UNITED STATES PATENT AND TRADEMARK OFFICE
`_______________
`
`BEFORE THE PATENT TRIAL AND APPEAL BOARD
`______________
`
` APPLE, INC., HTC CORPORATION, HTC AMERICA, INC.,
`MICROSOFT CORPORATION, MICROSOFT MOBILE OY, MICROSOFT
`MOBILE, INC., SAMSUNG ELECTRONICS CO., LTD., SAMSUNG
`ELECTRONICS AMERICA, INC., AND ZTE (USA) INC.,
`PETITIONER,
`
`v.
`
`EVOLVED WIRELESS LLC,
`PATENT OWNER.
`______________
`
`Cases IPR2016-01208 and IPR2016-01209
`Patent 7,746,916 B2
`______________
`
`Record of Oral Hearing
`Held: September 15, 2017
`
`
`
`Before CHRISTOPHER L. CRUMBLEY, PATRICK M. BOUCHER,
`AND TERRENCE W. MCMILLIN, Administrative Patent Judges.
`
`
`
`
`_______________
`
`BEFORE THE PATENT TRIAL AND APPEAL BOARD
`______________
`
` APPLE, INC., HTC CORPORATION, HTC AMERICA, INC.,
`MICROSOFT CORPORATION, MICROSOFT MOBILE OY, MICROSOFT
`MOBILE, INC., SAMSUNG ELECTRONICS CO., LTD., SAMSUNG
`ELECTRONICS AMERICA, INC., AND ZTE (USA) INC.,
`PETITIONER,
`
`v.
`
`EVOLVED WIRELESS LLC,
`PATENT OWNER.
`______________
`
`Cases IPR2016-01208 and IPR2016-01209
`Patent 7,746,916 B2
`______________
`
`Record of Oral Hearing
`Held: September 15, 2017
`
`
`
`Before CHRISTOPHER L. CRUMBLEY, PATRICK M. BOUCHER,
`AND TERRENCE W. MCMILLIN, Administrative Patent Judges.
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`APPEARANCES:
`
`ON BEHALF OF THE PETITIONER:
`
` ROBERTO J. DEVOTO, ESQUIRE
` W. KARL RENNER, ESQUIRE
` Fish & Richardson, P.C.
` 1425 K Street, NW
` 11th Floor
` Washington, D.C. 20005
` 202.626.6393
`
`
`ON BEHALF OF THE PATENT OWNER:
`
` MILES A. FINN, PH.D., ESQUIRE
` RYAN M. SCHULTZ, ESQUIRE
` Robins Kaplan, LLP
` 299 Park Avenue
` Suite 3600
` New York, New York 10022
` 212.980.7439
`
` ALSO PRESENT:
` BAILE XIE
` ROB LYTLE
` CHARLES MCMAHON
` MELISSA DUCCA
` KEN GRAY
`
`
`The above-entitled matter came on for hearing on Friday, September
`
`15, 2017, commencing at 10:02 a.m. at the U.S. Patent and Trademark
`Office, 600 Dulany Street, Alexandria, Virginia in Courtroom A.
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`P R O C E E D I N G S
`- - - - -
` JUDGE MCMILLIN: We are here today for the oral
` argument in IPR2016-01208. IPR2016-01277 has been
` consolidated with that proceeding. And we are here for the
` argument in IPR2016-01209. IPR2016-01280 has been
` consolidated with that proceeding.
` Can we please have the appearances of counsel first
` for the Petitioner and please also tell us who you represent.
` MR. RENNER: Thank you. And good morning, Your
` Honors. I'm Karl Renner, and I'm here as lead counsel as
` well representing Microsoft entities and Apple. Joined by
` Rob Devoto and Baile Xie and also by representatives from
` Microsoft, Rob Lytle; ZTE, Charles McMahon; and Samsung,
` Melissa Ducca.
` JUDGE MCMILLIN: Is that everyone?
