Attorney Docket No. 10,693,700
`IPR of U.S. Patent No. 19688-0196IP2
`
`DECLARATION OF JUNE ANN MUNFORD
`
`1
`
`LGE 1027
`
`

`

`
`
`
`Attorney Docket No. 10,693,700
`IPR of U.S. Patent No. 19688-0196IP2
`
`1. My name is June Ann Munford. I am over the age of 18, have personal
`
`knowledge of the facts set forth herein, and am competent to testify to the
`
`same.
`
`2. I earned a Master of Library and Information Science (MLIS) from the
`
`University of Wisconsin-Milwaukee in 2009. I have over ten years of
`
`experience in the library/information science field. Beginning in 2004, I
`
`have served in various positions in the public library sector including
`
`Assistant Librarian, Youth Services Librarian and Library Director. I have
`
`attached my Curriculum Vitae as Appendix CV.
`
`3. During my career in the library profession, I have been responsible for
`
`materials acquisition for multiple libraries. In that position, I have cataloged,
`
`purchased and processed incoming library works. That includes purchasing
`
`materials directly from vendors, recording publishing data from the material
`
`in question, creating detailed material records for library catalogs and
`
`physically preparing that material for circulation. In addition to my
`
`experience in acquisitions, I was also responsible for analyzing large
`
`collections of library materials, tailoring library records for optimal catalog
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`1
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`2
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`
`
`Attorney Docket No. 10,693,700
`IPR of U.S. Patent No. 19688-0196IP2
`
`search performance and creating lending agreements between libraries
`
`during my time as a Library Director.
`
`
`4. I am fully familiar with the catalog record creation process in the library
`
`sector. In preparing a material for public availability, a library catalog record
`
`describing that material would be created. These records are typically
`
`written in Machine Readable Catalog (herein referred to as “MARC”) code
`
`and contain information such as a physical description of the material,
`
`metadata from the material’s publisher, and date of library acquisition. In
`
`particular, the 008 field of the MARC record is reserved for denoting the
`
`date of creation of the library record itself. As this typically occurs during
`
`the process of preparing materials for public access, it is my experience that
`
`an item’s MARC record indicates the date of an item’s public availability.
`
`
`5. Typically, in creating a MARC record, a librarian would gather various bits
`
`of metadata such as book title, publisher and subject headings among others
`
`and assign each value to a relevant numerical field. For example, a book’s
`
`physical description is tracked in field 300 while title/attribution is tracked in
`
`field 245. The 008 field of the MARC record is reserved for denoting the
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`creation of the library record itself. As this is the only date reflecting the
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`inclusion of said materials within the library’s collection, it is my experience
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`
`
`Attorney Docket No. 10,693,700
`IPR of U.S. Patent No. 19688-0196IP2
`
`that an item’s 008 field accurately indicates the date of an item’s public
`
`availability.
`
`
`6. I have reviewed Exhibit LGE1014, “Turbo-coded APSK Modulations
`
`Design for Satellite Broadband Communications” by Riccardo De Gaudenzi,
`
`et al. as published in International Journal of Satellite Communications and
`
`Networking, May 2006.
`
`
`7. Attached hereto as Appendix DEGAUDENZI01 is a true and correct copy of
`
`the MARC record for International Journal of Satellite Communications
`
`and Networking as held by the Penn State University library. I secured this
`
`record myself from the library’s public catalog. The MARC record
`
`contained within Appendix DEGAUDENZI01 accurately describes the title,
`
`author, publisher, and ISSN number of International Journal of Satellite
`
`Communications and Networking. The ‘362’ field of this record visible on
`
`page 1 indicates this collection includes the May 2006 edition of
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`International Journal of Satellite Communications and Networking
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`containing “Turbo-coded APSK Modulations Design for Satellite Broadband
`
`Communications”.
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`
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`Attorney Docket No. 10,693,700
`IPR of U.S. Patent No. 19688-0196IP2
`
`8. Attached hereto as Appendix DEGAUDENZI02 is a true and correct copy of
`
`“Turbo-coded APSK Modulations Design for Satellite Broadband
`
`Communications” as published in International Journal of Satellite
`
`Communications and Networking, May 2006. I secured this PDF copy
`
`myself from the Penn State University library’s digital holdings. In
`
`comparing Exhibit LGE1014 to Appendix DEGAUDENZI02, it is my
`
`determination that Exhibit LGE1014 is a true and correct copy of “Turbo-
`
`coded APSK Modulations Design for Satellite Broadband Communications”
`
`by Riccardo De Gaudenzi, et al. as published in International Journal of
`
`Satellite Communications and Networking, May 2006.
`
`
`9. The 008 field of the MARC record in Appendix DEGAUDENZI01 indicates
`
`the date of record creation. The 008 field of Appendix DEGAUDENZI01
`
`indicates the Penn State University library first acquired this journal as of
`
`October 21, 2002 and still holds the journal in perpetuity. Considering this
`
`information, it is my determination that International Journal of Satellite
`
`Communications and Networking, May 2006 and therefore “Turbo-coded
`
`APSK Modulations Design for Satellite Broadband Communications” was
`
`made available to the public shortly after its initial release in May 2006.
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`
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`Attorney Docket No. 10,693,700
`IPR of U.S. Patent No. 19688-0196IP2
`
`10. I have been retained on behalf of the Petitioner to provide assistance in the
`
`above-illustrated matter in establishing the authenticity and public
`
`availability of the documents discussed in this declaration. I am being
`
`compensated for my services in this matter at the rate of $100.00 per hour
`
`plus reasonable expenses. My statements are objective, and my
`
`compensation does not depend on the outcome of this matter.
`
`
`11. I declare under penalty of perjury that the foregoing is true and correct. I
`
`hereby declare that all statements made herein of my own knowledge are
`
`true and that all statements made on information and belief are believed to
`
`be true; and further that these statements were made the knowledge that
`
`willful false statements and the like so made are punishable by fine or
`
`imprisonment, or both, under Section 1001 of Title 18 of the United States
`
`Code.
`
`
`
`Dated: 12/9/2022
`
`
`
`June Ann Munford
`
`
`
`5
`
`6
`
`

