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.
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`n;A
`1Pot/
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`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
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`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
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`
`

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`I .....
`.._
`~ .......
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`= c:>
`n...
`.._
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`
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`
`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,
`
`~
`....
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`Shokrollahi, 1999 .
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`
`

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`
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`
`Drawback of LDPC codes
`
`,
`
`--
`
`-At~nough decoding complexity is linear, natural
`-e·,·~coding complexity is quadratic.
`-
`
`== 0
`
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`
`Hughes, Exh. 1009, p. 6
`
`

`

`05-18-2DDB
`05-18-2000
`
`04:3me
`04:30pm
`
`Frnm-
`From-
`
`T-297
`T—297
`
`P.OOQ/037
`PMS/03?
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`
`Hughes, Exh. 1009, p. 7
`
`Hughes, Exh. 1009, p. 7
`
`

`

`_
`
`05-18·2000
`”WWW“
`
`04:30pm
`04=30Pm
`
`F ram-
`Frum-
`
`T·Z97
`T—ZBT
`
`P. 010/037
`REID/037
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`Hughes, Exh. 1009, p. 8
`
`Hughes, Exh. 1009, p. 8
`
`

`

`Irregular RA codes: Graph Representation
`Variable Node
`Check Node
`Fraetlon of nodes
`Degree K
`Degree i
`
`-,
`,
`\
`·---/~
`
`•
`•
`•
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`I
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`= = =
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`7
`
`Hughes, Exh. 1009, p. 9
`
`

`

`05-18-ZODD
`
`04:30pm
`
`From-
`
`T·Z97
`
`P.DlZ/037
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`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
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`I
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`
`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
`
`~
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`........
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`
`CD
`
`Hughes, Exh. 1009, p. 13
`
`

`

`.
`
`05·18·2000
`UE-Ia-Zflflfl
`
`04:32pm
`04:32pm
`
`From-
`Frum-
`
`T·Z97
`T-ZQ?
`
`P. 016/037
`Rum/037
`
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`8L
`
`
`
`991;uoglelndU-IOO
`
`Hughes, Exh. 1009, p. 14
`
`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"
`~
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`= g
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`
`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
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`
`Hughes, Exh. 1009, p. 16
`
`

`

`05-18-2000
`
`04:32pm
`
`From-
`
`T-Z97 P 019/037
`
`F-644
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`
`Hughes, Exh. 1009, p. 17
`
`

`

`Mean Propagation
`
`v :;-
`J....
`
`t(cid:173)
`tr.l
`......
`c::>
`c::>
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`
`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
`
`'<!'
`'¢
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`
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`co
`
`...... =
`= g
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`I
`~
`
`00
`
`Hughes, Exh. 1009, p. 19
`
`

`

`05-18-201}0
`
`04:33pm
`
`From-
`
`T-297
`
`P.OZZ/037
`
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`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
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`0.054441
`0.225297
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`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
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`= = =
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`
`Design Result II
`r!:lta -=- 1/? l"'~n::u"'it\t · n 1 Q I riR\
`J#&.-7 "''-"'t"""'"''"'] -
`-• •- ,._.-,.
`k
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`0.252341
`f7
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`0.0336604
`ftl
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`Nn
`
`0.0962193
`0.0303382
`
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`0.0280972
`0.972
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`
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`
`20
`
`1\.A.L'-'-
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`
`0.058720
`0.216137
`
`0.031812
`0.025439
`
`0.9589
`0.34
`
`Hughes, Exh. 1009, p. 22
`
`

`

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`
`Performance of rRA codes of lengths n=1cr, 104
`, rate=O.S
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