` MR. RENNER: That's us.
` JUDGE MCMILLIN: Who will be speaking on behalf of
` Petitioners today?
` MR. RENNER: Thanks for asking. Rob Devoto will be
` speaking, Your Honor.
` JUDGE MCMILLIN: Thank you.
` And Patent Owner?
` MR. SCHULTZ: Good morning, Your Honor. Ryan
` Schultz on behalf of the Patent Owner. With me is my
` colleague Dr. Miles Finn and representative Ken Gray from
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` Evolved Wireless.
` Miles Finn will be doing the argument this morning.
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` JUDGE MCMILLIN: Thank you.
` Before we start, I had a question. The Patent
` Owner response indicates that Patent Owner is no longer
` contesting the validity of Claims 1 through 5. What does
` that mean?
` JUDGE CRUMBLEY: I guess the question -- to be more
` blunt about it, are you conceding the unpatentability of
` those Claims? Should we -- no matter what we do on 6 through
` 10, should we enter judgment against you on 1 through 5?
` JUDGE MCMILLIN: And even more specifically, how do
` you wish us to treat Claims 1 through 5 in the
` final written decision, should we enter judgment against you,
` could we do that immediately? What --
` MR. SCHULTZ: Well, they still bear the burden of
` proof so --
` JUDGE MCMILLIN: Yes.
` MR. SCHULTZ: -- if the board believes that what
` they set forth is sufficient to satisfy that burden, then the
` board is free to enter in that judgment. Our arguments are
` just focused on Claims 6 and on. We didn't make any
` arguments as to Claims 1 through 5.
` JUDGE CRUMBLEY: So you're not conceding the
` patentability, you just haven't presented arguments on that
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` side, but you still consider it their burden to meet all
` the --
` MR. SCHULTZ: That's correct.
` JUDGE CRUMBLEY: Okay. I think that was just -- we
` wanted that clarification going forward.
` MR. SCHULTZ: Okay.
` JUDGE MCMILLIN: So you're not requesting judgment
` against --
` MR. SCHULTZ: No, we are not.
` JUDGE MCMILLIN: Thank you.
` MR. SCHULTZ: Yeah.
` JUDGE MCMILLIN: Petitioner, we have --
` Petitioners, excuse me, we have allocated 60 minutes for your
` argument. You are allowed to reserve time to speak after
` Patent Owner's presentation, do you wish to do so?
` MR. DEVOTO: We do indeed. We'd like to reserve 20
` minutes of time for rebuttal.
` JUDGE MCMILLIN: Thank you.
` MR. DEVOTO: Shall we begin?
` JUDGE MCMILLIN: Sure. Please. Thank you.
` MR. DEVOTO: Good morning, Your Honors. If we
` could switch to Slide 2 -- actually, let's jump all the way
` to Slide 3, please.
` While we've already discussed the overview of the
` state of the proceedings at this point in time, it's worth
` just reiterating that the Patent Owner no longer addresses
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` the validity of method Claims 1 through 5. Therefore, at
` issue here is really the validity of apparatus Claims 6 to
` 10. We certainly believe that we have satisfied our burden
` in showing that Claims 1 to 5 are not patentable.
` And with respect to the currently instituted
` grounds on Claims 6 to 10, just to refresh your memory, the
` 01208 original petition we filed was primarily based on the
` Zhuang 327 reference. Grounds 1A to C rely primarily on
` Zhuang 327 with Grounds 2A to B relying primarily on
` Zhuang 327 combined with the Hou reference.
` The 01209 proceeding were based primarily in the
` Zhuang 175 reference with Grounds 1 to 4 relying on
` Zhuang 175. And Grounds 5 to 6 relying on Zhuang 175
` combined with Fukuta.
` It's worth noting that were some dependent claims,
` like Claims 4 and 9, that have an additional secondary
` reference in Popovic; however, the Patent Owner response
` did not separately argue against those claims or contest the
` validity of those claims.
