PTO/SB/16 (2-98)
`Approved for use through 01/31/2001. OMB 0651-0037
`Patent and Trademark Office: U.S. DEPARTMENT OF COMMERCE
`Under the Paperwork Reduction Act of 1995, no persons are required to respond to a collection of information unless it displays a
`valid OBM control number.
`
`s--22-UU
`
`n;A
`1Pot/
`
`PROVISIONAL APPLICATION FOR PATENT COVER SHEET
`This is a reauest for filina a PROVISIONAL APPLICATION FOR PATENT under 37 CFR 61.53lcl.
`INVENTORlSl
`
`""''
`
`Given Name (first and middle rif anvn
`Hui
`Aamod
`Robert
`
`Familv Name or Surname
`
`Jin
`Khandekar
`McEiiece
`
`Residence
`rcitv and e1ther State or Foreian Countrvl
`Pasadena, CA
`Pasadena, CA
`Pasadena, CA
`
`n Additional inventors are beina named on the _o_ seJ)aratehf_numbered sheets attached hereto.
`TITLE OF THE INVENTION 1280 characters max)
`SERIAL INTERCONNECTION OF A LOW-DENSITY GENERATOR CODE WITHA DIGITAL RECURSIVE
`FILTER
`
`Direct all correspondence to-
`[x] Customer Numb+:20985
`OR
`[X] Firm or
`Individual Name
`Address
`
`CORRESPONDENCE ADDRESS
`
`I
`
`• Place Customer Number
`
`Bar Code Label Here
`
`Fish & Richardson P.C. (Southern California)
`
`Countrv
`
`[X] Specification
`
`[] Drawing(s)
`
`4350 La Jolla Village Drive, Suite 500
`San Dieao CA 92122
`I Fax I (858) 678-5m~9
`I Telephone I (858) 678-5070
`United States
`ENCLOSED APPLICATION PARTS (c_hec_k all that aDD/vJ
`Number of Pages~ [] Small Entity Statement
`Number of Sheets ~ [] Other (specify) I
`
`I
`
`METHOD OF PAYMENT OF FILING FEES FOR THIS PROVISIONAL APPLICATION FOR PATENT fcheck 01neJ
`[X] A check or money order is enclosed to cover the filing fees.
`FILING FEE
`AMOUNT($)
`
`[] The Commissioner is hereby authorized to charge filing
`
`I
`fees or credit any overpayment to Deposit Account Number: 06-1050 I
`
`l $150
`
`]
`
`The invention was made by an agency of the United States Government or under a contract with an
`agency of the United States Government.
`[] No.
`[X] Yes, the name of the U.S. Government agency and the Government contract number are: Grant No.
`CCR-9804793
`
`Respectfully submitted,
`
`Sign~ture
`
`Name Scott C Harris, Reg No 32,030
`
`Telephone No. \-0-i.l.llf-.u..Lo=~~-------­
`
`CERTIFICATE OF MAILING BY EXPRESS MAIL
`Express Mail Label No. XFI 584936525115
`I hereby certify that this correspondence is being
`deposited with the United States Postal Service as
`Express Mail Post Office to Addressee with sufficient
`postage on the date indicated below and is
`addressed to the Commissioner of Patents,
`Washington, D.C. 20231.
`
`Date of Depo~ XMF>¥-J~~o
`
`Signature J WA i/1/t -l--f'_ ?"';)/
`
`I
`
`Docket No. 06618/63700 1/CII3220
`10034769.doc
`
`Typed Name of Person Signing XDerek w Norwood
`
`Hughes, Exh. 1009, p. 1
`
`

`
`Attorney's Docket No.: 06618/637001/ CIT3220
`
`PROVISIONAL APPLICATION FOR PATENT
`
`under
`
`37 CFR §1.53(c)
`
`TITLE:
`
`SERIAL INTERCONNECTION OF A LOW-DENSITY
`GENERATOR CODE WITHA DIGITAL RECURSIVE
`FILTER
`
`APPLICANT:
`
`HUI JIN, AAMOD KHANDEKAR AND ROBERT
`MECLIECE
`
`CERTIFICATE OF MAILING BY EXPRESS MAIL
`
`Express Mail Label No.
`
`EL584936525US
`
`I hereby certifY under 3 7 CFR § 1.10 that this correspondence is being
`deposited with the United States Postal Service as Express Mail Post
`Office to Addressee with sufficient postage on the date indicated below
`is addressed to the Commissioner of Patents, Washington,
`and
`D.C. 20231.
`
`Derek W. Norwood
`Typed or Printed Name of Person Signing Certificate
`
`Hughes, Exh. 1009, p. 2
`
`

`
`05-18-ZOOO
`
`04:28pm
`
`From-
`
`T-297
`
`P.OOS/037
`
`F-644
`
`.::t:
`
`c: -· c.. -· ::l
`
`Hughes, Exh. 1009, p. 3
`
`