`

`APPENDIX CV
`APPENDIX CV
`
`7
`
`

`

`J. Munford
`Curriculum Vitae
`
`Education
`
`University of Wisconsin-Milwaukee - MS, Library & Information Science, 2009
`Milwaukee, WI
`
`
`● Coursework included cataloging, metadata, data analysis, library systems,
`management strategies and collection development.
`● Specialized in library advocacy, cataloging and public administration.
`
`
`Grand Valley State University - BA, English Language & Literature, 2008
`Allendale, MI
`
` ●
`
` Coursework included linguistics, documentation and literary analysis.
`● Minor in political science with a focus in local-level economics and
`government.
`
`
`
`Professional Experience
`
`Researcher / Expert Witness, October 2017 – present
`Freelance ● Pittsburgh, Pennsylvania & Grand Rapids, Michigan
`
`
`● Material authentication and public accessibility determination.
`Declarations of authenticity and/or public accessibility provided upon
`research completion. Experienced with appeals and deposition process.
`
` ●
`
` Research provided on topics of public library operations, material
`publication history, digital database services and legacy web resources.
`
` ●
`
` Past clients include Alston & Bird, Arnold & Porter, Baker Botts, Fish &
`Richardson, Erise IP, Irell & Manella, O'Melveny & Myers, Perkins-Coie,
`Pillsbury Winthrop Shaw Pittman and Slayden Grubert Beard.
`
`Library Director, February 2013 - March 2015
`Dowagiac District Library ● Dowagiac, Michigan
`
`
`● Executive administrator of the Dowagiac District Library. Located in
`
`8
`
`

