Second Declaration of Jose Tellado
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`UNITED STATES PATENT AND TRADEMARK OFFICE
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`———————
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`BEFORE THE PATENT TRIAL AND APPEAL BOARD
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`———————
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`Cisco Systems, Inc.,
`Petitioner
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`———————
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`
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`IPR2016-01020
`U.S. Patent No. 9,014,243
`
`IPR2016-01021
`U.S. Patent No. 8,718,158
`
`———————
`
`SECOND DECLARATION OF DR. JOSE TELLADO
`UNDER 37 C.F.R. § 1.68
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`UNITED STATES PATENT AND TRADEMARK OFFICE
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`———————
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`BEFORE THE PATENT TRIAL AND APPEAL BOARD
`
`———————
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`
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`Cisco Systems, Inc.,
`Petitioner
`
`
`
`———————
`
`
`
`IPR2016-01020
`U.S. Patent No. 9,014,243
`
`IPR2016-01021
`U.S. Patent No. 8,718,158
`
`———————
`
`SECOND DECLARATION OF DR. JOSE TELLADO
`UNDER 37 C.F.R. § 1.68
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`TABLE OF CONTENTS
`I. Background ........................................................................................................ 1
`II. Clipping is just one example of a “PAR problem” ............................................ 1
`III. Because Shively’s bit spreading technique employs multiple carriers to
`carry the same data, Shively’s technique increases PAR .................................. 3
`IV. Shively’s bit spreading technique is not limited to 18,000 foot cables ............. 3
`V. Likelihood of phase alignment of random data and data using Shively’s
`bit spreading technique ...................................................................................... 9
`VI. The 12,000 foot cable example shows how Shively’s technique increases
`PAR and the likelihood of signal clipping ....................................................... 17
`VII. A simulation of a transmitter shows that Shively’s technique increases
`PAR and the likelihood of clipping ................................................................. 25
`VIII. A POSITA would have wanted to reduce to cost of a transmitter
`employing Shively’s bit-spreading technique ................................................. 32
`IX. Stopler describes phase scrambling QAM symbols ........................................ 33
`X. Stopler does not require diagonalization ......................................................... 35
`XI. My PhD Thesis ................................................................................................ 36
`XII. Conclusion ....................................................................................................... 36
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`Second Declaration of Dr. Jose Tellado
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`I, Dr. Jose Tellado, do hereby declare as follows:
`
`I.
`
`Background
`1.
`
`I have been retained as an independent expert declarant on behalf of
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`Cisco Systems, Inc. (“Cisco”) for the above captioned Inter Partes Reviews of U.S.
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`Patent No. 9,014,243 (“the ’243 Patent”) and U.S. Patent No. 8,718,158 (“the ’158
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`Patent”). I am being compensated at my usual and customary rate for the time I
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`spend in connection with these matters. My compensation is not affected by the
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`outcome of either matter.
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`2.
`
`I have been asked to provide a supplemental declaration regarding
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`certain arguments and statements made by the Patent Owner, TQ Delta, and its
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`expert declarant, Dr. Robert T. Short.
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`II.
`
`Clipping is just one example of a “PAR problem”
`3.
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`Dr. Short appears to suggest that a “PAR problem” exists only when a
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`system encounters an unacceptable level of transmission errors due to signal
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`clipping. See, e.g., Ex. 2003, ¶30 (“A PAR “problem” exists when the actual
`
`clipping rate exceeds the maximum allowable rate.”). I disagree because Dr.
`
`Short’s conception of a “PAR problem” is too narrow. A person of ordinary skill
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`in the art (POSITA) would have understood that in addition to causing problems
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`during a transceiver’s operation (such as clipping), a high PAR is associated with
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`problems and disadvantages that arise during the transceiver’s design. For
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`example, while a transmitter can be designed to handle a high PAR signal without
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`clipping, the resulting transmitter will generally be more expensive, less efficient,
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`and larger. From both an engineering and a practical standpoint, the size, cost, and
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`efficiency of a high-PAR transmitter are disadvantages and potential problems.