` If you can move to the next slide, please. So if
` you -- among the ten challenged claims -- our petitions were
` advanced to challenge ten claims as we noted, method Claims 1
` to 5, as indicated previously, are not contested. They
` consisted of one independent claim as shown here, Independent
` Claim 1. Apparatus Claim 6 to 10 have one independent claim,
` Independent Claim 6. And if you look closely at these two
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` claims, you'll find that they largely -- it's basically
` recasting the method claim as an apparatus claim by and
` large.
` JUDGE MCMILLIN: I hate to interrupt you, but you
` changed slides.
` MR. DEVOTO: I'm sorry.
` JUDGE MCMILLIN: In order for -- so we have Judge
` Crumbley with us today. Judge Boucher is in Colorado. You
` must refer to the slide number --
` MR. DEVOTO: My apologies.
` JUDGE MCMILLIN: -- and exhibit and page number or
` Judge Boucher will not know what you're talking about.
` MR. DEVOTO: My apologies to Judge Boucher. We are
` on Slide 4 right now.
` JUDGE BOUCHER: It's okay, I'm following along.
` Thanks.
` MR. DEVOTO: So moving to Slide 5. The Patent
` Owner's entire case largely rests on two, what we would call,
` unreasonably narrow claim constructions. And both of these
` claim constructions relate to language in the first element
` of the Apparatus Claim 6.
` The first term is the generating a code sequence
` term. The second term is the a code sequence generator term.
` The satisfaction of the second term, as they have interpreted
` it, in what we would say, an unreasonably narrow way, it's
` not in dispute that that term is satisfied by the Zhuang 327
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` and Zhuang 327 plus Hou combinations. That's just not in
` dispute.
` And, similarly, with respect to the second term,
` the code sequence generator term, where they have imposed a
` requirement that that be in a single device or circuit. It's
` not in dispute that term -- excuse me, I misspoke.
` The Term 1, it's not in dispute that the Zhuang 175
` grounds satisfy the Term 1 even under their narrow view of
` that Term 1. And with --
` JUDGE BOUCHER: When you say not in dispute, are
` you saying that the Patent Owner agrees with that position or
` is it not in dispute because the Patent Owner has decided not
` to contest the validity of those claims?
` MR. DEVOTO: So I say it's not in dispute in that,
` for example, in Zhuang 327, they have never argued that the
` Zhuang 327 grounds are flawed because they failed to disclose
` the Term 2 under their interpretation, which is a requirement
` that the code sequence generator be a single device.
` The Zhuang 327 combination has shown that, indeed,
` in that combination, the code sequence generator is a single
` device. So they have never argued otherwise, thus they have
` not distinguished the Zhuang 327 grounds based on their
` construction of Term 2 that's not in dispute.
` Does that help, Judge Boucher?
` JUDGE BOUCHER: Yes, that helps. They have not --
` but they have not expressly conceded that --
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` MR. DEVOTO: They have not expressly conceded.
` They simply did not make the argument.
` JUDGE BOUCHER: Okay. Thank you.
` MR. DEVOTO: And for these the Zhuang 175 base
` grounds, they have not argued that the Zhuang 175 base
` grounds fail to satisfy the Term 1 even under their narrow
` construction of Term 1. They have not argued that they
` failed to satisfy Claim 1 under their narrow construction
` and, again, this is based on them not arguing it. So in that
` sense, I'm referring to that as being not in dispute.
` So if you look back at this matrix, you can see
` that the construction advance for Term 1 by and large is a
` construction used to distinguish the Zhuang 327 base grounds
` while the construction advance for Term 2 is a construction
` largely advanced to distinguish the Zhuang 175 base grounds.
` Does that make sense?
` JUDGE MCMILLIN: Yes.
` Let me remind you when you switch slides --
` MR. DEVOTO: Lord have mercy.
` JUDGE MCMILLIN: -- to let us know.