`
`05·18-2000
`
`04:29pm
`
`From·
`
`r-zer
`
`P. oos/037
`
`f!-644
`
`(D
`
`G)
`$l) -
`
`-Ill(
`
`r
`0
`~ I c
`~ t.n -·
`,....
`.,
`<
`-$l) "'
`.... -·
`(C
`.....
`CD
`....... <
`co
`0) n
`c.u
`::T
`C1) n
`n
`0 c.
`(I)
`tn
`
`I
`
`~
`
`Hughes, Exh. 1009, p. 4
`
`

`
`""'" :;
`I .....
`.._
`~ .......
`.._
`= c:>
`n...
`.._
`.... I
`
`CD
`
`I -
`
`Irregular LDPC Codes
`
`• Idea: introduce irregularity into degree of variable nodes
`and check nodes.
`
`• Binary erasure channel: Luby, Mitzenmacher, Shokrol(cid:173)
`lahi, Spielman, 1997.
`
`• AWGN, Binary symmetric channel: Richardson, Urbanke,
`
`~
`....
`
`Shokrollahi, 1999 .
`
`CJ3
`
`E a..
`.....
`....,.
`
`c::>
`
`c::>
`Cl
`~
`J.
`~
`
`3
`
`Hughes, Exh. 1009, p. 5
`
`

`
`"'<!"
`~
`I
`~
`
`,.._
`""' Cl
`~
`Cl
`c:J
`
`0...
`
`,.._
`m .... I
`
`1-
`
`Drawback of LDPC codes
`
`,
`
`--
`
`-At~nough decoding complexity is linear, natural
`-e·,·~coding complexity is quadratic.
`-
`
`== 0
`
`LL
`
`E ... en
`"'
`
`"'<!"
`0
`
`<=I
`0
`
`a:>
`
`0 "' I
`J: c:J
`
`4
`
`Hughes, Exh. 1009, p. 6
`
`

`
`05-18-2000
`
`04:30pm
`
`From-
`
`T-297
`
`P.OOQ/037
`
`F-644
`
`::0
`
`(1) < -·
`~
`0 ....
`::0
`l>
`n
`0 c.
`
`(I)
`fl)
`
`I
`I
`
`•
`
`I
`
`•
`
`•
`
`I
`I
`
`•
`
`I
`I
`I
`
`•
`
`I
`
`•
`
`Hughes, Exh. 1009, p. 7
`
`

`
`05-18·2000
`
`04:30pm
`
`F ram-
`
`T·Z97
`
`P. 010/037
`
`i=-644
`
`•
`
`•
`
`I
`
`~:;J
`
`I
`I
`
`•
`
`•
`
`I
`I
`
`•
`
`I
`I
`I
`
`•
`
`•
`
`I
`I
`
`•
`
`~n
`
`::a
`:l=-
`10 c.
`tD
`D) en
`tu
`:::J
`r
`c
`-a
`0
`n
`0
`c.
`CD
`
`Hughes, Exh. 1009, p. 8
`
`

`
`Irregular RA codes: Graph Representation
`Variable Node
`Check Node
`Fraetlon of nodes
`Degree K
`Degree i
`
`-,
`,
`\
`·---/~
`
`•
`•
`•
`
`I
`\
`l
`I
`r
`r
`l
`I
`\
`I
`\
`I
`·----\-o~
`'
`,_
`~ ..............
`
`...r
`~
`J_
`,.__ ..,
`c:>
`........
`=
`
`Q_
`
`,.__
`<»
`Nl
`I
`I -
`
`I
`E
`0
`
`LL.
`
`E ... =
`"" ..... =
`= = =
`"' J, ::: =
`
`f2
`
`f3
`
`fJ
`
`-,
`,
`•··- .. ~~
`' :-1--
`
`\
`
`,
`,
`
`1
`I
`l
`
`I
`I
`I
`
`·---'\--~
`\ -~
`,_
`~
`\
`
`____ /_,_-~',
`I
`\
`r
`I
`l
`
`:
`I •
`I
`
`:
`•
`
`·---~--~
`.
`'-"
`
`\
`\
`
`I
`
`:
`
`z
`0
`E=:
`~
`
`~
`
`~
`~
`~
`
`0-------
`
`-----e
`
`-----e
`
`-----e
`
`----..
`
`_____ ..
`
`7
`
`Hughes, Exh. 1009, p. 9
`
`

`
`05-18-ZODD
`
`04:30pm
`
`From-
`
`T·Z97
`
`P.DlZ/037
`
`F-644
`
`~ ~
`
`p ~
`
`p ~ ~ ~
`
`.... .. -.
`m
`~ c .....
`~ -.
`~ >
`n
`0
`~
`~
`0
`• •
`0
`~ c
`n
`~ c
`-. m
`
`~
`
`~:G
`
`Hughes, Exh. 1009, p. 10
`
`