`

`Southwest Michigan, this library has a service area of 13,000, an annual
`operating budget of over $400,000 and total assets of approximately
`$1,300,000.
`
`● Developed careful budgeting guidelines to produce a 15% surplus during
`the 2013-2014 & 2014-2015 fiscal years while being audited.
`
`
`
` ●
`
` Using this budget surplus, oversaw significant library investments
`including the purchase of property for a future building site, demolition of
`existing buildings and building renovation projects on the current facility.
`
` Led the organization and digitization of the library's archival records.
`
` ●
`
` ●
`
` Served as the public representative for the library, developing business
`relationships with local school, museum and tribal government entities.
`
` ●
`
` Developed an objective-based analysis system for measuring library
`services - including a full collection analysis of the library's 50,000+
`circulating items and their records.
`
`November 2010 - January 2013
`Librarian & Branch Manager, Anchorage Public Library ● Anchorage, Alaska
`
`
`● Headed the 2013 Anchorage Reads community reading campaign
`including event planning, staging public performances and creating
`marketing materials for mass distribution.
`
` ●
`
` Co-led the social media department of the library's marketing team,
`drafting social media guidelines, creating original content and instituting
`long-term planning via content calendars.
`
` ●
`
` Developed business relationships with The Boys & Girls Club, Anchorage
`School District and the US Army to establish summer reading programs for
`children.
`
`
`June 2004 - September 2005, September 2006 - October 2013
`Library Assistant, Hart Area Public Library
`Hart, MI
`
`
`● Responsible for verifying imported MARC records and original MARC
`
`9
`
`

`

`
`
`cataloging for the local-level collection as well as the Michigan Electronic
`Library.
`
`● Handled OCLC Worldcat interlibrary loan requests & fulfillment via
`ongoing communication with lending libraries.
`
`
`
`Professional Involvement
`
`Alaska Library Association - Anchorage Chapter
`● Treasurer, 2012
`
`
`Library Of Michigan
`● Level VII Certification, 2008
`● Level II Certification, 2013
`
`
`Michigan Library Association Annual Conference 2014
`● New Directors Conference Panel Member
`
`
`Southwest Michigan Library Cooperative
`● Represented the Dowagiac District Library, 2013-2015
`
`
`
`Professional Development
`
`Library Of Michigan Beginning Workshop, May 2008
`Petoskey, MI
`● Received training in cataloging, local history, collection management,
`children’s literacy and reference service.
`
`
`Public Library Association Intensive Library Management Training, October 2011
`Nashville, TN
`● Attended a five-day workshop focused on strategic planning, staff
`management, statistical analysis, collections and cataloging theory.
`
`
`Alaska Library Association Annual Conference 2012 - Fairbanks, February 2012
`Fairbanks, AK
`● Attended seminars on EBSCO advanced search methods, budgeting,
`cataloging, database usage and marketing.
`
`10
`
`

`

`Depositions
`
`2019 ● Fish & Richardson
`
`IPR Petitions of 865 Patent, Apple v. Qualcomm (IPR2018-001281 /
`
`39521-00421IP & IPR2018-01282 / 39521-00421IP2)
`
`2019 ● Erise IP
`
`Implicit, LLC v. Netscout Systems, Inc (Civil Action No. 2:18-cv-53-JRG)
`
`2019 ● Perkins-Coie
`
`Adobe Inc. v. RAH Color Technologies LLC (Cases IPR2019-00627,
`
`IPR2019-00628, IPR2019-00629 and IPR2019-00646)
`
`2020 ● O’Melveny & Myers
`
`Maxell, Ltd. v. Apple Inc. (Case 5:19-cv-00036-RWS)
`
`2021 ● Pillsbury Winthrop Shaw Pittman LLP
`
`Intel v. SRC (Case IPR2020-1449)
`
`
`Limited Case History & Potential Conflicts
`
`Alston & Bird
`
`● Nokia (v. Neptune Subsea, Xtera)
`
`Arnold & Porter
`
`● Ivantis (v. Glaukos)
`
`Erise I.P.
`
`● Apple
`
`
`v. Future Link Systems (IPRs 6317804, 6622108, 6807505, and
`
`
`7917680)
`
`
`v. INVT
`
`
`v. Navblazer LLC (Case No. IPR2020-01253)
`
`11
`
`