` MR. DEVOTO: Lord have mercy, I'm sorry. So that's
` Slide 5, Judge Boucher.
` Moving to Slide 6. What I would like to do is I'd
` like to talk first about the construction of Term 1. I would
` like to explain why the construction of Term 1 that we're
` advancing is the correct one and why the construction
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` advanced by the Patent Owner is unreasonably narrow.
` After explaining the construction, then I'll turn
` to why Zhuang 327 satisfies the claims even under -- not only
` under our correct construction, but also under the Patent
` Owner's unreasonably narrow construction as we would
` characterize it.
` As you can see here in Slide 6, you can see that
` the claim language of the -- of the Term 1. And when we're
` talking about Term 1, we're talking about the generating a
` code sequence having a second length by cyclic extension of a
` code sequence having first length and performing a circular
` shift to the code sequence having the second length.
` Our proposed construction of that sequence is based
` on the recognition that the term "by" is open-ended. In
` fact, as we advanced in both our petition and reiterated it
` in our reply, "by" -- the plain and ordinary meaning of "by"
` is simply with the use or help of comma through. Not only
` with the use or help of comma through. It is an open-ended
` meaning. And that is the construction that we've advanced is
` the plain and ordinary meaning.
` Now, we can turn to, if we could, the construction
` advanced by the Patent Owner. As we have understood from
` their arguments, they are effectively changing the word "by"
` to be "only by." They're closing it up using the word
` "only." As you can see here, they are asserting that the
` code sequence generator for generating a code sequence having
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` a second length is only done, that is it's generated only by
` a cyclic extension of the code sequence having a first length
` and then performing a circular shift to the code sequence
` having the second length.
` We do not believe that there's anything in the
` intrinsic or extrinsic record that would mandate departure
` from the plain meaning of the -- from the plain meaning of
` this term, which includes "by," it does not include "only
` by." And we see their construction is effectively an
` amendment. And of course they had every opportunity to do an
` amendment in these proceedings and yet choose to forgo doing
` such an amendment.
` We can move to the next slide, please, which is
` Slide 7. So looking at the correct construction as we would
` advance, as the plain and ordinary meaning of this phrase, we
` notice that generating by cyclic extension of the code
` sequences "by" as an open-ended term. And, again, we have
` shown what that means. It means with the use or help of
` comma through.
` So as long as the code sequence having a second
` length is generated with the use or help of comma through
` cyclic extension of the code sequence having a first length
` then we would say that this term is indeed satisfied.
` Moreover, we believe that this plain and ordinary meaning is
` fully consistent with the intrinsic evidence as you can look
` at the specification examples.
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` And, in fact, of the '916 patent perhaps the best
` embodiment that represents the Claims of the '916 patent is
` shown in Figure 13. And you can see that in Figure 13, as in
` all of the other embodiments that rely on cyclic extension
` rather than cyclic truncation to achieve their sequences, you
` will see that all of them actually have degeneration of the
` code sequence having a second length with the use or help of
` comma through cyclic extension of the code sequence having
` the first length.
` Could we move to Slide 8, please.
` JUDGE CRUMBLEY: Before you move on, let me ask you
` a question.
` MR. DEVOTO: Uh-huh.
` JUDGE CRUMBLEY: I didn't understand their -- and
` maybe this is something for Patent Owner to address when they
` go. I didn't understand the argument to be that "by" meant
` "only by," but that what you had to perform the cyclic
` extension on was the code sequence having a first length.
` And in the prior art because you're doing the Fourier
` transform, you now have something other than your code
` sequence having that first length because you already
` performed some other process in step one beforehand. So now
` you have a cyclic extension of something else?
` MR. DEVOTO: So the way that the Patent Owner has
` characterized the plain meaning of this term is a little
` different than this "only by." They said that to properly
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` understand this generating feature they argue that you have
` to circularly shift the cyclically extended sequence.