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`For example, the low efficiency of such a transmitter will cause it to consume a
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`large amount of electrical power, raising its operating expense and generating
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`significant waste heat. At a telephone company’s central offices, many such
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`transmitters would be used in close proximity to one another, and their waste heat
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`would have to be removed through additional cooling equipment—at still further
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`operational cost—to prevent them from overheating and destroying themselves. A
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`POSITA would have considered that to be a problem, and therefore a POSITA
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`would have been motivated to look for ways to reduce the need for high-cost, high-
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`power, low-efficiency transmitters by reducing the PAR of the signals to be
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`transmitted.
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`4.
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`Indeed, PAR reduction was an active area of research in the 1990s. It
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`was well-known to use a bit-scrambler (or, equivalently, a phase scrambler) to
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`produce a pseudorandomly phase-aligned multicarrier signal, which (as discussed
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`above) has an amplitude with a Gaussian distribution. The active research areas
`
`focused on trying to achieve better than Gaussian performance, that is, to achieve
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`PAR values that are even lower than would occur in a random system. Simply
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`achieving Gaussian-level performance—which is all that the simple randomization
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`techniques of the ’243 and ’158 patents achieve—was trivial and well-known.
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`III. Because Shively’s bit spreading technique employs multiple carriers to
`carry the same data, Shively’s technique increases PAR
`5.
`
`Shively describes a bit spreading technique that “replicates (‘spreads’)
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`a k-bit symbol over multiple adjacent bands.” Ex. 1011, 11:17-18. This causes the
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`bands (which are also called carriers) to carry the same bit or bits, and more
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`specifically, to be modulated using the same QAM symbol. Because these carriers
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`carry the same data and are modulated with the same QAM symbol, the phases of
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`these carriers align. I agree with Dr. Short’s statement that phases of the phase-
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`aligned carriers will add coherently and create a transmission signal with a spike in
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`power. Ex. 2003, ¶ 22; Ex. 1027, 97:21-23.
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`6.
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`In a system that does not implement Shively’s technique, this spike in
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`power would not occur because these carriers would be deemed impaired and
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`would not carry data. Because Shively’s technique causes the impaired carriers to
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`carry the same data, Shively’s technique increases probability of new spikes in the
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`amplitude. And, because of these spikes, Shively’s technique increases PAR.
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`IV.
`
`Shively’s bit spreading technique is not limited to 18,000 foot cables
`7.
`
`Dr. Short considered the application of Shively’s bit-spreading
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`technique to a line of 18,000 feet with narrow gauge (AWG 26) and therefore very
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`high attenuation. See Ex. 2003, ¶¶58-68. However, Shively’s technique is not
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`limited to lines of only 18000 feet and AWG 26 gauge, nor is it limited to lines
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`suffering from very high attenuation. Shively broadly describes using its bit-
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`spreading technique “to compensate for high attenuation and/or high noise in those
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`parts of the communication channel frequency band that would otherwise not be
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`unusable due to noise and attenuation effects” and reduce near-end crosstalk noise.
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`Ex. 1011, 15:50-53, 4:35-37. Thus, Shively’s bit-spreading technique can be
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`applied to other kinds of line impairments, such as crosstalk noise. Crosstalk noise
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`is caused by signal coupling between adjacent lines (telephone wire pairs). The
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`amount of crosstalk noise on a line depends on its proximity to other lines and the
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`types of signals transmitted over those other lines. There are many sources of
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`crosstalk (near-end cross talk, far-end cross talk, etc.) and even relatively short
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`lines can have significant crosstalk noise.
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`8.
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`The ANSI T1.413-1995 standard describes both near-end and far-end
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`crosstalk as possible noise sources in the ADSL system. See, e.g., ANSI T1.413-
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`1995, pp. 116 & 137-146. A person of ordinary skill in the art would have been
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`familiar with both near-end and far-end crosstalk noise. The near-end crosstalk
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`noise is the crosstalk noise on a line that is caused by other transmitters at the same
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`end of the line as where the noise is being measured. Far-end crosstalk noise refers
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`to crosstalk noise on a line that is caused by transmitters at the opposite end of the
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`line from where the noise is being measured.
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`9.
