2 with five stages of thirty two
`
`switches for satisfying communication requests, such as setting up a telephonecall ora
`
`data call, or a connection between configurable logic blocks, between an input stage 110
`
`and output stage 120 via middle stages 130, 140, and 150 is shown where inputstage 110
`
`consists of four, two by four switches IS1-IS4 and output stage 120 consists of four, four
`
`by two switches OS1-OS4. And all the middle stages namely middle stage 130 consists of
`
`eight, two by two switches MS(1,1) - MS(1,8), middle stage 140 consists of eight, two by
`
`two switches MS(2,1) - MS(2,8), and middle stage 150 consists of eight, two by two
`
`tNa
`
`switches MS(3,1) - MS(3,8).
`
`Such a network can be operated in strictly non-blocking mannerfor unicast
`
`connections, because the switches in the input stage 110 are of size two by four, the
`
`-13-
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`M-0037 US
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`switches in output stage 120 are of size four by two, and there are eight switches in each
`
`of middle stage 130, middle stage 140 and middle stage 150. Such a network can be
`
`operated in rearrangeably non-blocking manner for multicast connections, because the
`
`switches in the input stage 110 are of size two by four, the switches in output stage 120
`
`are of size four by two, and there are eight switches in each of middle stage 130, middle
`
`stage 140 and middle stage 150.
`
`In one embodiment of this network each of the input switches IS1-IS4 and output
`
`switches OS1-OS4 are crossbar switches. The numberof switches of input stage 110 and
`
`of output stage 120 can be denoted in general with the variable = , WhereJNisthe total
`
`10
`
`numberof inlet links or outlet links. The number of middle switches in each middle stage
`
`is denoted by 2xa . The size of each input switch IS1-IS4 can be denoted in general
`
`with the notation d*2d and each output switch OS1-OS4 can be denoted in general with
`
`the notation 2d *d. Likewise, the size of each switch in any of the middle stages can be
`
`denoted as d *d. A switch as used herein can be either a crossbar switch, or a network
`
`15
`
`of switches each of which in turn may be a crossbar switch or a network of switches. The
`
`symmetric multi-stage network of FIG. 1A2 is also the network of the type V(N, d,s),
`
`where N represents the total numberofinlet links of all input switches (for example the
`
`links IL1-IL8), d represents the inlet links of each input switch or outlet links of each
`
`output switch, and s is the ratio of number of outgoing links from each input switch to
`
`the inlet links of each input switch. Although it is not necessarythat there be the same
`
`numberof inlet links [L1-IL8 as there are outlet links OL1-OL8, in a symmetrical
`
`network they are the same.
`
`Eachof the = input switches IS1 —IS4 are connected to exactly 2xd switches
`
`a
`
`in middle stage 130 through 2xd links (for example input switch IS1 is connected to
`
`i) ws
`
`middle switches MS(1,1), MS(1,2), MS(1,5) and MS(1,6) through the links ML(1,1),
`
`ML(1,2), ML(1,3) and ML(1,4) respectively).
`
`-[4-
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`M-0037 US
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`Each of the 2x0 middle switches MS(1,1) - MS(1,8) in the middle stage 130
`
`are connected from exactly d input switches through d links (for example the links
`
`ML(1,1) and ML(1,14) are connected to the middle switch MS(1,1) from input switch IS1
`
`and IS4 respectively) and also are connected to exactly d switches in middle stage 140
`
`through d links (for example the links ML(2,1) and ML(2,2) are connected from middle
`
`switch MS(1,1) to middle switch MS(2,1) and MS(2,2) respectively).
`
`Similarly each of the 2x= middle switches MS(2,1) — MS(2,8) in the middle
`
`stage 140 are connected from exactly d switches in middle stage 130 through d links
`
`(for example the links ML(2,1) and ML(2,8) are connected to the middle switch MS(2,1)
`
`10
`
`from middle switches MS(1,1) and MS(1,4) respectively) and also are connected to
`
`exactly d switches in middle stage 150 through d links (for example the links ML(3,1)
`
`and ML(3,2) are connected from middle switch MS(2,1) to middle switch MS(3,1) and
`
`MS(3,2) respectively).
`
`Similarly each of the 2x middle switches MS(3,1) — MS(3,8) in the middle
`
`15
`
`stage 150 are connected from exactly d switches in middle stage 140 through d links
`
`(for example the links ML(3,1) and ML(3,8) are connected to the middle switch MS(3,1)
`
`from middle switches MS(2,1) and MS(2,4) respectively) and also are connected to
`
`exactly d output switches in output stage 120 through d links (for example the links
`
`ML(4,1) and ML(4,2) are connected to output switches OS1 and OS2 respectively from
`
`middle switches MS(3,1)).
`
`Fach of the
`
`d
`
`output switches OS1 — OS4 are connected from ex