`

`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`v. Qualcomm (IPR2018-001281, 39521-00421IP, IPR2018-01282,
`39521-00421IP2)
`v. Quest Nettech Corp, Wynn Technologies (Case No. IPR2019-
`00XXX, RE. Patent Re38137)
`
`● Fanduel (v CGT)
`
`● Garmin (v. Phillips North America LLC, Case No. 2:19-cv-6301-AB-KS
`Central District of California)
`
`● Netscout
`
`v. Longhorn HD LLC)
`
`v. Implicit, LLC (Civil Action No. 2:18-cv-53-JRG)
` ● Sony Interactive Entertainment LLC
`v. Bot M8 LLC
`v. Infernal Technology LLC
`● Unified Patents (v GE Video Compression, Civil Action No. 2:19-cv-248)
`
`
`Fish & Richardson
`
`● Apple
`
`
`v. LBS Innovations
`
`
`v. Masimo (IPR 50095-0012IP1, 50095-0012IP2, 50095-0013IP1,
`
`
`50095-0013IP2, 50095-0006IP1)
`
`
`v. Neonode
`
`
`v. Qualcomm (IPR2018-001281, 39521-00421IP, IPR2018-01282,
`
`
`39521-00421IP2)
`
`
`
`
`● Dish Network
`
`v. Realtime Adaptive Streaming, Case No 1:17-CV-02097-RBJ)
`
`12
`
`

`

`v. TQ Delta LLC
`
` Huawei (IPR 76933211)
`
` Kianxis
`
`
`
` ●
`
` ●
`
` ●
`
` LG Electronics (v. Bell Northern Research LLC, Case No. 3:18-cv-2864-
`CAB-BLM)
`
` ●
`
` ●
`
` Samsung (v. Bell Northern Research, Civil Action No. 2:19-cv-00286-
`JRG)
`
` Texas Instruments
`
` ●
`
`
`Irell & Manella
`
`● Curium
`
`O’Melveny & Myers
`
`● Apple (v. Maxell, Case 5:19-cv-00036-RWS)
`
`Perkins-Coie
`
`● TCL Industries (v. Koninklijke Philips NV, PTAB Case Nos. IPR2021-
`
`00495, IPR2021-00496, and IPR2021-00497)
`
`Pillsbury Winthrop Shaw Pittman
`
`● Intel (v. FG SRC LLC, Case No. 6:20-cv-00315 W.D. Tex)
`
` Metaswitch
`
` MLC Intellectual Property (v. MicronTech, Case No. 3:14-cv-03657-SI)
`
` Realtek Semiconductor
`
` Quectel
`
` ●
`
` ●
`
` ●
`
`13
`
`

`

`APPENDIX DEGAUDENZI01
`APPENDIX DEGAUDENZIO01
`
`14
`
`

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`International journal of satellite co
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`Uniform Title:
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`Additional Titles:
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`Int. j. satell. commun. netw. (Online) and Satellite co
`
`Published:
`
`(Chichester, West Sussex] : John Wiley & Sons
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`Access Online
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`Continues:
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`International journal of satellite communications (Online) 1099-1247
`
`Dates of Publication and/or Sequential Designation:
`Vol. 21, issue 1 (Jan./Feb. 2003)-
`
`Subject(s):
`Digital communications—Periodicals
`Artificial satellites in telecommunication—Periodicals
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`Genre(s):
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`ISSN:
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`Advertisement
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`international journal of satellite
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`Volume 24, Issue 4
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`Pages: 261-317
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`7” Export Citation(s)
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`| Research Articles
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`@) Full Access
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`Turbo-coded APSK modulations design for satellite broadband communications
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`Riccardo De Gaudenzi, Albert Guillén i Fabregas, Alfanso Martinez
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`Pages: 261-281 | First Published: 19 May 2006
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`Abstract | PDF | References|Request permissions
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`Review and comparison of tropospheric scintillation prediction models for satellite
`communications
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`P. Yu, |. A. Glover, P. A. Watson, O. T. Davies, S. Ventouras, C. Wrench
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`Pages: 283-302 | First Published: 18 May 2006
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`Semi-random LDPC codes for CDMA communication over non-linear band-limited
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`satellite channels
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`Mohamed Adnan Landolsi
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`Pages: 303-317 | First Published: 08 June 2006
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`APPENDIX DEGAUDENZI02
`APPENDIX DEGAUDENZI02
`
`21
`
`

