CLAIM CONSTRUCTION ORDER

MARIANA R. PFAELZER, District Judge.

I. Introduction

Plaintiff California Institute of Technology ("Caltech") has asserted U.S. Patent No. 7,116,710 ("the '710 patent"), U.S. Patent No. 7,421,032 ("the '032 patent"), U.S. Patent No. 7,916,781 ("the '781 patent"), and U.S. Patent No. 8,284,833 ("the '833 patent,") against Defendants Hughes Communications, Inc., Hughes Network Systems, LLC, DISH Network Corporation, DISH Network L.L.C., and dishNET Satellite Broadband L.L.C. (collectively, "Hughes"). Hughes has asserted several defenses, including the invalidity and non-infringement of the aforementioned patents. In this Order, the Court construes certain claim terms in dispute.

II. Technical Background

The asserted claims in the patents are method and apparatus claims relating to error correction.1 In modern electronic systems, data are stored in the form of bits having the value "1" or "0." In the process of transmitting data, a random or irregular fluctuation (noise) can occur in the signal and corrupt the data. For example, a transmitter may send a bit with the value "1," but noise may corrupt it and cause the receiver to read the value as "0." People using technology have a low tolerance for these kinds of errors. For example, we assume that when we email a file, the recipient will receive it uncorrupted.

To mitigate the problem of corruption, electronic systems use error correction. In general terms, error correction depends on redundancy. Redundancy refers to "extra" bits that are transmitted along with the original information bits. These extra bits are not necessary, in that the original information exists without them, but they serve an important purpose. The extra bits allow the receiver to ensure that the original information bits were not corrupted in transmission. The form of error correction in Caltech's patents is an irregular repeat and accumulate (IRA) code. An IRA code can operate as follows: The code can introduce redundancy by repeating different original bits a different number of times. These information bits may then be randomly permuted and combined to form intermediate bits, which are accumulated to form parity bits. These parity bits reflect the values of a number of original information bits. These parity bits are transmitted along with the original information bits. The receiver can ensure that bits were not corrupted by summing the original information bits and parity bits. Assuming the sum of the bits is supposed to be odd, but the result is instead even, the receiver knows that an error occurred and can perhaps correct the error by using other information it has received. IRA codes may utilize randomness to ensure a burst of noise does not affect a contiguous group of bits contributing to a parity bit. This is important, because the receiver uses these bits' values to ensure the accuracy of other bits. If too many errors occur in the group of bits, the receiver may be unable to perform this task.

The benefit of an IRA code is that not all bits are repeated the same number of times. The greater repetition of some bits provides more redundancy for error correction. Although greater repetition of every bit would allow for better error correction, it would also force the transmitter to send more bits, thereby increasing data transfer time.2 Greater redundancy may also result in increased coding complexity due to the creation of more parity bits. Coding complexity refers to the number of calculations performed in an error correction scheme: the more calculations, the greater the coding complexity. Complex schemes need more processing power. Therefore, a less complex coding scheme is more efficient and preferable. IRA codes attempt to balance two goals: data accuracy and efficiency.

III. Legal Standards

A. Claim Construction

"It is a bedrock principle of patent law that the claims of a patent define the invention to which the patentee is entitled the right to exclude." Innova/Pure Water, Inc. v. Safari Water Filtration Sys., 381 F.3d 1111, 1115 (Fed.Cir.2004). The purpose of claim construction is to determine the meaning and scope of the patent claims alleged to be infringed. O2 Micro Int'l Ltd. v. Beyond Innovation Tech. Co., Ltd., 521 F.3d 1351, 1360 (Fed. Cir.2008). Claim construction is a question of law. See Markman v. Westview Instruments, Inc., 517 U.S. 370, 372, 116 S.Ct. 1384, 134 L.Ed.2d 577 (1996); see generally Lighting Ballast Control LLC v. Philips Elecs. N. Am. Corp., 744 F.3d 1272 (Fed.Cir.2014).

"The words of a claim are generally given their ordinary and customary meaning as understood by a person of ordinary skill in the art when read in the context of the specification and prosecution history."3 Thorner v. Sony Computer Entm't Am. LLC, 669 F.3d 1362, 1365 (Fed.Cir.2012) (citing Phillips v. AWH Corp., 415 F.3d 1303, 1313 (Fed.Cir.2005) (en banc)).

"[T]he claims themselves provide substantial guidance as to the meaning of particular claim terms." Phillips, 415 F.3d at 1314. Claims "must be construed in light of the appropriate context in which the claim term is used." Aventis Pharm. Inc. v. Amino Chems. Ltd., 715 F.3d 1363, 1373 (Fed.Cir.2013). "[T]he usage of a term in one claim can often illuminate the meaning of the same term in other claims." Phillips, 415 F.3d at 1314. Similarly, "the presence of a dependent claim that adds a particular limitation gives rise to a presumption that the limitation in question is not present in the independent claim" under the doctrine of claim differentiation. Id. at 1315.

The specification is "highly relevant" in claim construction and is the "single best guide" for construing ambiguous claim terms. Phillips, 415 F.3d at 1315. But the Court must be wary of "improperly importing a limitation from the specification into the claims." Retractable Techs., Inc. v. Becton, 653 F.3d 1296, 1305 (Fed.Cir.2011). A patent's prosecution history is also relevant in claim construction, but it "often lacks the clarity of the specification and thus is less useful for claim construction purposes." Phillips, 415 F.3d at 1317.

The Court may consider extrinsic evidence in claim construction. Id. at 1317. Dictionaries, especially technical dictionaries, may aid the Court "in determining the meaning of particular terminology to those of skill in the art." Id. at 1318. While extrinsic evidence can shed light on claim meaning, it is "less significant than the intrinsic record in determining the legally operative meaning of claim language." Id. (internal quotation marks omitted). "Extrinsic evidence ... may be useful in claim construction, but it should be considered in the context of the intrinsic evidence." Biagro W. Sales, Inc. v. Grow More, Inc., 423 F.3d 1296, 1302 (Fed.Cir.2005).