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`The ANSI T1.413-1995 standard provides multiple graphs showing
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`examples of potential near-end crosstalk (NEXT) noise levels that could impact an
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`ADSL system. The NEXT noise levels depend on types of signals that are
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`transmitted on the adjacent communication line (or lines). Figure B.1, below,
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`shows that having 24 adjacent DSL lines could cause significant noise levels,
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`particularly in much of the frequency range from 0 kHz to about 530 kHz. As a
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`reference point, I’ve annotated the diagrams with a horizontal line at -140 dBm/Hz,
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`which was the “background noise” level shown in the attenuation graph relied
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`upon by Dr. Short. See Ex. 2003, ¶¶ 59, 61.
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`background
`noise floor
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`ANSI T1.413-1995, p.138.
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`10. Figure B.2 from the ANSI T1.413-1995 standard shows that having
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`ten adjacent HDSL communication lines could cause significant noise levels in
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`much of the frequency range below about 380 kHz and from 410 kHz to 650 kHz.
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`I have similarly annotated this diagram with a background noise threshold at -140
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`dBm/Hz:
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`background
`noise floor
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`
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`ANSI T1.413-1995, p. 140.
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`11. Figure B.3 from the ANSI T1.413-1995 standard shows that having
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`either 4 or 20 adjacent T1 communication lines could cause increasing noise levels
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`throughout most of the frequency range used by ADSL (0-1.1 MHz). I have
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`annotated this diagram with a background noise threshold at -140 dBm/Hz:
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`background
`noise floor
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`
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`ANSI T1.413-1995, p. 142.
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`12. The ANSI T1.413-1995 standard also includes a graph showing
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`potential far-end crosstalk in a typical ADSL system. Figure B.4 shows that
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`having 10 adjacent lines being used for ADSL communications could cause
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`significant noise levels in the lower half of the frequency spectrum used for ADSL
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`communications, with the most significant noise levels generally in the frequency
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`range from 10 kHz to 740 kHz. I have annotated this diagram with a background
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`noise threshold at -140 dBm/Hz:
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`background
`noise floor
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`ANSI T1.413-1995, p. 142.
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`13.
`
` These near-end and far-end crosstalk graphs show that crosstalk can
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`be a significant impairment in a communication system and can significantly
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`exceed the -140 dBm/Hz background noise level.
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`14. A POSITA would have recognized that Shively’s bit-spreading
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`technique could be usefully applied to lines suffering from noise-induced
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`impairments, such as the examples of crosstalk noise discussed above. As I
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`mentioned previously, Shively states that bit-spreading is a way to “compensate for
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`high attenuation and/or high noise.” Ex.1011, 15:50. Since noise can occur on a
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`line of any length, a POSITA would not have considered Shively’s bit-spreading
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`technique to be limited to being used on only long lines.
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`Likelihood of phase alignment of random data and data using Shively’s
`V.
`bit spreading technique
`15. DMT systems generally sought to randomize the data being
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`transmitted to reduce the likelihood of phase alignment among the multiple carriers
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`used to transmit data. To do so, they typically employed a bit-scrambler that
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`would apply an exclusive-OR operation between each bit being transmitted and a
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`bit generated by pseudorandom number generator. The resulting stream of bits
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`encodes the desired data but is mathematically pseudorandom. The ANSI T1.413-
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`1995 standard describes a typical arrangement in Section 6.3. See ANSI T1.413-
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`1995, p. 35. A corresponding pseudorandom number generator in the receiver and
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`another exclusive-OR operation could then be used to recover the original data
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`bits.
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`16. When a bit-scrambled data stream is transmitted, the bits are mapped
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`to QAM symbols that then specify the phase of each carrier. Since the bits are
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`pseudorandom, the QAM symbols are pseudorandom, and the resulting carrier
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`phases are pseudorandom.1 This makes the amount of phase-alignment among the
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`1 To be exact, the phase of each carrier is pseudorandomly selected from a discrete
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`number of possible phase values, which depend on the modulation scheme. QAM-
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`carriers also be pseudorandom, so that the sum of the signals (representing the
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`power required to transmit the summed signal) can be appropriately approximated
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`using a Gaussian random variable. When the carriers’ phase-alignment is not
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`random (or pseudorandom), then the Gaussian approximation does not hold and
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`should not be used. Shively’s bit-spreading technique causes multiple carriers to
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`be intentionally aligned, and therefore the likelihood of their alignment is no longer
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`randomized. A system using Shively’s bit-spreading technique cannot be
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`reasonably approximated by a Gaussian random variable. Thus, Dr. Short was not
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`correct in applying the Gaussian approximation to a system using Shively’s bit-
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`spreading technique. See Ex. 2003, ¶66.