`

`INTERNATIONAL JOURNAL OF SATELLITE COMMUNICATIONS AND NETWORKING
`Int. J. Satell. Commun. Network. 2006; 24:261–281
`Published online 19 May 2006 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/sat.841
`
`Turbo-coded APSK modulations design for satellite
`broadband communications
`
`Riccardo De Gaudenzi1,*,y, Albert Guille´ n i Fa` bregas2, and Alfanso Martinez3
`
`1 European Space Agency (ESA-ESTEC), Noordwijk, The Netherlands
`2 Institute for Telecommunications Research, University of South Australia, Australia
`3 Technische Universitat Eindhoven, Eindhoven, The Netherlands
`
`SUMMARY
`
`This paper investigates the design of power and spectrally efficient coded modulations based on amplitude
`phase shift keying (APSK) modulation with application to satellite broadband communications. APSK
`represents an attractive modulation format for digital transmission over nonlinear satellite channels due to
`its power and spectral efficiency combined with its inherent robustness against nonlinear distortion. For
`these reasons APSK has been very recently introduced in the new standard for satellite Digital Video
`Broadcasting named DVB-S2. Assuming an ideal rectangular transmission pulse, for which no nonlinear
`inter-symbol interference is present and perfect pre-compensation of the nonlinearity, we optimize the
`APSK constellation. In addition to the minimum distance criterion, we introduce a new optimization based
`on the mutual
`information; this new method generates an optimum constellation for each spectral
`efficiency. To achieve power efficiency jointly with low bit error rate (BER) floor we adopt a powerful
`binary serially concatenated turbo-code coupled with optimal APSK modulations through bit-interleaved
`coded modulation. We derive tight approximations on the maximum-likelihood decoding error
`probability, and results are compared with computer simulations. The proposed coded modulation
`scheme is shown to provide a considerable performance advantage compared to current standards for
`satellite multimedia and broadcasting systems. Copyright # 2006 John Wiley & Sons, Ltd.
`
`Received 1 May 2005; Revised 1 February 2006; Accepted 29 March 2006
`
`KEY WORDS:
`
`turbo codes; amplitude-phase shift keying (APSK); modulation; bit-interleaved coded
`modulation (BICM); coded modulation; nonlinear channels; satellite communications
`
`1. INTRODUCTION
`
`A major strength of satellite communications systems lies on their ability to efficiently broadcast
`digital multi-media information over very large areas [1]. A notable example is the
`
`*Correspondence to: Riccardo De Gaudenzi, European Space Agency (ESA-ESTEC), RF Payload Systems division,
`Keplerlaan 1, P.O. Box 299, AG Noordwijk, The Netherlands.
`y E-mail: riccardo.de.gaudenzi@esa.int
`
`Copyright # 2006 John Wiley & Sons, Ltd.
`
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`262
`
`R. DE GAUDENZI, A. GUILLE´ N I FA` BREGAS AND A. MARTINEZ
`
`so-called direct-to-home (DTH) digital television broadcasting. Satellite systems also provide a
`unique way to complement
`the terrestrial
`telecommunication infrastructure in scarcely
`populated regions. The introduction of multi-beam satellite antennas with adaptive coding
`and modulation (ACM) schemes will allow an important efficiency increase for satellite systems
`operating at Ku or Ka-band [2]. Those technical enhancements require the exploitation of
`power- and spectrally efficient modulation schemes conceived to operate over the satellite
`nonlinear channel. In this paper, we will design high-efficiency 16- and 32-ary coded modulation
`schemes suited for nonlinear satellite channels. The analysis presented here is complemented in
`[3] with the effects related to satellite nonlinear distortion, band-limited transmission pulse,
`demodulator timing, amplitude and phase estimation errors.
`To the authors’ knowledge there are few references in the literature dealing with 16-ary
`constellation optimization over nonlinear channels,
`the typical environment
`for satellite
`channels. Previous work showed that 16-QAM does not compare favourably with either
`trellis-coded (TC) 16-PSK or uncoded 8-PSK in satellite nonlinear channels [4]. The concept of
`circular APSK modulation was already proposed 30 years ago by Thomas et al. [5], where
`several nonband-limited APSK sets were analysed by means of uncoded bit error rate bounds;
`the suitability of APSK for nonlinear channels was also made explicit, but concluded that for
`single carrier operation over nonlinear channel APSK performs worse than PSK schemes. In the
`current paper, we will revert the conclusion. It should be remarked that Reference [5] mentioned
`the possibility of modulator pre-compensation but did not provide performance results related
`to this technique. Foschini et al. [6] optimized QAM constellations using asymptotic uncoded
`probability of error under average power constraints, deriving optimal 16-ary constellation
`made of an almost equilateral lattice of triangles. This result is not applicable to satellite
`channels. In Reference [7] some comparison between squared QAM and circular APSK over
`linear channels was performed based on the computation of the error bound parameter,
`showing some minor potential advantage of APSK. Further work on mutual information for
`modulations with average and peak power constraints is reported in Reference [8], which proves
`the advantages of circular APSK constellations under those power constraints. Mutual
`information performance loss for APSK in peak power limited Gaussian complex channels is
`reported in Reference [9] and compared to classical QAM modulations; it is shown that under
`this assumption APSK considerably outperforms QAM in terms of mutual information, the
`gain particularly remarkable for 16- and 64-ary constellations.
`Forward error correcting codes for our application must combine power efficiency and low
`BER floor with flexibility and simplicity to allow for high-speed implementation. The existence
`of practical, simple, and powerful such coding designs for binary modulations has been settled
`with the advent of turbo codes [10] and the recent re-discovery of low-density parity-check
`(LDPC) codes [11]. In parallel, the field of channel coding for nonbinary modulations has
`evolved significantly in the latest years. Starting with Ungerboeck’s work on TC modulation
`(TCM) [12], the approach had been to consider channel code and modulation as a single entity,
`to be jointly designed and demodulated/decoded. Schemes have been published in the literature,
`where turbo codes are successfully merged with TCM [13]. Nevertheless, the elegance and
`simplicity of Ungerboeck’s original approach gets somewhat lost in a series of ad hoc
`adaptations; in addition, the turbo-code should be jointly designed with a given modulation, a
`solution impractical for system supporting several constellations. A new pragmatic paradigm
`has crystallized under the name of bit-interleaved coded modulation (BICM) [13], where
`extremely good results are obtained with a standard nonoptimized, code. An additional
`
`Copyright # 2006 John Wiley & Sons, Ltd.
`
`Int. J. Satell. Commun. Network. 2006; 24:261–281
`DOI: 10.1002/sat
`
`23
`
`