`
`-~
`
`.t
`....
`~
`~
`c:J
`
`0....
`
`Problem Specification
`
`I-(cid:173)
`CD
`
`.... I
`
`1-
`
`... _,·•·6iven a degree profile, how to compute the
`
`iterative decoding threshold?
`
`• How to optimize this degree profile, i.e. find a
`
`..
`
`profile giving the best threshold?
`
`9
`
`I
`E
`~
`1L
`
`E
`a..
`
`..,
`...,.
`=
`
`c:J
`c::J
`c:J
`
`"" I co
`I
`:g
`
`Hughes, Exh. 1009, p. 11
`
`

`
`--to
`....... -c::>
`
`.L
`,__
`tr.l =
`
`0...
`
`,__
`""" I
`
`CD
`
`1-
`
`Message Passing: Variable nodes
`
`·---
`
`~ cr-----•
`~
`
`• The output message depends on the incoming mes(cid:173)
`sages from the other neighbors.
`
`• Assume messages are log-likelihood ratios, i.e. M =
`In :f~~,
`
`Mout = E Mi.
`iEin
`
`10
`
`1
`
`E a.
`
`tr.l
`
`~
`
`CJ
`
`= c:>
`"" J,
`I
`~
`
`Hughes, Exh. 1009, p. 12
`
`

`
`Message Passing: Check nodes
`
`-
`
`•. The output message depends on· the incoming mes(cid:173)
`
`sages from the other neighbors.
`
`•· (Po- Pl)out = IliEinCPo - Pl)i, i.e.,
`M·
`M
`au = IT tanh__!.
`tanh
`2
`2
`
`iEin
`
`t
`
`11
`
`-.t v
`.L
`
`Ul
`
`~
`c::J
`........
`
`1£)
`
`0
`
`ll..
`
`~ .....
`
`I
`1-
`
`I
`E
`0
`
`lL
`
`E
`0..
`..,
`...:!"
`c::>
`
`= g
`"" I
`~
`
`CD
`
`Hughes, Exh. 1009, p. 13
`
`

`
`05·18·2000
`
`04:32pm
`
`From-
`
`T·Z97
`
`P. 016/037
`
`!=·644
`
`Hughes, Exh. 1009, p. 14
`
`

`
`Density Evolution
`
`Assume P(M) is the probability density function of ran-
`
`dom variable M, we can track the density evolution by the
`
`message passing rule .
`
`• -Variable nodes:
`
`P(Mout) = P(Mi1 ) ® P(Mi2 ) ... ® P(Mik),
`
`• Check nodes: similar.
`
`13
`
`"<I"
`~
`.L
`.....
`<">
`c:>
`.......
`,.__
`=
`
`03..
`
`~
`
`I -
`
`:: 0
`
`...__
`
`E
`<L
`Nl
`
`....
`"<I" =
`= g
`
`Nl
`I
`ttl
`
`~
`
`t
`
`I
`
`Hughes, Exh. 1009, p. 15
`
`

`
`. Simplification
`
`Assume the messages from check nodes to vari(cid:173)
`
`able nodes are Gaussian distributed.
`
`• Approximation is good at variable nodes, poor
`at check nodes. But it's OK for design pur(cid:173)
`
`pose.
`
`• With a consistency condition (2J.L = u 2}, we
`can just propagate the mean Jl;.
`
`14
`
`...q(cid:173)
`...q(cid:173)
`U>
`.L
`
`:;;-
`<=>
`......
`lXI
`<=>
`"-
`,.__
`......
`I
`1-
`
`CJ3
`
`I
`E
`0
`.......
`
`E
`D..
`~
`"""'" =
`= :5
`.....
`
`I
`CXl
`I
`~
`
`I
`
`•
`
`Hughes, Exh. 1009, p. 16
`
`

`
`05-18-2000
`
`04:32pm
`
`From-
`
`T-Z97 P 019/037
`
`F-644
`
`1;:
`~
`
`c.""io-
`~
`
`~ ~
`II
`~.M
`;3
`1:
`~~ ..........,
`
`~-
`
`~
`
`?!
`~
`'"""" -· SJ)
`C"" -CD
`::l
`0 a.
`CD
`CIJ -
`
`/• •'
`
`'
`
`....
`
`U'l
`
`' I
`
`I
`I
`
`9 I
`~ •
`
`I
`I
`
`:s:
`(I)
`!OJ
`::1
`1-a
`I~ 10
`'iC
`:D)
`tQ
`
`,::J
`
`\! Q)
`1 . . . -· 10
`
`Hughes, Exh. 1009, p. 17
`
`