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`17. The likelihood that a given number of carriers transmitting random
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`symbols will all be phase-aligned depends on the number of carriers. Basically,
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`with an increasing number of carriers, it becomes less likely that all of those
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`carriers will be phase-aligned. The examples below further explain this concept.
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`18. First, consider the case in which single bits are transmitted by
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`modulating the phases of individual carriers. This modulation scheme is known as
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`4, for example, has four phase values. In systems with a sufficient number of
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`carriers (such as the 256 carriers called for in ANSI T1.413-1995), the difference
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`between (a) each carrier having one of a set number of possible phases and (b)
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`each carrier having any phase value, is not significant.
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`binary phase shift keying (“BPSK”), because each carrier has one of two phase
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`values. For example, the bit value of “0” can correspond to a sine wave, while the
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`bit value of “1” can correspond to a sine wave with a 180º phase shift. If two bits
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`are modulated onto two distinct carriers, the carriers will have the same phase
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`when they encode the same bit values. As shown in Table I below, there are four
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`possible combinations of bit values. In two of those combinations, the bit values
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`are the same (either both “1” or both “0”). If all four possible combinations are
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`equally likely (e.g., because the bit values are random), then the likelihood that
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`both bits have the same value, and hence the likelihood of both carriers having the
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`same phase, is 2 in 4, or 50%.
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`Carrier #1
`Bit = 0
`Phase = 0º
`Bit = 0
`Phase = 0º
`Bit = 1
`Phase = 180º
`Bit = 1
`Phase = 180º
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`Table 1
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`Carrier #2
`Bit = 0
`Phase = 0º
`Bit = 1
`Phase = 180º
`Bit = 0
`Phase = 0º
`Bit = 1
`Phase = 180º
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`Phases Aligned?
`Aligned
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`Not aligned
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`Not aligned
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`Aligned
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`
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`19. When three carriers are phase-modulated with three bits (one bit on
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`each carrier), there are 23 = 8 possible combinations of bit values on the carriers.
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`The bits will all be the same only if they are all 0’s or all 1’s. Thus, the likelihood
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`of all three carriers carrying the same value, and therefore having the same phase,
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`is 2 in 8, or 25%. This is illustrated using the Table 2 below:
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`Table 2
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`Carrier #1
`Bit = 0
`Phase = 0º
`Bit = 0
`Phase = 0º
`Bit = 0
`Phase = 0º
`Bit = 0
`Phase = 0º
`Bit = 1
`Phase = 180º
`Bit = 1
`Phase = 180º
`Bit = 1
`Phase = 180º
`Bit = 1
`Phase = 180º
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`Carrier #2
`Bit = 0
`Phase = 0º
`Bit = 0
`Phase = 0º
`Bit = 1
`Phase = 180º
`Bit = 1
`Phase = 180º
`Bit = 0
`Phase = 0º
`Bit = 0
`Phase = 0º
`Bit = 1
`Phase = 180º
`Bit = 1
`Phase = 180º
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`Carrier #3
`Bit = 0
`Phase = 0º
`Bit = 1
`Phase = 180º
`Bit = 0
`Phase = 0º
`Bit = 1
`Phase = 180º
`Bit = 0
`Phase = 0º
`Bit = 1
`Phase = 180º
`Bit = 0
`Phase = 0º
`Bit = 1
`Phase = 180º
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`
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`Phases Aligned?