The Court will not give a term its plain meaning under two circumstances. First, a patentee can depart from the plain and ordinary meaning by acting as its own lexicographer. To be its own lexicographer, the patentee "must clearly set forth a definition of the disputed claim term other than its plain and ordinary meaning." Thorner, 669 F.3d at 1365 (internal quotation marks omitted). "It is not enough for a patentee to simply disclose a single embodiment or use a word in the same manner in all embodiments, the patentee must clearly express an intent to redefine the term." Id. (internal quotation marks omitted). An "`implied' redefinition must be so clear that it equates to an explicit one." Id. at 1368. Second, a patentee can depart from the plain and ordinary meaning by clearly "disavow[ing] the full scope of a claim term either in the specification or during prosecution." Id. at 1365. "The patentee may demonstrate intent to deviate from the ordinary and accustomed meaning of a claim term by including in the specification expressions of manifest exclusion or restriction, representing a clear disavowal of claim scope." Teleflex, Inc. v. Ficosa N. Am. Corp., 299 F.3d 1313, 1325 (Fed.Cir.2002).

B. Section 112(b) (Indefiniteness)

The Patent Act provides that "[t]he specification shall conclude with one or more claims particularly pointing out and distinctly claiming the subject matter which the inventor or a joint inventor regards as the invention." 35 U.S.C. § 112(b). Recently, in Nautilus Inc. v. Biosig Instruments, Inc., ___ U.S. ___, 134 S.Ct. 2120, 189 L.Ed.2d 37 (2014), the Supreme Court interpreted Section 112(b) "to require that a patent's claims, viewed in light of the specification and prosecution history, inform those skilled in the art about the scope of the invention with reasonable certainty." Id. at 2129. Failure to do so renders a claim indefinite and, therefore, invalid. 35 U.S.C. § 282(b)(3). The Supreme Court observed that Section 112 strikes a careful balance. On the one hand, "[s]ome modicum of uncertainty ... is the price of ensuring the appropriate incentives for innovation." Id. at 2128 (internal quotation marks omitted). It is important to remember that "patents are not addressed to lawyers, or even to the public generally, but rather to those skilled in the relevant art." Id. (internal quotation marks omitted). On the other hand, "a patent must be precise enough to afford clear notice of what is claimed" in order to inform "the public of what is still open to them." Id. at 2129 (citing Markman, 517 U.S. at 373, 116 S.Ct. 1384). These purposes inform the "reasonable certainty" standard.

Before Nautilus, the Federal Circuit had held that a claim was indefinite if it was "not amenable to construction or insolubly ambiguous." Biosig Instruments, Inc. v. Nautilus, Inc., 715 F.3d 891, 898 (Fed.Cir.2013) (internal quotation marks omitted), rev'd, ___ U.S. ___, 134 S.Ct. 2120, 189 L.Ed.2d 37 (2014). Under this standard, claim construction and indefiniteness were essentially one and the same: The district court would ascertain whether a term was "amenable to construction" by attempting to construe the claim, and if it could construe the claim, the court would ask whether its construction was insolubly ambiguous. Post-Nautilus, a district court must undertake a slightly different analysis. First, the court should attempt to construe a claim. If the claim is not amenable to construction, then the claim is indefinite. A claim that is not amenable to construction cannot inform a person of ordinary skill of the scope of the invention with reasonable certainty. Cf. Nautilus, 134 S.Ct. at 2130 ("It cannot be sufficient that a court can ascribe some meaning to a patent's claims."). Second, the court must ask whether a person of ordinary skill, after reading the specification and prosecution history, would be reasonably certain of the correct scope of the claim. A claim would fail this standard if a person of ordinary skill would not be reasonably certain of the correct construction of a term. For example, if a person of ordinary skill would determine that there are multiple equally plausible but materially dissimilar constructions of a claim term, the claim would fail the "reasonable certainty" standard, even if none of the competing constructions are "insolubly ambiguous." Even if a person of ordinary skill could determine a term's correct construction, a court must undertake a second step of analysis. If the correct construction is ambiguous such that it does not inform a person of ordinary skill of the scope of the invention with reasonable certainty, the term is indefinite.

Like claim construction, indefiniteness is a question of law. Takeda Pharm. Co. v. Zydus Pharm. USA, Inc., 743 F.3d 1359, 1366 (Fed.Cir.2014). At the same time, "[a]ny fact critical to a holding on indefiniteness... must be proven by the challenger by clear and convincing evidence." Intel Corp. v. VIA Techs., 319 F.3d 1357, 1366 (Fed.Cir.2003).4

IV. Claim Construction

A. "transmitting"/"transmission"

The Court finds that "transmitting" means "sending over a channel." Hughes argues that the proper construction of "transmitting" is "sending over a physical channel." In Hughes' view, the term "transmitting" encompasses only "sending bits between a transmitter and receiver (i.e., over a `physical channel')." Defendants' Opening Claim Construction Brief at 9, Dkt. No. 65. Hughes seeks to exclude internal data transfers within a device from the scope of the claims. In doing so, Hughes attempts to impermissibly read a limitation into the term "transmitting."

The plain meaning of "transmitting" does not require bits to be sent over a physical channel. The specification consistently describes transmissions generically as occurring over a "channel," and the specification never explicitly limits transmissions to external data transfers. See, e.g., '032 Patent, 2:8-10 ("The encoded data output from the inner coder may be transmitted on a channel...."); '032 Patent, 7:1-3 ("The selection of a degree profile for use in a particular transmission channel is a design parameter, which may be affected by various attributes of the channel."). The word "physical" never appears in the patent, either.