`

`TURBO-CODED APSK MODULATIONS DESIGN
`
`263
`
`advantage of BICM is its inherent flexibility, as a single mother code can be used for several
`modulations, an appealing feature for broadband satellite communication systems where a large
`set of spectral efficiencies is needed.
`This paper is organized as follows. Section 2 gives the system model under the ideal case of a
`rectangular transmission pulse.z Section 3 gives a formal description of APSK signal sets,
`describes the maximum mutual information and maximum minimum distance optimization
`criteria and discusses some of the properties of the optimized constellations. Section 4 deals with
`code design issues, describes the BICM approach, provides some analytical considerations based
`on approximate maximum-likelihood (ML) decoding error probability bounds, and provides
`some numerical results. The conclusions are finally drawn in Section 5.
`
`2. SYSTEM MODEL
`
`The baseband equivalent of the transmitted signal at time t; sT ðtÞ, is given by
`L1
`
`
`
`ffiffiffiffip X
`
`sT ðtÞ ¼
`
`P
`
`xðkÞpT ðt kTsÞ
`
`k¼0
`
`ð1Þ
`
`where P is the signal power, xðkÞ is the kth transmitted symbol, drawn from a complex-valued
`APSK signal constellation X; with jXj ¼ M; pT is the transmission filter impulse response, and
`Ts is the symbol duration (in seconds), corresponding to one channel use. Without loss of
`generality, we consider transmission of frames with L symbols. The spectral efficiency R is
`defined as the number of information bits conveyed at every channel use, and in measured in
`bits per second per Hertz (bps/Hz).
`The signal sT ðtÞ passes through a high-power amplifier (HPA) operated close to the saturation
`point. In this region, the HPA shows nonlinear characteristics that induce phase and amplitude
`distortions to the transmitted signal. The amplifier is modelled by a memoryless nonlinearity,
`with an output signal sAðtÞ at time t given by
`sAðtÞ ¼ FðjsT ðtÞjÞejðfðsT ðtÞÞþFðjsT ðtÞjÞÞ
`
`ð2Þ
`
`where we have implicitly defined FðAÞ and FðAÞ as the AM/AM and AM/PM characteristics of
`the amplifier for a signal with instantaneous signal amplitude A: The signal amplitude is the
`is decomposed as sT ðtÞ ¼
`instantaneous complex envelope, so that the baseband signal
`jsT ðtÞjejfðsT ðtÞÞ:
`In this paper, we assume an (ideal) signal modulating a train of rectangular pulses. These
`pulses do not create inter-symbol interference when passed through an amplifier operated in the
`nonlinear region. Under these conditions, the channel reduces to an AWGN, where the
`modulation symbols are distorted following (2). Let xA denote the distorted symbol
`corresponding to x ¼ jxjejfðxÞ 2 X; that is, xA ¼ FðjxjÞejðfðxÞþFðjxjÞÞ: After matched filtering and
`sampling at time kTs; the discrete-time received signal at time k; yðkÞ is then given by
`
`p
`
`ffiffiffiffiffi
`
`yðkÞ ¼
`
`Es
`
`xAðkÞ þ nðkÞ;
`
`k ¼ 0; . . .; L 1
`
`ð3Þ
`
`z This assumption has been dropped in the paper [14].
`
`Copyright # 2006 John Wiley & Sons, Ltd.
`
`Int. J. Satell. Commun. Network. 2006; 24:261–281
`DOI: 10.1002/sat
`
`24
`
`