`Aligned
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`Not aligned
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`Not aligned
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`Not aligned
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`Not aligned
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`Not aligned
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`Not aligned
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`Aligned
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`20. Similarly, when four carriers are phase-modulated with one bit per
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`carrier, there are 24 = 16 possible combinations of bit values. The likelihood of all
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`four carriers carrying the same bit value, and thus having the same phase, is 2 in
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`16, or 12.5%. This is illustrated using the Table 3 below:
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`Table 3
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`Carrier #1
`Bit = 0
`Phase = 0º
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`Carrier #2
`Bit = 0
`Phase = 0º
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`Carrier #3
`Bit = 0
`Phase = 0º
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`Carrier #4
`Bit = 0
`Phase = 0º
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`Phases Aligned?
`Aligned
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`Carrier #1
`Bit = 0
`Phase = 0º
`Bit = 0
`Phase = 0º
`Bit = 0
`Phase = 0º
`Bit = 0
`Phase = 0º
`Bit = 0
`Phase = 0º
`Bit = 0
`Phase = 0º
`Bit = 0
`Phase = 0º
`Bit = 1
`Phase = 180º
`Bit = 1
`Phase = 180º
`Bit = 1
`Phase = 180º
`Bit = 1
`Phase = 180º
`Bit = 1
`Phase = 180º
`Bit = 1
`Phase = 180º
`Bit = 1
`Phase = 180º
`Bit = 1
`Phase = 180º
`
`Carrier #2
`Bit = 0
`Phase = 0º
`Bit = 0
`Phase = 0º
`Bit = 0
`Phase = 0º
`Bit = 1
`Phase = 180º
`Bit = 1
`Phase = 180º
`Bit = 1
`Phase = 180º
`Bit = 1
`Phase = 180º
`Bit = 0
`Phase = 0º
`Bit = 0
`Phase = 0º
`Bit = 0
`Phase = 0º
`Bit = 0
`Phase = 0º
`Bit = 1
`Phase = 180º
`Bit = 1
`Phase = 180º
`Bit = 1
`Phase = 180º
`Bit = 1
`Phase = 180º
`
`Carrier #3
`Bit = 0
`Phase = 0º
`Bit = 1
`Phase = 180º
`Bit = 1
`Phase = 180º
`Bit = 0
`Phase = 0º
`Bit = 0
`Phase = 0º
`Bit = 1
`Phase = 180º
`Bit = 1
`Phase = 180º
`Bit = 0
`Phase = 0º
`Bit = 0
`Phase = 0º
`Bit = 1
`Phase = 180º
`Bit = 1
`Phase = 180º
`Bit = 0
`Phase = 0º
`Bit = 0
`Phase = 0º
`Bit = 1
`Phase = 180º
`Bit = 1
`Phase = 180º
`
`
`Carrier #4
`Bit = 1
`Phase = 180º
`Bit = 0
`Phase = 0º
`Bit = 1
`Phase = 180º
`Bit = 0
`Phase = 0º
`Bit = 1
`Phase = 180º
`Bit = 0
`Phase = 0º
`Bit = 1
`Phase = 180º
`Bit = 0
`Phase = 0º
`Bit = 1
`Phase = 180º
`Bit = 0
`Phase = 0º
`Bit = 1
`Phase = 180º
`Bit = 0
`Phase = 0º
`Bit = 1
`Phase = 180º
`Bit = 0
`Phase = 0º
`Bit = 1
`Phase = 180º
`
`Phases Aligned?
`Not aligned
`
`Not aligned
`
`Not aligned
`
`Not aligned
`
`Not aligned
`
`Not aligned
`
`Not aligned
`
`Not aligned
`
`Not aligned
`
`Not aligned
`
`Not aligned
`
`Not aligned
`
`Not aligned
`
`Not aligned
`
`Aligned
`
`21. Likewise, when eight carriers are phase modulated with one bit per
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`carrier, there are 28 = 256 possible combinations of bit values. The likelihood of all
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`eight carriers having the same phase is 2 in 256, or 0.78%.
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`22.
`
`In general, when n bits are modulated on n carriers, there are 2n
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`possible combinations of bit values. There are only two possible ways for all of
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`the bit values to be the same (either all 0’s or all 1’s), so the likelihood of n carriers
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`all having the same phase is:
`
`
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`
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`(cid:2870)(cid:2870)(cid:3289)
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`Eq. 1
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`23. Shively’s technique changes the likelihood of multiple carriers having
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`the same phase significantly. When Shively’s bit-spreading technique is applied to
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`the carriers, the bits on these carriers are no longer independent of one another.