Faced with these facts, Hughes relies on carefully selected lines in the specification and claims to argue that "transmitting" implicitly contains a physical channel limitation. Hughes' arguments are unpersuasive. First, it is true that claim 18 of the '032 patent recites a "decoder configured to decode a received data stream," but one must suspend logic to conclude that this entirely separate phrase requires the Court to impose a physical channel requirement on all uses of "transmitting." Second, Hughes cannot point to anywhere in the specification that shows a clear disavowal or redefinition of "transmitting." Hughes cites to a sentence in the specification that notes a turbo coder can overcome corruption caused by a noisy channel. Def. Op. Brief at 10. But this sentence describes a general purpose that neither implicitly nor explicitly changes the meaning of "transmitting." Hughes also observes that the specification clarifies that transmissions "may be transmitted on a channel and decoded ... at a destination," '032 Patent, 2:8-10 (emphasis added), and that the specification uses the words "input" and "output" when explaining particular transfers within the coding system. Def. Op. Brief at 11. Such statements are neither a clear disavowal of scope nor a clear redefinition of the term. See Thorner, 669 F.3d at 1365. As such, the Court cannot depart from the plain meaning of "transmitting."

B. "codeword"

The Court finds that "codeword" means "a discrete encoded sequence of data elements." Once again, Hughes attempts to improperly inject a limitation into a clear term. This time, Hughes does so by arguing that to constitute a "codeword," data elements must be encoded for transmission. But the plain meaning of "codeword" does not require data elements to be encoded for transmission, and the specification never clearly redefines or disavows the plain meaning of "codeword." The specification notes only that "encoded data output from the inner coder may be transmitted" and that "[t]he coder may be used to format blocks of data for transmission." '781 patent, 2:11-12, 2:41-42 (emphasis added). These examples show only that it is possible to transmit encoded or formatted data. They do not even weakly suggest that a codeword must be transmitted.

Hughes argues that the preamble of claims in the '781 patent clarifies that a codeword must be encoded for transmission. The preamble in relevant claims, except claim 21, recites "[a] method of encoding a signal." See, e.g., '781 Patent, 7:25. But this preamble does not clearly redefine "codeword." Hughes is implicitly arguing for a different contention: namely, that the preamble is acting as a claim limitation. The Federal Circuit has recognized this possibility. See Bicon, Inc. v. Straumann Co., 441 F.3d 945, 952 (Fed. Cir.2006) ("[T]he preamble is regarded as limiting if it recites essential structure that is important to the invention or necessary to give meaning to the claim."). This issue is not before the Court, and the Court expresses no opinion on its merits. It is plain, however, that the proper way to resolve this dispute is by determining whether the preamble is a limitation, not by importing the preamble's language into "codeword."

Hughes also contends that the use of "L transformed bits" in claim 1 in the '781 patent indicates that a codeword is more than a discrete encoded sequence of data elements. The gravamen of Hughes' argument is this: the L transformed bits are a discrete encoded sequence of data elements. Because the claim uses the phrase "L transformed bits" instead of "codeword," "codeword" cannot merely mean a discrete encoded sequence of data elements. This argument is a distraction tactic. The use of the phrase does not change the meaning of "codeword." Hughes is correct that "different terms in the claims connote[] different meanings." CAE Screenplates Inc. v. Heinrich Fiedler GmbH & Co. KG, 224 F.3d 1308, 1317 (Fed.Cir.2000). But this principle is consistent with the Court's construction of "codeword." The Court's construction does not render the claim's use of the phrase "L transformed bits" superfluous. Even if "codeword" encompasses the L transformed bits, a patentee is allowed to use different language to refer to an example of a broader term. In fact, the claims have a good reason for differentiating between the specific L transformed bits and the broader "codeword." The claim language uses the phrase "L transformed bits" to describe the creation of codeword within the context of this particular claim. The claim notes that the second encoding operation accumulates the L transformed bits and produces at least a portion of a codeword "wherein L is two or more." '781 Patent, 7:37-38. Using the phrase "L transformed bits" helps explain how a codeword is produced in the claimed invention. Hughes' argument rests on a flimsy implication, and it does not refute the plain meaning of "codeword" supported by the specification. The Court declines Hughes' invitation to read a transmission limitation into "codeword."

C. "repeat"

The Court adopts the plain meaning of "repeat." In this section, the Court seeks to explain in detail the scope of "repeat."

First, the plain meaning of "repeat" requires the creation of new bits corresponding to or reflecting the value of the original bits. In other words, repeating a bit with the value 0 will produce another bit with the value 0. The Court will refer to this concept as duplication. Caltech argues that "repeat" can also refer to the re-use of a bit, but the patent's claims and specification support the Court's construction.

To begin with, the claim language of the patents-in-suit supports this construction. Claim 13 of the '032 Patent refers to a low-density generator matrix (LDGM) coder "configured to perform an irregular repeat on message bits having a first sequence in a source data stream to output a random sequence of repeats of the message bits." '032 Patent, 9:39-42. The claim goes on to describe an accumulator that exclusive-OR sums a predecessor parity bit and "`a' bits of the random sequence of repeats of the message bits." '032 Patent, 9:43-45. This claim clarifies that performing a repeat on message bits outputs "repeats of the message bits." A person of ordinary skill would not interpret this phrase to mean "bits that reflect the re-use of the incoming message bits." See Plaintiff's Responsive Claim Construction Brief at 6, Dkt. No. 74. Nothing in the claim language or specification suggests this meaning for the phrase. A person of ordinary skill would likely interpret the phrase according to its evident meaning: duplicates of the message bits on which the LDGM coder performed an irregular repeat. See also '710 Patent, Claim 1, 7:19-23 (referring to "repeating the data elements" resulting in "repeated data elements").