` JUDGE CRUMBLEY: Right.
` MR. DEVOTO: The problem with that plain meaning is
` it smuggles in an "only by" into it. It smuggles it in
` because it says that the sequence that you're circularly
` shifting is thus cyclically extended sequence meaning a
` sequence that has undergone a single operation of cyclic
` extension. The correct --
` JUDGE CRUMBLEY: Let me ask you this a slightly
` different way.
` MR. DEVOTO: Sure.
` JUDGE CRUMBLEY: If I run a Fourier transform on
` a sequence having a first length --
` MR. DEVOTO: Yes.
` JUDGE CRUMBLEY: -- does it still have that first
` length or does the length change?
` MR. DEVOTO: It does in the art that we've
` advanced. So it will have the same exact length in the art
` that we've advanced. In other words --
` JUDGE CRUMBLEY: Can you show me where in the art
` it says that the length doesn't change?
` MR. DEVOTO: Sure. I can show it to you. If we
` could -- could you show the -- show the slide that we were
` talking about. I think it's Slide 44 that shows the
` Zhuang 327. This is the mapping of Zhuang 327.
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` Do you have it up there? It's a little hard to
` see.
` JUDGE CRUMBLEY: What slide are we on?
` MR. DEVOTO: I'm sorry, this is Slide 44.
` So what you'll notice here -- and this is something
` that we were very careful of as we advanced this mapping.
` You'll see here that we've got a sequence having a first
` length in the form of this sequence, I believe it's labeled
` 110. That's your sequencing having a first length.
` And then you cyclically extend it in accordance
` with the teachings of Zhuang 327 using a cyclic post, it's a
` well-known mathematical operation of cyclic extension. And
` then you use an IFFT.
` Now, that IFFT importantly -- so the length of a
` sequence after it's cyclically extended is K. It has K
` numbers in it because these sequences are simply sequences of
` complex numbers and there are K of them as shown here.
` If you do a fast Fourier transform, in this case an
` inverse fast Fourier transform, that's a K point fast Fourier
` transform, which we explain in some detail in our petition is
` within the scope of the teachings of the Zhuang 327, then the
` resulting sequence will also have K length. It will have --
` the number of complex numbers in the resulting sequence will
` also be K. And that's important to recognize that.
` So, indeed -- and that is the sequence that we're
` pointing to as the code sequence having a second length. And
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` you'll notice here that that generation of that code sequence
` having a second length was indeed achieved with the help
` of -- with the use of comma through the cyclic extension of
` the code sequence having a first length.
` And, moreover, the extended length remains the
` difference between the length of -- remains the difference
` between the K value, its length, and the length of the first
` -- of the sequence having the first length thereby satisfying
` the other wherein clauses of the claim.
` JUDGE CRUMBLEY: Let me take it a step further. I
` appreciate your answer on the length.
` MR. DEVOTO: Sure.
` JUDGE CRUMBLEY: But as I understand the claim also
` and, again, I think the Patent Owner's argument is the code
` sequence having the second length is what results from the
` cyclic extension?
` MR. DEVOTO: It does. It does result from the
` cyclic extension, but it's not -- but, again, "by." It
` results from it in the sense that the -- it results with the
` use or help of the cyclic extension. It results through the
` cyclic extension with the use or help of it. Not only with
` the use or help of it --
` JUDGE CRUMBLEY: So what you're saying is that the
` code sequence having a second length --
` MR. DEVOTO: Is generated --
` JUDGE CRUMBLEY: -- must be obtained by using a
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` cyclic extension, but it may be obtained by other processing
` steps as well?
` MR. DEVOTO: Indeed. Indeed. And, in fact,
` that -- if you -- in the technology, that makes perfect sense
` because as disclosed repeatedly in, for example, the Hou
` reference, you know that when you convert from one domain to
` the other, the desirable correlation properties of these
` sequences remain completely preserved.