`
`Mean Propagation
`
`v :;-
`J....
`
`t(cid:173)
`tr.l
`......
`c::>
`c::>
`"" c::>
`
`13-
`
`t(cid:173)
`en
`
`"" I
`
`I-
`
`At check nodes,
`
`=
`
`E[tanh Mout]
`2
`
`M·
`II E[tanh
`t]
`2 '
`iEin
`_.
`M
`= 4> 1(E[tanh ;ut)),
`~t(Mout)
`where 4>(~t) = Eg(p,) [tanh 21.
`
`..
`..
`
`16
`
`I
`E
`0
`
`1..1...
`
`«:1
`
`E a.
`...,
`~
`
`C3
`c::>
`c::>
`
`"" J.
`~
`
`Hughes, Exh. 1009, p. 18
`
`

`
`Recursion
`
`Let uz = E[tanh ~],where mz is the message
`from right variable node to check node at lth iter(cid:173)
`ation. We obtain uz+l = F(uz), where F(x) is
`a ~!near function of fi, the degree profile.
`
`• We require ul --+ 1 as l approaches infinity.
`
`• Sufficient and necessary condition: F(x) > x ·
`for any x E [uo, 1).
`
`17
`
`'<!'
`'¢
`tD
`
`D...
`
`I .....
`,_
`~ ......
`.... =
`,._
`.... I
`
`CD
`
`1-
`
`I
`E
`0
`
`lL
`
`E
`<L
`co
`co
`
`...... =
`= g
`""' I
`I
`~
`
`00
`
`Hughes, Exh. 1009, p. 19
`
`

`
`05-18-201}0
`
`04:33pm
`
`From-
`
`T-297
`
`P.OZZ/037
`
`~-b44
`
`c: .,
`f..l..
`tD
`""""' n
`0
`:::l c. -·
`~ .-.... -· o·
`~ ::::s
`H
`...,.,_,
`v
`H -
`<(
`H
`m
`~
`0 -~
`
`... 114,
`
`s:
`s:u
`~-
`3 -· N
`
`CD
`0
`........
`C""
`CD
`
`Sl -· < CD
`
`~-M
`>
`
`~.
`
`-h c:
`::::s
`Sl
`-·
`0 ::s
`
`r -· ::s
`CD m
`...
`-a a c.a ... D)
`3 -· :l c.c
`... 0
`-c
`C" -CD
`3
`
`3
`
`~;
`
`....--""
`
`'--""
`•
`
`Hughes, Exh. 1009, p. 20
`
`

`
`Design Result I
`rate=1/3, capacity= -0.495 (dB)w
`4
`k
`2
`3
`12.
`0.278010 0.234698 0.218052
`!3
`0.296168 0.256297 0.278317
`/s
`0.193071
`!6
`0.425822 0.036196 0.169094
`f1o
`0.183948
`0.011995
`i l l
`f12
`f13
`f27
`128
`lTGA
`u*
`lfl
`(E1L)*(dB)
`Nn
`
`I
`
`~
`
`~ ..,
`l..
`::;;
`= ....... .., .....
`=
`
`D...
`
`.......
`.....
`CJl
`I
`1-
`
`D .._
`==
`
`E c..
`~
`...... =
`= g .....
`I :g
`
`I
`00
`
`0.054441
`0.225297
`
`1.1840
`1.1981
`0.190
`
`1.2415
`1.2607
`-0.250
`
`0.133492
`0.005100
`1.2615
`1.278
`-0.371
`
`I
`
`19
`
`Hughes, Exh. 1009, p. 21
`
`

`
`.q
`~
`.L
`,._
`~
`.......
`..q
`"' =
`a...
`,._
`CJ) "' I
`
`I--
`
`I
`E
`~
`u..
`
`E a.
`...:t
`(">
`...:t =
`= = =
`"" I
`I
`::g
`
`CD
`
`Design Result II
`r!:lta -=- 1/? l"'~n::u"'it\t · n 1 Q I riR\
`J#&.-7 "''-"'t"""'"''"'] -
`-• •- ,._.-,.
`k
`8
`8
`f2
`0.232757
`!3
`0.667892 0.314727
`0.252341
`f7
`fa
`0.0336604
`ftl
`112
`f1a
`f2o
`/46
`!48
`fss
`fsa
`u*
`J:i1
`( E1L )*(dB)
`Nn
`
`0.0962193
`0.0303382
`
`0.0118597
`0.0280972
`0.972
`0.26
`
`:-<
`
`20
`
`1\.A.L'-'-
`
`~-
`
`0.058720
`0.216137
`
`0.031812
`0.025439
`
`0.9589
`0.34
`
`Hughes, Exh. 1009, p. 22
`
`