The specification supports this construction as well. The specification describes an outer coder embodiment in which the outer coder is "a repeater that repeats the k bits in a block a number of times q to produce a block with n bits, where n=qk." '710 Patent, 2:50-52. Thus, if bits with the values 0 and 1, respectively (the k bits), are repeated two times (q), then the resulting block will have two bits with the value 0 and two bits with the value 1 for a total of four bits (n). This use of "repeat" strongly supports its plain meaning.

Caltech argues that this sentence does not support construing "repeat" to mean duplicating bits. Caltech correctly notes that courts should not import limitations from the embodiment into the claims. See Retractable, 653 F.3d at 1305. This principle has a limited effect in this instance, however. An embodiment is simply an example of an invention encompassed by the patent. See Black's Law Dictionary 599 (9th ed.2009) (defining "embodiment" as a "tangible manifestation of an invention"). The Court generally should not limit the claims to the exemplary aspects of an embodiment. See Phillips, 415 F.3d at 1323 ("[A]lthough the specification often describes very specific embodiments of the invention, we have repeatedly warned against confining the claims to those embodiments."). On the other hand, the specification may describe the embodiment by using a claim term that is not the exemplary aspect of the embodiment. See id. at 1323 ("[T]he line between construing terms and importing limitations can be discerned with reasonable certainty and predictability if the court's focus remains on understanding how a person of ordinary skill in the art would understand the claim terms."). In that case, the embodiment's use of the claim term may suggest its meaning. If the exemplary aspect of the cited embodiment is the meaning of "repeat," then Caltech's point may be valid. However, if the exemplary aspect of the embodiment is some other element, then the embodiment's use of "repeat" is highly probative of its meaning.

Caltech essentially argues that the "exemplary" aspect of the first embodiment is the meaning of "repeat" as duplication. The "exemplary" aspect of the LDGM embodiment, Caltech also argues, is the use of "repeat" as re-use. See '710 Patent, 3:51-59 (describing LDGM embodiment). This explanation is plausible, but barely. No language in the specification differentiates these embodiments based on different meanings of "repeat." Instead, the specification differentiates them by the structure of their outer coders. The first embodiment describes repetition of bits using non-matrix multiplication. The second embodiment describes repetition of bits using matrix multiplication. These structures are the exemplary aspects of the embodiments, not the meaning of "repeat."

Admittedly, "there is sometimes a fine line between reading a claim in light of the specification, and reading a limitation into the claim from the specification." Comark Commc'ns, Inc. v. Harris Corp., 156 F.3d 1182, 1186 (Fed.Cir.1998). But Caltech cannot point anywhere in the specification or prosecution history where "repeat" means re-use. Caltech argues that the LDGM embodiment repeats bits by re-using bits, but the specification does not explicitly or implicitly suggest this redefinition. Caltech cannot point to any technical or non-technical dictionary definition that defines "repeat" as re-use, either. Caltech claims that dictionary definitions such as "to say or do again" and "to undergo again" indicate that "reuse" is a definition for "repeat." But the phrases "to do a bit again" or "to undergo a bit again" hardly convey Caltech's construction: "re-use a bit." A reasonable person could as easily interpret "doing a bit again" to mean duplicating a bit.

Construing "repeat" to require duplication does not exclude the LDGM embodiment. Although an LDGM does not necessarily duplicate bits, it is beyond dispute that an LDGM can duplicate bits. Imagine the vector [101] multiplied by the following matrix:

The result of the multiplication would be [101110], with each bit repeated twice, in this example corresponding to the number of `1's in each row. The key point is that the multiplication must result in new bits corresponding to or reflecting the value of the input bits.5

Caltech is correct that an LDGM can create parity bits through re-using bits. Caltech is also correct that it is efficient and valuable to re-use bits. Caltech is incorrect that the patents-in-suit express this concept through the term "repeat." One can imagine a specification or claims that clarified that "repeat" meant "reuse," either explicitly, or implicitly by an example. It would not have been difficult. These patents do not do so. They instead suggest that "repeat," consistent with its plain meaning, requires duplication. "It is well-settled that an inventor may act as his own lexicographer to define a patent term.... It is likewise well-settled that courts generally may not re-draft claims; we must construe the claims as written." Ecolab, Inc. v. FMC Corp., 569 F.3d 1335, 1344 (Fed.Cir.2009). This Court will not redefine "repeat" to encompass "re-use" even though the patentees could have, and perhaps should have, done it themselves.

The Court's construction does not exclude the Tanner graph representation. The Tanner graph does not unequivocally demonstrate a re-use of bits. In fact, the specification indicates that the lines exiting the information nodes represent a duplication of bits. See '710 Patent, 3:39-43 (describing Tanner Graph demonstrating a "repeat of q=2," where the specification previously defined "q" as the number of times a bit is duplicated). Technical literature uses Tanner graphs to express the duplication of bits. See, e.g., Sarah J. Johnson, Iterative Error Correction: Turbo, Low-Density Parity-Check and Repeat-Accumulate Codes 211-12, 218-20 (Cambridge University 2010) (using a Tanner graph to represent a repeat-accumulate code that repeats (i.e. duplicates) bits).6

Technical literature incorporates the plain meaning of "repeat" as duplication, as used in the outer coder embodiment. See, e.g., Robert J. McEliece, The Theory of Information and Coding: A Mathematical Framework for Communication, in 3 Encyclopedia of Mathematics and Its Applications 2 (Addison Wesley 1977) ("[T]he source output can be encoded before transmission by repeating each bit three times.