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`Instead, Shively’s bit spreading technique intentionally modulates multiple carriers
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`with the same bit, which results in these carriers having the same phase.
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`24. Shively suggests using groups of 4 carriers. Ex. 1011, 13:49-52. This
`
`means that the 4 carriers in each group will carry the same data and be modulated
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`using the same symbol. Shively contemplates that the 4 carriers will collectively
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`transmit a single bit of data, and thus they will have a 1-bit symbol. The phase-
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`modulation of a single bit of data is known as BPSK. If 4 carriers use Shively’s
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`technique, the likelihood that these 4 carriers will phase-align is 100%. It is a stark
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`contrast to 12.5% chance of phase alignment when the 4 carriers carry random bits.
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`If 8 carriers use Shively’s technique (two groups of 4), then the likelihood of all 8
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`carriers being phase-aligned is 50%. Again, it is a stark contrast to the 0.78%
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`chance if these same carriers carried random bits.
`
`25.
`
`In general, when n bits are modulated onto n carriers that are divided
`
`into groups of 4, and each group carries the same bit values, there are 2n/4 possible
`
`combinations of bit values. So, the likelihood of n carriers all having the same
`
`phase if they are employing Shively’s technique is:
`
`(cid:2870)(cid:2870)(cid:4672)(cid:3289)(cid:3120)(cid:4673)
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`
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`Eq. 2
`
`26. Graphing equations #1 and #2 illustrates that probability of n-carriers
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`having perfect phase alignment when carriers carry random bits and bits using
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`Shively’s bit spreading technique is never close, and only grows further apart as
`
`the number of carriers increase:
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`Graph 1
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`likelihood of perfect phase alignment
`
`number of carriers
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`27. As illustrated above, the probability of carriers phase-aligning is
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`radically different between the random-data case (equation #1) and the Shively’s
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`bit spreading technique case (equation #2).
`
`28. The enormity of the differences also becomes apparent when
`
`considering how often the phases of carriers align in a multicarrier system, such as
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`ADSL as defined by the ANSI T1.413-1995 standard. ADSL transmits 4000 DMT
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`symbols per second. ANSI T1.413-1995, p. 24. Table 4 below summarizes the
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`frequency with which n carriers will have a perfect phase alignment when a given
`
`number of carriers carry random BPSK data (equation #1) and when they carry
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`BPSK data using Shively’s bit spreading technique (equation #2). To determine the
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`frequency with which a set of carriers have perfect phase alignment, the
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`likelihoods of equation #1 and equation #2 are multiplied by the DMT symbol rate
`
`(4000 symbols/second).
`
`Number of phase-
`aligned carriers
`4
`8
`16
`24
`32
`48
`52
`
`
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`Table 4
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`Random data frequency Shively frequency
`
`500 times per second
`31 times per second
`Once every 8 seconds
`Once every 35 minutes
`Once every 6 days
`Once every 1100 years
`One every 17,850 years
`
`4000 times per second
`2000 times per second
`500 times per second
`125 times per second
`31 times per second
`2 times per second
`Once per second
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`16
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`29.
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`In his analysis of an 18,000 foot cable, Dr. Short determined that a
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`maximum of 16 carriers (4 groups of 4) carried bits using Shively’s bit spreading
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`technique. Ex. 2003, ¶66. Dr. Short’s analysis is flawed because, in assuming a
`
`Gaussian approximation, he treats Shively’s carriers as if they carried random data
`
`and thus grossly underestimates the likelihood that those carriers will have their
`
`phases align. Dr. Short erroneously assumed that Shively’s bit spreading technique
`
`will, on average, cause all 16 carriers to have the same phase about once every 8
`
`seconds. But Table 4 demonstrates that Shively’s bit spreading technique will
`
`cause all 16 carriers to align approximately 500 times per second. Thus, Dr. Short’s
`
`numerical analysis is based entirely on an erroneous assumption and is unreliable.