`
`""" ~
`l
`,_
`
`to
`0
`~
`"" CJ
`"-
`
`:;;
`
`Nl
`I
`t-
`
`: : :: : : : : : : : : : : : : : : :: : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : :: : : : : : : : r
`
`Performance of rRA codes of lengths n=1cr, 104
`, rate=O.S
`-I
`10
`f~:-:-::--::-::-:-::-::-:-::-::-:-::-::-::-:-::-::~.-.:-::-:.-·:-::-::-:-::-::-:-::-::-::-:-::-::-::-:~:!~::-:-::-::-:-::-::-:.-·:-::-::-:-::-::-:-::-::-::~:~
`length 1 000
`, ..
`I
`th 1 0000
`eng
`
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`................................ ...............................
`
`• • ~ ~ . . . . . . . . . . . . . . . . . . . . . . ~ ·""'-· . . . . . . . . . . . . I . . . . . . . . . . . . ~ . . . . . . . . s
`
`~ . . . . . . . . . . . . ~ ' . . . \ . . . . . . . . . . ,. . . . . . . . I
`
`I . . . . . . . . . . . . . . . . . . . ' . . . . . . . ..
`
`: : : : : : : : : : : ; : : : : : : : : : : : : : : : : :~ : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : ; : : : : : : : : : : : : : : : : ; : : : : : : : : : :
`.................................. ; ..... ··"'· ...... ' ' .............. ; .... ' ....... ' .................. .
`.................................. , .... ~·-························~································
`. . . . . . . . . ... . . . . . . . . . . . . . . . . . . . . . : .... ' ..... ·'-:.. ............... ' ' . ' : .... ' ................... ' .... ' ..
`
`: ~ ~ : ~ ~ ~ ~ ~ i ~ ~ \~ ~ ~ : ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
`
`~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ! ; ~ ~ ~ ~ >(] ~ ~ ~ ~ i ~ ~ ~
`
`! ) ~ ~ ~ ~ ~ ! : ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ : ~ ~ ~ [ ~ ~ ~
`
`"0 0. 01110 ..
`
`t
`
`0
`
`11 C
`
`I
`
`.. " " , • • e
`
`t
`
`0 0 " I t I
`
`0
`
`I
`
`I
`
`I . . . r •. l
`
`..
`
`oo " 0 I " " 0 0 . 0 . " ~"I 0
`
`I
`
`l
`
`0 I"~" o
`
`0
`
`,_
`
`..
`
`.:.
`
`..
`
`"
`
`0
`
`I
`
`I
`
`0
`
`~ 0 a . 4
`
`4
`
`~ 0
`
`I
`
`I
`
`I
`
`I . . . I
`
`0 ~. ~. '0
`
`'0
`
`a
`
`o0
`
`0
`
`0
`
`a:
`w
`m
`
`10--3
`
`10-4
`
`p
`
`:
`
`0
`
`0
`
`S
`
`I
`
`...........
`
`I
`
`I
`
`0
`
`I
`
`0
`
`0
`
`._
`
`I'
`
`•
`
`"
`
`I
`
`..
`
`..
`
`"
`
`0o
`
`'"-
`
`I
`
`0
`
`'a
`
`I
`
`0
`
`•
`
`"
`
`0
`
`I
`
`"
`
`"-
`
`"
`
`o
`
`•
`
`~ •
`
`•
`
`o
`
`"
`
`'
`
`I
`
`•
`
`I
`
`I
`
`I
`
`I
`
`•
`
`0. ~ t
`
`I
`
`•
`
`~ •
`
`t
`
`I
`
`"
`
`"
`
`._
`
`I
`
`•
`
`0
`
`0
`
`o
`
`0
`
`I
`
`I
`
`~ I
`
`"
`
`..
`
`I
`
`o
`
`0
`
`I
`
`0
`
`0
`
`~ J ~ "
`
`11
`
`"
`
`I
`
`o
`
`'
`
`~ ~ I
`
`a
`
`'" ~ I
`
`o
`
`. . ' ... ' ................ '·" ..... ': .......... ' .... '
`
`' ........ ' ...... : ..... ' . ' ' .... '·"-· .............. .
`
`•
`
`!0
`
`p
`
`0'
`
`0'
`
`0-
`
`lo.
`
`•
`
`•
`
`•
`
`4
`
`..
`
`I
`
`•
`
`•
`
`•
`
`•
`
`0.
`
`•
`
`•
`
`•
`
`•
`
`a
`
`•
`
`I
`
`o
`
`•
`
`.. "
`
`0
`
`o.
`
`0
`
`0
`
`'0 1
`
`I
`
`"
`
`l
`
`"
`
`,_
`
`o.
`
`•
`
`•
`
`a
`
`•
`
`"
`
`I
`
`;> J
`
`"
`
`•
`
`o
`
`a o • • "
`
`a
`
`•
`
`10-6
`
`01'
`
`•
`
`1
`"
`
`1
`I
`
`0
`•
`
`ol
`
`..
`
`"
`
`•
`
`0
`
`•
`
`0
`
`I
`
`..
`
`I
`
`"
`
`!0
`
`0
`
`0.
`
`"
`
`l
`
`•
`
`II
`
`.0
`
`0'
`
`0.
`
`0
`
`I
`
`0
`
`S
`
`0
`
`0
`
`"
`
`"
`
`•
`
`0
`
`"
`
`t
`
`"
`
`"
`