For example, if the source's first five bits were 10100, the encoded stream would be 111000111000000."). Caltech cannot point to a single clear, nonambiguous use of "repeat" as "re-use" in any relevant literature. At best, Caltech can point to discussions of LDGMs that do not define or clarify "repeat" or "repetition." See generally Declaration of Kathy Peng in Support of Plaintiff's Responsive Claim Construction Brief Ex. J, K, and L, Dkt. No. 74. On the whole, the extrinsic evidence supports the plain meaning of "repeat" when "considered in the context of the intrinsic evidence." Biagro, 423 F.3d at 1302.

Second, the plain meaning of "repeat" is not limited to "sequential duplication" of bits. That is, repeating the bits 101 three times does not only mean the following result: 111000111. Certainly, "repeat" encompasses this result, but the term also encompasses the non-sequential duplication of bits. Thus, repeating the bits 101 three times can also result in three copies of each bit interspersed with other bits that do not originate from the original bits.

No intrinsic or extrinsic source before the Court defines "repeat" narrowly as "sequential duplication." The specification clarifies that repeating bits means duplicating bits in the outer coder embodiment, but neither this embodiment nor the rest of the specification suggests that "repeat" encompasses only sequential duplication. Even Hughes' cited dictionary definition fully supports construing "repeat" to include non-sequential duplication as well as sequential duplication. See Def. Op. Brief at 6 (citing dictionary defining "repeat" as "a duplication or reproduction"). As such, Hughes resorts to arguing that the claims and extrinsic evidence implicitly define "repeat" as "sequential duplication," but these implications are weak at best and non-existent at worst.

First, Hughes argues that if "repeat" does not require sequential duplication, claim limitations involving interleaving and scrambling would be rendered superfluous. See, e.g., '710 Patent, Claim 1, 7:14-25 (reciting limitation of "interleaving the repeated data elements"); '710 Patent, Claim 15, 8:1-6 (reciting "first coder operative to repeat said stream of bits irregularly and scramble the repeated bits"). The Federal Circuit has noted that courts should construe "claim terms in light of the surrounding claim language, such that words in a claim are not rendered superfluous." Digital-Vending Servs. Int'l, LLC v. Univ. of Phoenix, Inc., 672 F.3d 1270, 1275 (Fed.Cir.2012). But this doctrine does not apply here. Allowing "repeat" to encompass non-sequential duplication does not render the "interleaving" or "scrambling" claim language necessarily superfluous or unnecessary. Cf. Phillips, 415 F.3d at 1314 (noting that the language "steel baffles" meant that baffles were not necessarily made of steel, or else the word "steel" would be unnecessary). Hughes essentially argues that if the repeated bits have any inherent randomness, there is no purpose in interleaving or scrambling. The specification contradicts this argument squarely. The specification acknowledges that in an LDGM embodiment, the "interleaver... may be excluded due to the randomness already present in the structure of the LDGM code." '710 Patent, 3:57-59 (emphasis added). As an initial matter, this embodiment suggests that repeating bits can result in non-sequential duplication. It explicitly contemplates that an LDGM may have enough randomness to exclude an interleaver. The embodiment is referring to non-sequential duplication, because sequential duplication is hardly random. At the same time, the word "may" indicates that it is also possible for an LDGM embodiment to include an interleaver, despite the inherent randomness. Hughes cannot fairly say "interleaving would be pointless" when the specification contemplates interleaving even in the presence of existing randomness. Def. Op. Brief at 8.

Hughes' second argument points to a single example by a named inventor of the patents, Robert J. McEliece. In a paper, McEliece explained repetition of bits, explaining that "if the source's first five bits were 10100, the encoded stream would be 111000111000000." McEliece, supra, at 2. Two problems exist with this argument. First, this example does not explicitly limit the repetition of bits to only sequential duplication. Second, Hughes cannot point to anywhere in the specification that confirms or suggests this understanding. The outer coder embodiment says nothing about the sequence of repeated bits. As discussed above, non-sequential duplication does not render interleaving and scrambling superfluous. Therefore, the claim language does not support limiting "repeat" to sequential duplication. Given that there is no support for Hughes' construction in the patent, it would be unwise for the Court to place significant weight on an ambiguous extrinsic source. See Phillips, 415 F.3d at 1319 ("[U]ndue reliance on extrinsic evidence poses the risk that it will be used to change the meaning of claims in derogation of the `indisputable public records consisting of the claims, the specification and the prosecution history,' thereby undermining the public notice function of patents.").

To summarize, the claim term "repeat" requires the creation of new bits corresponding to or reflecting the value of the original bits. "Repeat" is not limited to sequential duplication. This summary captures the general scope of the claim term's construction, but the parties should rely on the full discussion in this section, rather than the summary, in interpreting this order.

D. "combine"/"combining"

The Court finds that "combine" means "perform logical operations on." "Combine" and "combining" are not indefinite.

i. Claim construction

The claims themselves help clarify the meaning of "combine." Claim 1 of the '833 Patent recites a permutation module that "combine[s] the read bit to a bit," '833 Patent, 7:26, and dependent claim 2 recites "[t]he apparatus of claim 1, wherein the permutation module is configured to perform the combine operation to include performing mod-2 or exclusive-OR sum." '833 Patent, 7:36-38. "Although each claim is an independent invention, dependent claims can aid in interpreting the scope of claims from which they depend." Laitram Corp. v. NEC Corp., 62 F.3d 1388, 1392 (Fed.Cir.1995). Exclusive-OR summing is a logical operation that produces a Boolean value. Presumably, "combine" is broader than exclusive-OR summing, or else dependent claim 2 would be redundant. See Dow Chem. Co. v. United States, 226 F.3d 1334, 1341 (Fed. Cir.2000) ("The doctrine of claim differentiation can support a broader construction of step (c) of claim 1 because the doctrine creates a rebuttable presumption that each claim in a patent has a different scope."). A person of ordinary skill would thus reasonably interpret "combine" to encompass logical operations generally.