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`VI. The 12,000 foot cable example shows how Shively’s technique increases
`PAR and the likelihood of signal clipping
`30. Dr. Short stated that his analysis of an 18,000 foot narrow gauge and
`
`high loss (AWG26) cable without crosstalk is based in part on Figure 6 in Exhibit
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`2009. Ex. 1027, 32:2-8. Figure 6, replicated below, shows line attenuation for five
`
`different cable lengths.
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`Ex. 2009, p. 31, Fig. 6.
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`31. Figure 6 shows line attenuation in the frequency band from 0 kHz to
`
`1100 kHz, which generally corresponds to the frequency range used for
`
`communication in the ANSI T1.413-1995 standard. The ANSI standard employs
`
`256 carriers, with each carrier spaced 4.3125 kHz apart. ANSI T1.413-1995, p. 46.
`
`Because low frequency carriers, such as carriers #1 through #6, are often reserved
`
`for analog voice and a guardband, ADSL services typically start with carrier #7.
`
`Ex. 1016, p. 187. Thus, out of 256 carriers there may be 250 downstream carriers
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`that can carry ADSL data.2 It is appropriate to focus on the use of Shively’s
`
`technique in the downstream direction because it generally uses more carriers than
`
`the upstream direction, so the engineering considerations regarding signal power
`
`and PAR are generally greater for the downstream direction.
`
`32.
`
`In his analysis of an 18,000 foot cable, Dr. Short categorizes the
`
`carriers into three groups:
`
`
`
`Unimpaired carriers are those carriers above a threshold that can be
`
`used for ordinary ADSL communication (i.e., above the 2-BIT
`
`THRESHOLD (DMT) shown in Figure 6). Unimpaired carriers can
`
`2 The availability of 250 downstream carriers is for systems employing echo
`
`cancellation, allowing the upstream subchannels to also be used for downstream
`
`data. If echo cancellation is not used, then there will be fewer carriers used for
`
`downstream data. See ANSI T1.413-1995, p. 46:
`
`The channel analysis signal defined in 12.6.6 allows for a maximum
`of 255 carriers (at frequencies nΔf , n = 1 to 255) to be used. If echo
`cancelling (EC) is used to separate downstream and upstream signals,
`then the lower limit on n is determined by the ADSL/POTS splitting
`filters; if frequency division multiplexing (FDM) is used the lower
`limit is set by the down – up splitting filters. The cut-off frequencies
`of these filters are completely at the discretion of the manufacturer
`because, in either case, the range of usable n is determined during the
`channel estimation.
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`carry data with high probability of success. Ex. 2003, ¶¶ 27-28; Ex.
`
`1027, 27:9-16.
`
`
`
`Impaired carriers are those carriers that cannot be used for ordinary
`
`ADSL communication (i.e., below the 2-BIT THRESHOLD) but are
`
`above the -140 dBm/Hz background noise floor. Impaired carriers
`
`can carry data using Shively’s bit spreading technique. Ex. 2003, ¶¶
`
`49-50; Ex. 1027, p. 22:24-23:7 and 90:12-14.
`
`
`
`Unusable carriers are those carriers below the noise floor (-140
`
`dBm/Hz). Unusable carriers are not used to carry data. Ex. 2003, ¶51;
`
`Ex. 1027, 28:17-20.
`
`33. Below I have applied Dr. Short’s categories to the 12,000-foot
`
`example shown in Dr. Short’s source for attenuation information. To assist with
`
`applying Dr. Short’s categories, I have annotated Fig. 6 with a horizontal line
`
`at -135 dBm/Hz, which approximates the minimum received signal strength
`
`required to reliably use a carrier to transmit one bit, when that carrier is part of a
`
`group of four carriers employing Shively’s bit-spreading technique. I arrived at the
`
`-135 dBm/Hz value as follows: First, the 1-bit threshold would normally lie about
`
`11.3 dBm/Hz above the -140 dBm/Hz noise floor, or at about -128.7 dBm/Hz.
`
`That value is approximately where Dr. Short drew his 1-bit threshold on Fig. 6.