`I
`
`"
`
`0
`
`I
`
`4
`
`'0
`
`0
`
`0
`
`I
`
`..-
`
`I
`
`"
`
`0
`
`0
`
`"
`
`0
`
`0
`
`'
`
`0
`
`"
`
`•
`
`S
`
`"
`
`I
`
`"
`
`I
`
`"
`
`"
`
`0
`
`I
`
`I
`
`I
`
`•
`
`"
`
`"
`
`I
`
`0
`
`"
`
`J.
`
`0
`
`J.
`
`I
`
`•
`
`S
`
`•
`
`•
`
`"
`
`"
`
`0
`
`•
`
`0.
`
`k
`
`I
`
`S
`
`0
`
`•
`
`.0
`
`'
`
`"'
`
`"
`
`"
`
`"
`
`0.
`
`"
`
`•
`
`~ I
`~ •
`,. " > +
`•
`>
`•
`•
`'"
`"
`"
`._
`"' a
`o
`s
`•
`'
`o. o
`o
`•
`•
`.. o
`..
`;
`o
`•
`"
`0 o
`•
`•
`a
`0 o
`r
`•
`"
`a
`a
`..
`l
`I-
`"
`•
`"
`t
`t
`0
`I
`•
`•
`•
`I
`I
`I
`0
`I
`I
`"
`•
`0
`I
`I
`I
`'"
`0
`•
`"
`"
`0
`I
`I
`I
`"
`I
`"
`I
`..
`I
`0
`0
`0
`•
`0
`•
`!0
`• o " " " ' • • ..
`..... 0 . " " "> " ' ' " - " I I " 0
`o . . . . . . . " I • ,_ I . . . . . . . . . " " 0 • • "
`0 . . . . •0 0.0 0 " • " " I . " 0 • • I
`. . . . " " . , ..
`0 I " .. 0
`0
`0 . . . . . . . ' "0 . 4 " "0 " " I • • "
`•
`.. + 0
`t
`.. "
`r
`;. o o
`o
`o
`•
`"
`o
`II o
`o
`•
`o
`•
`o
`o
`a
`<t
`.o
`,.
`~ "
`, .. ._,.,.•••••••'"•••••••••·•~'"''''l"'l"'""••·-·~•a••'"•~••••P•""~•~••• .. •L'" .. '""""'"""' .. "'"',.'"""""''"""''""'"'~""
`~ ..
`~ 0
`~ 0
`t-
`> .... '
`"
`..
`<
`a
`o
`•
`•
`._
`a
`a
`a
`r
`•
`•
`o.
`
`l
`
`I
`
`"
`
`"
`
`"
`
`I
`
`I
`
`..
`
`"
`
`0
`
`I• •
`
`0
`
`•
`
`4
`
`0
`
`I
`
`•
`
`I
`
`•
`
`4
`
`"
`
`11
`
`"
`
`0
`
`..
`
`"
`
`•
`
`0
`
`._
`
`•
`
`•
`
`"
`
`I
`
`I
`
`"
`
`..
`
`"
`
`0
`
`,a
`
`•
`
`0-
`
`0-
`
`•
`
`I
`
`0
`
`0.
`
`0'
`
`"
`
`0.
`
`0
`
`I
`
`"
`
`I
`
`•
`
`._
`
`•
`
`•
`
`0
`
`0
`
`"
`
`..
`
`I
`
`I
`
`"
`
`0
`
`l
`
`I
`
`I
`
`J.
`
`0
`
`•
`
`I
`
`"
`
`.. I
`
`I
`
`.0
`
`•
`
`I
`
`"
`
`0
`
`•
`
`"
`
`I
`
`I
`
`.. 0
`
`"
`
`I
`
`0
`
`I
`
`.. 0
`
`..
`
`I
`
`•
`
`a
`
`S
`
`0
`
`o • • •
`
`a ~ ..
`
`I
`
`«
`
`II
`
`I
`
`"
`
`"'
`
`"
`
`•
`
`I
`
`I
`
`o
`
`0
`
`._
`
`"
`
`I
`
`0
`
`•
`
`t
`
`•
`
`t-
`
`~ • • 10
`
`o-
`
`0
`
`"
`
`oo . . . .
`
`lo
`
`I
`
`•
`
`l
`
`-
`
`I
`
`"
`
`•
`
`I
`
`,.
`
`"
`
`.. "'
`
`•
`
`•
`
`•
`
`•
`
`0
`
`•
`
`I
`
`"
`
`I
`
`0
`
`1-
`
`•
`
`S
`
`0
`
`•
`
`-......................................... " . ~ .. : " " ................ -...................... ~ ..
`'
`.
`.
`
`•
`
`•
`
`~ '"
`
`I
`
`0
`
`•
`
`"
`
`I
`
`.o
`
`"'
`
`•
`
`•
`
`•
`
`•
`
`•
`
`"
`
`•
`
`o
`
`I
`
`•
`
`•
`
`"'
`
`'
`
`•
`
`o
`
`•
`
`•
`
`•
`
`0
`
`•
`
`"'
`
`I
`
`l
`
`o
`
`•
`
`..
`
`I
`
`I
`
`•
`
`•
`
`•
`
`"
`
`I
`
`o
`
`•
`
`•
`
`>
`
`.
`";. -. . ........................................... ..
`.
`.
`
`t
`
`•
`
`< •
`
`r
`
`..
`
`•
`
`•
`
`•
`
`•
`
`•
`
`•
`
`"
`
`o
`
`•
`
`•
`
`t
`
`~ •
`
`"' ~ "
`
`0.
`
`•
`
`•
`
`•
`
`•
`
`•
`
`'0
`
`0
`
`I
`E
`~
`u..
`
`a u::J
`
`<"> -=
`
`c::J =
`~
`J.
`J: =
`
`.. 0
`
`•
`
`. . . . l
`
`•
`
`•
`
`• • • 1
`
`"
`
`'
`
`"
`
`l
`
`. . . . o-
`
`"
`
`"
`
`•
`
`•
`
`I
`
`o
`
`-.
`
`:
`
`I
`
`"
`
`•
`
`S
`
`• + 0
`
`•
`
`0
`
`•
`
`<t
`
`•
`
`.. ~ "
`
`•
`
`0
`
`~ •
`
`•
`
`o
`
`•
`
`"
`
`o
`
`o
`
`0
`
`..
`
`"
`
`0
`
`•
`
`-.
`
`"'
`
`:
`
`I
`
`I
`
`..
`
`•
`
`I
`
`,. 0
`
`•
`
`o
`
`•
`
`>0 «
`
`'
`
`I
`
`"
`
`«
`
`..
`
`I
`
`I
`
`•
`
`-o
`
`0
`
`•
`
`•
`
`10~~------------------~------------------~----------------~
`0.5
`2
`1.5
`1
`SNR
`Hui Jin, 5/12/2000
`
`21
`
`Hughes, Exh. 1009, p. 23
`
`