Of course, the Court should not place undeserved weight on this difference in claim language. The Court must remember that claim differentiation "cannot broaden the claims beyond their correct scope." Id. However, evidence of ordinary understandings of "combine" fully supports the Court's construction. For example, U.S. Patent 3,222,506, a patent issued in 1965, relates to a logic unit that performs logical operations on bits and uses "combine" to refer to logical operations: "P and Q values can be combined by logical AND ... or by logical OR.... P and Q can also be combined by other logical connectives such as ... (EXCLUSIVE OR)." U.S. Patent No. 3,222,506, 2:17-28 (emphasis added). U.S. Patent 5,386,523, issued in 1995, continues to reflect this understanding: "The overlapped bits are logically combined in a boolean operation when generating the complete address for the bus. For example, each pair of overlapped bits can be logically ORed to one another to provide a combined bit for use in generating the bus address." U.S. Patent 5,386,523 2:47-52. Although this example refers to bits that are "logically combined," the patent also uses the word "combine" unmodified by "logically." '523 Patent, 6:19-20 ("Other logical functions can be used to combine overlapping bits besides an OR function."). This ordinary understanding of the word "combine" persists today, even in introductory computer science courses. See Boolean Expressions Introduction to Computer Programming — Fall 2013, http://cims.nyu.edu/~kapp/courses/cs0002fall2013/category/boolean-expressions/ (discussing "how to combine Boolean expressions using logical operators"); see also 5. Conditionals — How to Think Like a Computer Scientist: Learning with Python 3, http://www.faculty.fairfield.edu/spoerri/sp2014/Lab3.html (defining "logical operator" as "[o]ne of the operators that combines Boolean expressions: and, or, and not"); Programming — Truth Tables and Logic, http://www.cs.utah.edu/~germain/PPS/Topics/truth_tables_and_logic.html, ("We can combine several `boolean' statements that have true/false meaning into a single statement using the key concepts AND and OR (and NOT)."). This evidence supports "perform logical operations on" as the correct construction of "combine" when read in light of the intrinsic evidence. See '833 Patent, 2:10-12 (describing accumulator that performs "modulo two addition operations on the input bit stream").

Hughes argues that Caltech's construction cannot be correct because it would include relational operators. However, relational operators, such as "greater than," are not included in the Court's construction. Relational operators compare values as opposed to combining them. Relational operators merely define the relationship between two terms. The difference between the two types of operators is wellknown and relatively straightforward. See Tim McGuire, Relational and Logical Operators, http://www.shsu.edu/csc_tjm/fall2000/cs164/unit7.html (defining relational operators and logical operators). Caltech never argued that logical operators encompass relational operators, and the Court does not construe "combine" to encompass relational operators.

ii. Indefiniteness

It is not enough that the Court can construe the claim terms. Hughes contends that the terms are indefinite. Hughes' indefiniteness arguments focus primarily on alleged shortcomings of the specification.7 But in its analysis, Hughes disregards the hypothetical reader of the specification: the person of ordinary skill in the art. A person of ordinary skill does not approach a patent with a blank slate. This person has pre-existing knowledge of the art and can refer to this knowledge while reading the patent. This person would be able to determine the meaning of "combine" with relative ease and would correctly conclude that "combine" means "perform logical operations on."

As discussed above, the word "combine" is commonly used in the art to refer to logical operations. A person of ordinary skill would be familiar with this use of the term "combine." Moreover, the specification and the claims confirm this understanding by discussing mod-2 or exclusive-OR summing. See, e.g., '833 Patent, 2:10-12; '833 Patent, 7:36-38. Hughes is correct that the specification does not use the word "combine" or explicitly define it, but neither of these actions is necessary for a claim to be definite. Nautilus does not mandate absolute certainty, but only reasonable certainty. The Supreme Court recognized that "[s]ome modicum of uncertainty... is the price of ensuring the appropriate incentives for innovation." Nautilus, 134 S.Ct. at 2128 (internal quotation marks omitted). A person of ordinary skill, reading the claims in light of the specification, would not have trouble deducing that "combine" means "perform logical operations on," and this person would be reasonably certain that this construction was correct.

Hughes also objects to breadth of the construction. Hughes argues that it is impossible to know which logical operations "combine" encompasses. But logical operators — including AND, OR, XOR, and NOT — are well-known in the art, as described in the above section. A person of ordinary skill would at least have reasonable certainty as to the scope of "combine," if not complete certainty. The patent adequately fulfills its public notice function by providing enough guidance as to the meaning of "combine."

E. Equation in Claim 1 of the '032 patent

The Court finds that the equation in claim 1 of the '032 patent means "the parity bit xj is the sum of (a) the parity bit xj-1 and (b) the sum of a number, `a,' of randomly chosen irregular repeats of the message bits."8

The plain meaning of the equation is clear, and Hughes offers no alternative construction. Rather, Hughes contends that the equation is indefinite because it does not define the value of the base case. This argument is unconvincing. In the context of the patent, a person of ordinary skill could ascertain with complete certainty the possible values of the base case: 1 or 0. A bit can have only those two values. See, e.g., '032 Patent, 5:24-27 ("A probability density on a bit is a pair of non-negative real numbers p(0), p(1) satisfying p(0)+p(1)=1, where p(0) denotes the probability of the bit being 0, p(1) the probability of it being 1."); '032 Patent, 6:38-39 ("In the BSC, there are two possible inputs (0, 1) and two possible outputs (0, 1)."). Even absent the guidance of a specification, a person of ordinary skill would understand that a bit can take on only these two values. As such, a person of ordinary skill would be aware of all possible base case values.