` In fact, Hou shows two very thorough mathematical
` proofs that show when you take a sequence -- a CAZAC sequence
` that was given length K, you convert it from the time domain
` to the frequency domain, you get another sequence with the
` same optimal correlation properties.
` JUDGE CRUMBLEY: But you're not arguing that it's
` the same sequence?
` MR. DEVOTO: It's not the same sequence. It's
` definitely not the same sequence, but we can label it as the
` code sequence having a second length. And, indeed, it was
` generated with the use or help of cyclically extending the
` code sequence having a first length.
` JUDGE CRUMBLEY: Okay. I appreciate it.
` MR. DEVOTO: So we can -- why don't we move to --
` we were on Slide 7. So why don't we move to Slide 8.
` And so after having set forth the plain and
` ordinary meaning of the generating step and noting that it's
` generating a code sequence having a second length with the
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` use or help of comma through a cyclic extension the code
` sequence having a first length, then of course we always
` should consider the intrinsic evidence. We should look
` towards the specification and see if there's anything there
` that would mandate departure from that common,
` well-understood meaning. This is the typical Thorner
` framework.
` And in looking at the intrinsic evidence, what we
` find is there's nothing there that would mandate departure.
` What you have is a characterization of all the embodiments
` within the patent as being merely exemplary. In fact, the
` embodiment that most closely tracks the claims in the '916
` patent is the embodiment shown in Figure 13. And that
` embodiment is not only in the '916 patent specifically called
` out as exemplary, but it's also admitted to by the Patent
` Owner himself, as you can see in Slide 8, as being exemplary
` as well.
` So these exemplary embodiments do not constitute
` the type of cleared disavowal of claim scope that would
` mandate departure from that plain and ordinary meaning.
` So if we could move to Slide 9, please. So in sum,
` looking at the grounds that we advanced in the two petitions
` under the correct plain meaning of Term 1, the Zhuang 327
` grounds both the -- that are based on Zhuang 327 alone and
` those that combine Zhuang 327 with Hou indeed satisfy the
` Apparatus Claim 6. Both satisfy the Apparatus Claim 6.
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` Now, it's worth noting that even if the board were
` to adopt what we would argue to be the unreasonably narrow
` construction of Term 1 that limits the generation of the code
` sequence having a second length to only, being only by cyclic
` extension of the code sequence having a first length, then we
` note that our second set of grounds of Zhuang 327 plus Hou
` grounds actually satisfy that narrow interpretation.
` If we could move to Slide 10, please. Now, our
` second set of grounds based on the combination of Zhuang 327
` and Hou comes in two versions. There's a version that
` involves a process of generating the sequence and then
` transmitting the sequence that involves a single circular
` shift. And then there's a version that has a process of
` generating the sequence and ultimately transmitting the
` sequence; it has two circular shifts.
` The process that has one circular shift is
` uncontested. It was not addressed at all in the Patent Owner
` reply. The process having two circular shifts was addressed
` in the Patent Owner reply.
` I'd like to begin by talking about the first
` version of the Zhuang 327 plus Hou combination. If we could
` move to Slide 11, please. So in this version of Zhuang 327,
` first important thing to note is that Zhuang 327 does in its
` process have a circular shift. It has a circular shift in
` the time domain.
` In this combination that we're advancing, we're
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` actually replacing the circular shift in the time domain with
` Hou's circular shift in the frequency domain. And we are led
` to do that by the recognition as set forth in Hou that
` circular shifts of a code sequence can be performed in the
` frequency domain or the time domain as alternative
` embodiments.
` In fact, Hou teaches and, frankly, this is
` something that's also taught in Zhuang 327, it's also taught
` in Zhuang 175, it's taught in Fukuta itself, it's taught in
` all of these references, but we'll focus on Hou at the
` moment. Hou clearly teaches that you can use a cyclic shift
` of a base sequence, a base CAZAC sequence, to generate more
` CAZAC sequences. And as such -- and of course generating
` more of these sequences has advantages of which I can go into
` in whatever detail you wish, otherwise we'll just leave it at
` that.