`
`05-18·2000
`
`04:35pm
`
`From-
`
`T-297 P 026/037
`
`F-644
`
`Hughes, Exh. 1009, p. 24
`
`

`
`05-18-2000
`
`04:35pm
`
`From-
`
`•
`
`Hughes, Exh. 1009, p. 25
`
`

`
`05·18·2000
`
`04:36pm
`
`From·
`
`T-297 P 028/037
`
`F-B44
`
`Hughes, Exh. 1009, p. 26
`
`

`
`
`
`IESSS:Gammamofia/5omwmozw.
`
`
`
`
`
`
`
`
`
`am:an:.m:mBEwQ42332.39.Soosmssor
`
`
`
`.msmmsos3028Q:3%?
`
`8:8EmomwmomwomEm055:9.
`
`
`
`I>mm8a§_$5.95?03850.Wmm5:339.
`
`
`
`I:Wm26BmiB:B58E2:5:::n9.Bmmo:
`
`Hughes, Exh.
`
`Hughes, Exh. 1009, p. 27
`
`

`
`05-18-ZOOO
`
`04:38pm
`
`From-
`
`T-297
`
`P.D30/037
`
`F-644
`
`Hughes, Exh. 1009, p. 28
`
`

`
`05-18-ZOOO
`
`04:37pm
`
`From-
`
`T-Z97 P 031/037
`
`F-644
`
`II
`
`I
`
`Hughes, Exh. 1009, p. 29
`
`