More absurdly, Hughes argues that the equation does not define the variable that is the starting point. That is, Hughes argues that x0 depends on x-1, which depends on x-2, and so forth. No person of ordinary skill would believe that this equation starts at a point other than x0 unless the specification gave this person a reason to do so. But the specification gives an example where "x0 is set to 0." '032 Patent, 4:6-7. One reading the specification would conclude that x0 is the starting point for the equation. See '032 Patent, 4:1-18 (explaining equation). This person would also understand that x0 can be 0 or 1. It takes lawyerly convolution to assert that this equation is indefinite.

F. Tanner Graph Term in Claims 11 and 18 of '032 Patent

The Court finds that the Tanner Graph term is "a graph representing an IRA code as a set of parity checks where every message bit is repeated, at least two different subsets of message bits are repeated a different number of times, and check nodes, randomly connected to the repeated message bits, enforce constraints that determine the parity bits."9 The term is not indefinite.

i. Claim Construction

The left side of the Tanner graph depicts subsets of information nodes. The subsets repeat a different number of times, as shown by the edges exiting the subsets. These edges enter a "Random Permutation" box, which represents the scrambling of the edges joining the information nodes and check nodes. The right side of the graph depicts edges connected to check nodes. Each check node enforces a constraint by using the values of the bits connected to it, thereby determining the value of connected parity bits. See '032 Patent, 3:25-67, 4:1-19 (explaining meaning of Tanner graph depicted in Figure 3 of patent).

Hughes protests that the Tanner graph requires three groups of information bits, each contributing to a different number of parity checks. Absent the specification, Hughes' explanation would be reasonable. After all, the Tanner graph in the claims shows three subsets of information nodes, each repeating a different number of times. But by ignoring the specification, Hughes oversimplifies the meaning of the term. The specification deeply undermines Hughes' proposed construction.

The claim term and the Tanner graph appearing in the specification are identical for all material purposes. The specification clarifies that the Tanner graph in Figure 3 represents a class of IRA codes. See '032 Patent, 3:32-35 ("An IRA code is a linear code, and as such, may be represented in a bipartite graph, called the Tanner graph, of the code."). By way of example, the specification describes the operation of only two subsets of information nodes, noting that "each of the f2 information nodes are connected to two check nodes, corresponding to a repeat of q=2, and each of the f3 information nodes are connected to three check nodes, corresponding to q=3." '032 Patent, 3:46-49. The specification further demonstrates the graph's representative nature when it notes the "fraction of information nodes connected to exactly i check nodes is fi." '032 Patent, 3:44-45. Throughout the specification, the Tanner graph is described in generic, exemplary terms. See '032 Patent, 3:50-54 ("Each check node 304 is connected to exactly `a' information nodes 302.... These connections can be made in many ways, as indicated by the arbitrary permutation of the ra edges joining the information nodes 302 and check nodes 304....").

This exemplary nature is reflected by the identical Tanner graph in the claims. The code is irregular, so necessarily, at least two subsets must repeat a different number of times. But the Tanner graph term does not require three subsets to repeat a different number of times. The third subset represents to a person of ordinary skill that the graph may encompass more than two subsets of bits. This exemplary nature is demonstrated by the ellipses between the subsets, which indicates that the number of subsets may exceed two. The exemplary nature is also demonstrated by the labels on the graph: Uk, Vk, and Xk. The specification strongly suggests that these variables are placeholders for various other nodes. See '032 Patent, 3:65-67, 4:1-10 ("If the permutation performed in permutation block 310 is fixed, the Tanner graph represents a binary linear block code with k information bits (u1,..., uk) and r parity bits (x1, ..., xr), as follows.... Then if the values of the bits on the ra edges coming out the permutation box are (v1, ..., vra), then we have the recursive formula...."). The specification suggests that the third subset may be omitted. See '032 Patent, 3:46-49 ("For example, in the Tanner graph 300, each of the f2 information nodes are connected to two check nodes, corresponding to a repeat of q=2, and each of the f3 information nodes are connected to three check nodes, corresponding to q=3.").

Even Hughes acknowledges that in some regards, the Tanner graph term is exemplary. For example, Hughes does not contend that the graph requires one subset to be repeated two times, another three times, and another more than three times, even though the graph depicts edges representing these concepts. Hughes implicitly acknowledges that a subset can be a single bit, even though the Tanner graph term depicts two open circles in each subset. Hughes has arbitrarily and inconsistently decided that parts of the Tanner graph term are exemplary, while other parts are not. In reality, the Tanner graph term as a whole is exemplary. It informs a person of ordinary skill of the structure of the code, but it does not define specific parameters.

ii. Indefiniteness

Hughes advances numerous reasons why the Tanner graph term is indefinite. These reasons, taken individually or together as a whole, are insufficient to render the term indefinite. A person of ordinary skill would be more than reasonably certain regarding the scope of the term, especially given the detailed explanation in the specification.

Hughes contends that two small diagonal lines, extending from two of the information nodes to the dotted lines defining a subset, render the term indefinite. These small diagonal lines appear near the second node from the top and the third node from the top. See '032 Patent, 9:1-20. Hughes argues that it is impossible to discern the meaning of these lines. This is hardly the case. First, the diagonal lines are obviously clerical errors. The Tanner graph in the claims is identical to Figure 3, and it appears the same rendering of the Tanner graph in Figure 3 was transported to the claims. See Peng Dec. in Support of Plaintiff's Responsive Brief Ex. A at CALTECH000000326. However, the lines used for labeling in Figure 3 were not completely erased, resulting in two inadvertent lines in the claims. See '032 Patent, Figure 3. To begin with, the Court may correct the errors because "(1) the correction is not subject to reasonable debate based on consideration of the claim language and the specification and (2) the prosecution history does not suggest a different interpretation of the claims." Novo Indus., L.P. v. Micro Molds Corp., 350 F.3d 1348, 1357 (Fed.Cir.2003). Unlike the term in Novo Industries, there is only one reasonable interpretation of these two diagonal lines — that they are meaningless clerical errors that do not alter the meaning of the term. Hughes has not proposed an alternative interpretation that is plausible in light of the specification. See id. ("Indeed, Novo itself suggested two different corrections to the district court.... The interpretation by the district court ... raised still a third possibility."). Further, Hughes has not pointed to anything in the prosecution history to suggest a different interpretation of the Tanner graph term, and as discussed above, the specification describes in detail how to read the Tanner graph. The Court therefore corrects these errors.