`
`See Ex. 2003, ¶59. The annotated Figure 6 below shows the 1-bit threshold as a
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`dashed red line. Using Shively’s bit-spreading technique across four carriers
`
`provides approximately 6 dB of coding gain, meaning that the 1-bit threshold when
`
`using Shively’s technique is 6 dBm/Hz lower, at about -135 dBm/Hz.3
`
`1-bit (non-repeating)
`threshold
`
`1-bit, 4-carrier-
`repeating threshold
`
`
`
`Unimpaired
`Carriers
`
`Impaired
`Carriers
`
`Unusable
`Carriers
`
`
`
`Ex. 2009, Fig. 6 (annotated).
`
`3 This analysis does not take into account a ± 3dB ripple permitted in the ANSI
`
`T1.413 power spectral density mask. See ANSI T1.413-1995, p. 48, Fig. 17. The
`
`power spectral density mask allows slightly more power (up to 3dB) to be put into
`
`carriers whose attenuated signal strength would be close to the -135 dBm/Hz
`
`threshold. By exploiting the ±3dB ripple, a transmitter could potentially extend the
`
`application of Shively’s bit-spreading technique to even more carriers.
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`34.
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`In effect, consideration of the minimum signal strength required to
`
`reliably transmit one bit when using Shively’s technique (i.e., the -135 dBm/Hz
`
`threshold) differs from Dr. Short’s description of the delineation between
`
`“impaired” and “unusable” carriers. Dr. Short’s description would categorize
`
`carriers between -135 dBm/Hz and -140 dBm/Hz as “impaired,” whereas I am
`
`categorizing them as “unusable” when Shively’s technique is applied to groups of
`
`four carriers. However, using Shively’s bit-spreading on these “unusable” carriers
`
`(for example, by spreading over more than 4 carriers to achieve greater coding
`
`gain) would only cause PAR to climb even higher.
`
`35. When I apply Dr. Short’s carrier categories to the 12,000 foot
`
`AWG26 attenuation graph, the carriers with frequencies from 0 to approximately
`
`810 kHz are “unimpaired” carriers that can carry random data using ordinary
`
`ADSL modulation (e.g., QAM-4). The carriers with frequencies from
`
`approximately 810 kHz to approximately 1040 kHz are “impaired” carriers that
`
`could carry data using Shively’s bit spreading technique. The carriers with
`
`frequencies approximately 1040 kHz to 1104 kHz are “unusable” carriers when
`
`Shively repeats one bit on four carriers.
`
`36. To determine the number of unimpaired carriers, I divide the carriers
`
`in the unimpaired frequency range (0 kHz to 810 kHz) by the frequency width of
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`each carrier (4.3125 kHz). This analysis demonstrates that the 12,000 foot cable
`
`has approximately 188 unimpaired carriers (810 kHz / 4.3125 kHz = 188).
`
`37. To determine the number of impaired carriers, I divide the carriers in
`
`the impaired frequency range (810 kHz to 1040 kHz, or 230 kHz) by the frequency
`
`width of each carrier (4.3125 kHz). This analysis demonstrates that the 12,000 foot
`
`cable has approximately 53 impaired carriers (230 kHz / 4.3125 kHz = 53.3).
`
`Using a similar approach, I calculate that the unusable frequencies between 1040
`
`kHz and 1104 kHz correspond to approximately 15 unusable carriers: (1104 kHz –
`
`1040 kHz) / 4.3125 = 14.8 carriers.
`
`38. As I mentioned previously, the six lowest-frequency carriers were
`
`commonly left unused to avoid potential interference with ordinary analog voice
`
`communications. Thus, the 12,000 foot cable would use approximately 182
`
`unimpaired carriers (188 – 6 = 182). Shively suggests an example that uses the bit-
`
`spreading technique with carriers arranged in groups of four, which would allow
`
`for 52 of 53 impaired carriers to carry repeated data (arranged in 13 groups of 4
`
`carriers each). The leftover, 53rd carrier would be unused.
`
`39. When 52 carriers (13 groups of 4) carry repeated data, varying
`
`numbers of carriers will align at different DMT symbols, thereby creating a spike
`
`in the transmission signal amplitude. For example, Table 4
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