`

`264
`
`R. DE GAUDENZI, A. GUILLE´ N I FA` BREGAS AND A. MARTINEZ
`
`with Es the symbol energy, given by Es ¼ PTs; xAðkÞ is the symbol at the kth time instant, as
`defined above, and nðkÞ  NCð0; N0Þ is the corresponding noise sample.
`This simplified model suffices to describe the nonlinearity up to the nonlinear ISI effect, and
`allows us to easily design constellation and codes. In the paper [14], the impact of nonlinear ISI
`has been considered, as well as other realistic demodulation effects such as timing and phase
`recovery.
`
`3. APSK CONSTELLATION DESIGN
`
`In this section, we define the generic multiple-ring APSK constellation family. We propose new
`criteria for the design of digital QAM constellations of 16 and 32 points, with special emphasis
`on the behaviour on nonlinear channels.
`
`3.1. Constellation description
`
`M-APSK constellations are composed of nR concentric rings, each with uniformly spaced PSK
`points. The signal constellation points x are complex numbers, drawn from a set X given by
`r1ejðð2p=n1Þiþy1Þ;
`i ¼ 0; . . .; n1 1 ðring 1Þ
`r2ejðð2p=n2Þiþy2Þ;
`
`i ¼ 0; . . .; n2 1 ðring 2Þ
`
`ð4Þ
`
`8>>>>>>><
`>>>>>>>:
`
`. r
`
`..
`
`X ¼
`
`P
`
`nR ejðð2p=nRÞiþynR Þ;
`i ¼ 0; . . .; nnR 1 ðring nRÞ
`where we have defined n‘; r‘ and y‘ as the number of points, the radius and the relative phase
`shift for the ‘th ring. We will nickname such modulations as n1 þ þ nnR -APSK. Figure 1
`depicts the 4 þ 12- and 4 þ 12 þ 16-APSK modulations with quasi-Gray mapping. In
`particular, for next generation broadband systems [2, 15], the constellation sizes of interest
`are jXj ¼ 16 and 32; with nR ¼ 2 and 3 rings, respectively. In general, we consider that X is
`normalized in energy, i.e. E½jxj2Š ¼ 1; which implies that the radii r‘ are normalized such that
`nR
`‘ ¼ 1: Notice also that the radii r‘ are ordered, so that r15 5 rnR:
`‘¼1 n‘r2
`Clearly, we can also define the phase shifts and the ring radii in relative terms rather than in
`absolute terms, as in (4); this removes one dimension in the optimization process, yielding a
`practical advantage. We let f‘ ¼ y‘ y1 for ‘ ¼ 1; . . . ; nR be the phase shift of the ‘th ring with
`respect to the inner ring. We also define r‘ ¼ r‘=r1 for ‘ ¼ 1; ; nR as the relative radii of the
`‘th ring with respect to r1: In particular, f1 ¼ 0 and r1 ¼ 1:
`
`3.2. Constellation optimization in AWGN
`We are interested in finding an APSK constellation, defined by the parameters q ¼ ðr1; . . .; rnR
`Þ
`Þ; such that a given cost function f ðXÞ reaches a minimum. The simplest,
`