throbber
(12) United States Patent
`Yoshida et al.
`
`USOO6665831B1
`US 6,665,831 B1
`Dec. 16, 2003
`
`(10) Patent No.:
`(45) Date of Patent:
`
`(54) UNEQUAL ERROR PROTECTION IN
`MULTI-CARRIER TRANSMISSION
`(75) Inventors: Makoto Yoshida, Kawasaki (JP); Eizou
`Ishizu, Fukuoka (JP)
`(73) Assignee: Fujitsu Limited, Kawasaki (JP)
`(*) Notice:
`Subject to any disclaimer, the term of this
`patent is extended or adjusted under 35
`U.S.C. 154(b) by 0 days.
`
`(21) Appl. No.: 09/478,603
`(22) Filed:
`Jan. 6, 2000
`O
`O
`(30)
`Foreign Application Priority Data
`Mar. 31, 1999
`(JP) ........................................... 11-09 1884
`(51) Int. Cl." ........................ HO3M 13/00; HO3M 13/03
`(52) U.S. Cl. ........................................ 714/774; 714/790
`(58) Field of Search ................................. 714/774, 790,
`714/751
`
`(56)
`
`References Cited
`U.S. PATENT DOCUMENTS
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`5,467,132 A : 11/1995 Fazel et al.
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`5,699.369 A - 12/1997 Guha. 714/774
`5,729,526 A * 3/1998 Yoshida ...................... 370/206
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`7/2000 Stein .......................... 714/778
`6,108,810 A * 8/2000 Kroeger et al. ............. 714/790
`
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`JP
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`
`.
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`CIl el all. . . . . . . . . . . . . . . . . .
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`6/2001 Smallcomb ................. 714/786
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`FOREIGN PATENT DOCUMENTS
`OS4O 232
`10/1991
`2-84.836
`3/1990
`OTHER PUBLICATIONS
`Fazel, K. and Lhuillier, J.J.; Application of unequal error
`protection codes on combined Source-channel coding of
`images; Conference Record 1990 IEEE International Con
`ference on Communications (ICC), Including Supercomm
`Technical Sessions (SUPERCOMM/ICC 9.*
`(List continued on next page.)
`Primary Examiner Albert Decady
`Assistant Examiner Joseph D. Torres
`(74) Attorney, Agent, or Firm- Katten Muchin Zavis
`Rosenman
`
`ABSTRACT
`(57)
`A method of providing unequal error protection in a multi
`carrier transmission, includes the Steps of coding data for a
`multi-carrier-symbol duration by a coding process of a given
`minimum code distance, the given minimum code distance
`being a minimum of a distance between two codes that is
`measured in multidimensional code Space with N Sub
`carriers, and changing the minimum code distance for each
`multi-carrier-Symbol duration by changing the coding pro
`CCSS.
`
`9 Claims, 19 Drawing Sheets
`
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`US 6,665,831 B1
`Page 2
`
`OTHER PUBLICATIONS
`Calderbank, A.R. and Seshadri, N.; Multilevel codes for
`unequal error protection; IEEE Transactions on Information
`Theory; vol. 39 Issue: Jul. 4, 1993, Page(s): 1224–1248.*
`MoreloS-Zaragoza, R.H. and Shu Lin, Unequal error pro
`tection QPSK modulation codes; Singapore ICCS/ISITA
`92. “Communications on the Move', 1990 Page(s):
`1121-1125 vol. 3. *
`Barton, M.; Unequal error protection for wireless ATM
`applications; Global Telecommunications Conference 1996
`(GLOBECOM 96); Communications: The Key to Global
`Prosperity, vol.:3, 1996 Page(s): 1911–1915.*
`Zheng, H., Raghupathy, A. and Liu, K.J.R., A new loading
`algorithm for image transmitting over Spectrally shaped
`channels: combined Source coding and multicarrier modu
`
`lation approach; Conference Record of the Thirty-Second
`Asilomar Conference on Signals, S.*
`Zheng, H. and Liu, K.J.R.; Parallel transmission framework
`for layered coded multimedia data over spectrally shaped
`channels, This paper appears in: IEEE International Con
`ference on Communications1999; On page(s): 1678–1682
`vol. 3.
`Haitao Zheng and Liu, K.J.R., Robust image and Video
`transmission over spectrally shaped channels using multi
`carrier modulation; IEEE Transactions on Multimedia vol.:
`1 Issue: 1, Mar. 1999 Page(s): 88–103.*
`
`* cited by examiner
`
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`U.S. Patent
`
`Dec. 16, 2003
`
`Sheet 1 of 19
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`US 6,665,831 B1
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`U.S. Patent
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`Dec. 16, 2003
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`Sheet 3 of 19
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`US 6,665,831 B1
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`FIG. 3
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`U.S. Patent
`
`Dec. 16, 2003
`
`Sheet 4 of 19
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`US 6,665,831 B1
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`U.S. Patent
`
`Dec. 16, 2003
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`Sheet 5 of 19
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`US 6,665,831 B1
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`U.S. Patent
`
`Dec. 16, 2003
`
`Sheet 6 of 19
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`US 6,665,831 B1
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`IPR2018-1556
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`U.S. Patent
`
`Dec. 16, 2003
`
`Sheet 7 of 19
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`US 6,665,831 B1
`
`FIG. 7
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`U.S. Patent
`
`Dec. 16, 2003
`
`Sheet 8 of 19
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`US 6,665,831 B1
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`RECEIVED
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`U.S. Patent
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`Dec. 16, 2003
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`Sheet 9 of 19
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`US 6,665,831 B1
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`U.S. Patent
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`Dec. 16, 2003
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`Sheet 10 of 19
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`US 6,665,831 B1
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`U.S. Patent
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`Dec. 16, 2003
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`Sheet 11 of 19
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`US 6,665,831 B1
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`U.S. Patent
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`Dec. 16, 2003
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`Sheet 12 of 19
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`Sheet 13 of 19
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`U.S. Patent
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`Dec. 16, 2003
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`Sheet 14 Of 19
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`US 6,665,831 B1
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`#1
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`Dec. 16, 2003
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`Sheet 15 0f 19
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`US 6,665,831 B1
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`2
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`CODE.
`DISTANCE
`COMPARISON
`UNIT
`
`15-9
`
`MINIMUM
`DISTANCE
`STORAGE
`UNIT
`
`MEMORY
`TIMING
`SIGNAL
`
`MNMUMDISTANCE
`SIGNAL
`
`7
`
`TIMING MEMORY UNIT -- 15-1O
`4OrS
`PARALLELIOSERAL-- DECODEDDATA
`CONVERSION UNIT
`SIGNAL
`15-11
`
`IPR2018-1556
`HTC EX1020, Page 17
`
`