`
`•
`~
`
`0
`
`~
`(D
`
`~- s
`
`•
`0... 0
`(D c:
`~
`~ (D
`(D
`~ ~"""+--
`~ C/'J
`C/'J
`(D ~ Cj
`U"J.
`C/'J
`~ PJ
`0
`-~ ~~
`(l)(JQ 0.. ~ aao
`0-(D
`(/'). 0.. Oo
`s ~
`(/0 VJ
`0
`~ ::s
`(D
`,__
`~. ~
`C/1
`,_.
`(!)
`ri ~
`0
`= 0
`(/";J ~ [/)
`C/:1 ~ C/'J
`(")
`p.J ~
`~. (D
`(JO
`0
`{JQ
`~ 0-
`~ 3 (])
`,.......
`,.... .
`,......
`C) P-'
`r'\ ~
`0
`.
`~ (D
`(Jq
`
`(D
`C/'J
`
`I
`
`.
`
`~ ::r
`C/) .
`
`0
`~
`~
`~
`~
`~
`~
`PJ
`~.
`~
`~
`(jQ
`~
`(D
`~
`CfQ
`~
`p)
`
`~
`('"""'!'-
`
`('"""'!'-
`
`•
`(D ,.,
`p.;;
`joooool.. < (D
`~
`
`~
`~
`~
`~
`~
`~
`~
`
`~
`~
`
`~ a
`~
`~
`Vj
`~
`~
`~
`~
`~
`~
`~
`~
`0
`P"'i
`~
`
`• I
`f
`0
`
`I
`I
`
`/\
`
`·-··- e e
`
`Hughes, Exh. 1009, p. 30
`
`

`
`
`
`Bwmmmmamin333.0m:mo:..Q.mm_.:.om.
`
`
`
`
`
`IOfimowsmBwmmmmwWm259::2.5ooB3m
`
`
`
`.E5330comm?
`
`
`
`IN96?oswmE5Qmmcaom.
`
`
`
`.03%Emma36%omBmmmmmwmu
`
`.>%90%somwmn
`
`
`
`50035Bommmmo.
`
`
`
`IOimorpmBwmmmmwWmmesa8Si:o:-oBmE.a
`
`
`
`Ummbmb._sm3mm.§I,mE»m
`
`Q\\~Q~\SmN
`
`Hughes, Exh.
`
`Hughes, Exh. 1009, p. 31
`
`

`
`_ 05-18-2000
`
`04:38pm
`
`From-
`
`T-Z97
`
`P 034/037
`
`F-844
`
`Hughes, Exh. 1009, p. 32
`
`

`
`~
`
`05·18-ZOOO
`
`04:38pm
`
`From-
`
`T-297
`
`P 035/037
`
`~-644
`
`Hughes, Exh. 1009, p. 33
`
`

`
`..
`
`.msoonssmEwmmw3592.
`
`
`
`
`
`92%..Ema/SE:oBa<oamoonssm.
`
`
`
`moEm<mom_omQQonSo358%oBmEd
`
`
`
`
`
`.44.08aim»momaaomonswsoom2::2.0%;
`
`
`
`
`
`
`
`Q55582%:9.._§,amooonmsm.
`
`
`
`<0?moonmoE..9.Bm:owon:5>302
`
`
`
`.Uwmawwmmnswmowmom:3%am=&8mw/5
`
`@333
`
`
`
`Hughes, Exh. 1009, p. 34
`
`

`
`•
`
`05-18-2000
`
`04:39pm
`
`From-
`
`T-297 P 037/037
`
`F-844
`
`•
`
`~
`
`~
`
`~
`C/'J
`
`•
`•
`•
`(/) ~ ~ ~· ~
`(/)
`"""1 ~ ~
`~ ~ ~ '(J)
`t"'""'+- ~
`< ~ (FJ
`(D ~
`t"""t-
`c::
`(D ~ 0
`(D
`("D
`(D ~ (D a
`0... ~ p.:J ~ (FJ
`C/)
`u
`.
`C/)
`r-""1'-
`~ c
`0
`~· en
`(")
`0 ~ en
`~ '"'U
`p..
`~ ~
`~·
`~ = ~
`~ CL ~· (D
`0
`,...,
`~
`cro
`~· ("""""f'-
`CL ~
`0
`p.?
`~ ~
`.
`~--+-)
`0
`~ """"'!
`C/':J
`9
`~
`~
`0
`(D
`C/'J
`(")
`~ 0
`<
`.
`
`~
`~
`~
`ao
`(D
`0..
`~
`~
`~
`
`~
`(/)
`
`'-I>
`
`(D
`
`(D
`
`~·
`C/)
`(/)
`""""".
`0
`(D
`0
`'""""1
`(F)
`~ 'JJ
`0
`~· ~
`p.j
`C/)
`~ C/)
`;........
`(D
`~ ~
`C/J
`~ """"".
`0
`0 ~
`~ ~ <
`~
`~.
`\)
`(D ~
`~ ; ': ~, ·.~ ~
`•.• .. ·.· .. ,
`(J
`·.: . ·~
`~ :::r
`~ k·~:)::r-
`~:f.~~ ~
`,.~,~~ ~.
`c
`rJ)
`(D
`
`~
`
`'
`'
`
`I a
`
`~
`~
`
`\
`
`Hughes, Exh. 1009, p. 35