` So as taught by Hou, you can perform the circular
` shift in the time domain or in the frequency domain. And a
` person of ordinary skill in the art would have been led to
` perform the operation either in the frequency domain or in
` the time domain. And, frankly, it would have been obvious to
` try any of these permutations.
` If we can show the next slide, Slide 12. So in
` this slide, what we see is the combination of Zhuang 327 plus
` Hou using version one. And we have the slide animated to
` help illustrate the point we want to make here.
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` So if you begin -- at the upper left corner, you
` begin in accordance with the teachings of Zhuang 327 with a
` GCL sequence, that's general chirp-like sequence. These are
` sequences that have these very nice correlation properties,
` that's why you choose them, that's why Zhuang 327 says you
` should begin with them.
` We begin with a cyclic extension of that sequence.
` So that is the cyclic extension. And we do that for various
` reasons. We can discuss that if you wish. And then we
` perform in accordance with these, so that's the cyclic
` extension. It's a frequency-based cyclic extension. It's
` done in the frequency domain.
` And then in accordance with the Hou reference, we
` now perform a circular shift of that cyclically extended
` sequence in order to get more code sequences in accordance
` with the teachings of Hou. After having performed the
` circular shift, we now have more code sequences. And then we
` can simply convert the resulting code sequences that have
` been circularly shifted using an IFFT into the time domain
` and then we can add the typical cyclic prefix.
` Now, notice this is an important part here. If
` you'll notice the block that has this circular shift, that
` circular shift that's done in the time domain is Zhuang 327's
` circular shift. And as you'll notice, it's been drawn in
` dash marks to show that it's an optional step as it is an
` optional step. And in this version, we aren't using it.
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` And, in fact, I think that's Zhuang's circular shift, we have
` replaced it with Hou's circular shift. So in this process
` flow, we've got Hou's circular shift, we don't use Zhuang's
` circular shift, we're able to achieve these extra codes in
` accordance with using circular shifts as taught in all --
` multiple of these references.
` And then we're able to then add the typical cyclic
` prefix that's added in any orthogonal frequency division
` multiple access system to deal with multi-patent delay which
` is done at the end. And then we're able to transmit that
` full access wave form. That is the version one combination
` of the Zhuang 327 plus Hou. And you'll notice it involves a
` single circular shift. Okay. And that was never addressed
` by the Patent Owner in the Patent Owner response.
` So if we move to the next slide, 13, please. Just
` to reiterate, again, there were two flavors of the Zhuang 327
` plus Hou combination. The first one we just discussed is
` uncontested. The second -- and it involves a single circular
` shift where we simply use the Hou frequency domain circular
` shift as an alternative equivalent to Zhuang 327's time
` domain circular shift.
` The second one is where we actually have two
` circular shifts. That one was contested. And I would like
` to talk briefly about that one. If we could move to
` Slide 14. So in this combination or version of Zhuang 327
` plus Hou, a skilled artisan would have been led to use -- to
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` actually apply both Hou's and Zhuang 327's circular shifts in
` an effort to create more code sequences.
` Hou says that you can actually create -- you can
` use the circular shift in the frequency domain to create more
` code sequence. And you can also use one of the time domain
` to create more code sequence. So it certainly would have
` been obvious to try to combine the two, that is perform the
` two circular shifts, one in the frequency domain per Hou's
` teachings, and another in the time domain per Zhuang 327's
` teachings to get more code sequences.
` Now, we can see a process flow of that combination
` on Slide 15. This slide also has been animated. So we take
` a look above, again, we rely on Zhuang 327's cyclic extension
` operation, it begins with the general chirp-like sequence
` that's of a prime number length. We cyclically extend it to
` a desired length of K entries. Then we apply Hou's circular
` shift to thereby get more sequences i
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