In fact, even if the Court did not correct the errors, the Tanner graph term would be definite because of the extensive discussion of the identical Tanner graph in the specification. The specification takes care to discuss all material parts of the Tanner graph. From this discussion, a person of ordinary skill would be more than reasonably certain of the meaning of the Tanner graph term. Moreover, this person would recognize that the two diagonal lines are not material parts of the Tanner graph and therefore do not alter the meaning of the term. This is a far cry from Novo Industries, where the error rendered the sentence incomprehensible absent the district court's construction. Id. at 1352-57 (reversing district court's correction of error in claim reciting "[a] carrier assembly for movably supporting one of a plurality of vertical oriented slats in a vertical blind assembly, said carrier assembly comprising:... stop means formed on a rotatable with said support finger and extending outwardly therefrom into engaging relation with one of two spaced apart stop members formed on said frame").

Hughes' next argument is that the term is indefinite because more lines exit the "Random Permutation" box than enter it. This argument fails because Hughes misreads the graph. The ellipses between message bits and between subsets indicate that additional bits may be repeated, and these extra lines reflect that possibility. The specification indicates that the number of edges entering a check node is defined by "a," which is "a positive integer." '032 Patent, 3:37; see also '032 Patent, 3:50-51 ("Each check node 304 is connected to exactly `a' information nodes 302."). Claim 12, which is dependent on claim 11, affirms this view by reciting "the device of claim 11, wherein ... a number of inputs into nodes vi was not constant." '032 Patent, 9:35-37. A person of ordinary skill would understand the exemplary nature of the Tanner graph, as explained in the specification, and would understand why more lines exit the "Random Permutation" box than enter it. Rather than demonstrating indefiniteness, Hughes' observation merely supports the Court's construction.

In a variation on its indefiniteness argument regarding the equation, supra, Hughes notes that it is not possible to determine the value of parity bits because the graph does not define check node constraints. This argument ignores the teaching of the specification, which observes in an example that "[t]he value of a parity bit is determined uniquely by the condition that the mod-2 sum of the values of the variable nodes connected to each of the check nodes 304 is zero." '032 Patent, 4:4-6. A person of ordinary skill would know that the check nodes could either impose a constraint forcing connected bits to amount to only two possible values: 0 or 1. This argument does not demonstrate the term's indefiniteness.

Finally, Hughes argues that the ellipses in the Tanner graph render it indefinite because they allow the patent to cover an infinite number of possible structural combinations. There are two responses to this argument. First, a person of ordinary skill would understand the meaning of the ellipses, which indicate the exemplary nature of the Tanner graph. Ellipses between subsets and information nodes signify that the graph can encompass any number of information bits, as described in the specification. See '032 Patent, 3:43-45 ("Each information node 302 is connected to a number of check nodes 304. The fraction of information nodes connected to exactly i check nodes is fi."). Moreover, the specification explains the parameters that define the IRA code represented by the Tanner graph: the fi parameter (the subsets of information nodes repeated i times), the "a" parameter (the number of information nodes connected to a check node), and a random permutation. '032 Patent, 3:30-55. Second, the Tanner graph term represents a class of IRA codes, and the specification delineates the boundaries of that class. A person of ordinary skill would understand the boundaries of the claim term, given the specification's discussion. Hughes' argument that the term covers infinite possibilities is really a tautological argument that the term covers everything that it covers. While the scope of the term may be wide-ranging, a person of ordinary skill would be reasonably certain of its breadth. The fact that a term covers broad possibilities does not render it indefinite, as long as a person of ordinary skill can identify the outer boundaries, expansive though they may be.10

Finally, the Court notes that Tanner graphs are well understood. They have been and continue to be commonly used in the art. See, e.g., Johnson, supra, at 219 (using Tanner graph to express repeat-accumulate code). The specification confirms these understandings. Given these two facts, a person of ordinary skill would be able to decipher the Tanner graph term without difficulty or uncertainty.

V. Conclusion

The Court hereby adopts the following constructions:

Claim Term                                         Claim Construction

"transmitting"/"transmission"                      "sending over a channel"
'032 patent, claims 1, 8, 10

"codeword"                                         "a discrete encoded sequence of data
'781 patent, claims 1-4, 11, 13-16, 19-21          elements"

"repeat"                                           Plain meaning. See discussion of term,
'710 patent, claims 1, 6, 11, 15, 16, 19; '032     supra, at 1183-88.
patent, claim 1

"combine"/"combining"                              "perform logical operations on"
'833 patent, claims 1-3, 8-10, 13

Equation in claim 1 of the '032 patent             "the parity bit xj is the sum of (a) the parity
'032 patent, claim 1                               bit xj-1 and (b) the sum of a number, `a,' of
                                                   randomly chosen irregular repeats of the
                                                   message bits"

Claim Term                                         Claim Construction

Tanner Graph term in claims 11 and 18 of           "a graph representing an IRA code as a set
'032 Patent                                        of parity checks where every message bit is
'032 patent, claims 11, 18                         repeated, at least two different subsets of
                                                   message bits are repeated a different number
                                                   of times, and check nodes, randomly
                                                   connected to the repeated message bits, enforce
                                                   constraints that determine the parity
                                                   bits"

IT IS SO ORDERED.