`

`U.S. Patent
`
`Dec. 16, 2003
`
`Sheet 16 of 19
`
`US 6,665,831 B1
`
`16O
`
`#1
`2
`RECEIVED
`DATA SIGNAL #3
`14
`16-2 CODINGSIGNAL 16-4
`4
`
`8
`
`CODNGUNTF
`(R=1/2)
`
`COOING UNITH2
`(R=3/4)
`
`
`
`CODED DATA SIGNA
`TIMING CONTROL
`SIGNAL
`
`DECODER |
`
`TIMING
`CONTROL
`UNIT
`
`1 6-7
`
`
`
`CODED BT SIGNAL
`16-5\ 16-6
`MAPPING
`SIGNAL
`CODE
`ADISTANCE.
`CALCULATION
`UNIT
`
`8
`#2
`SELECTOR2MAPPING3
`UNIT
`UNIT
`H4
`
`
`
`CODE DISTANC
`E
`SIGNAL
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`CODE.
`DISTANCE
`COMPARISON
`UNIT
`
`
`
`
`
`6-9
`
`MINIMUM
`DISTANCE
`STORAGE
`UNIT
`
`MEMORY
`TIMING
`SIGNAL
`
`MINIMUM DISTANCE
`SIGNAL
`
`7
`
`TIMING MEMORY UNIT - 16-10
`4Ores
`PARALLE-TO-SERIAL
`DECODED DATA
`CONVERSION UNIT
`SIGNAL
`16-11
`ag
`
`
`
`YN
`DATA CONTROL
`SIGNAL
`
`
`
`DECODETIMING SIGNAL
`ENEATION UNIth 16-
`TIMING
`CODE
`FRAMETIMING
`
`IPR2018-1556
`HTC EX1020, Page 18
`
`

`

`U.S. Patent
`
`Dec. 16, 2003
`
`Sheet 17 of 19
`
`US 6,665,831 B1
`
`1
`2
`RECEIVED
`DATA SIGNAL #3
`#4
`
`17O
`--
`
`17-7
`
`
`
`4
`
`17-4
`
`8
`
`CODING UNIT
`(R=1/2)
`CODING UNITE2
`
`
`
`
`
`
`
`
`
`CODED BITSIGNAL
`175\ 17-6 MAPPING
`SIGNAL
`\ CODE
`:
`DISTANCE
`#2
`CALCULATION
`8
`SELECTOR2MAPPING
`UNIT
`UNIT
`UNT
`
`17-3
`TIMING
`CONTROL
`UNIT
`
`TIMING CONTROL
`
`| SIGNAL y
`
`
`
`YN
`DATA CONTROL
`SIGNAL
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`DECODE TIMING SIGNAL
`TMING
`17-1
`GENERATION UNIT
`
`CODE
`FRAMETIMING
`
`CODE DISTANC
`E
`SIGNAL
`
`
`
`
`
`
`
`17-9
`
`CODE.
`DISTANCE
`COMPARISON
`UNIT
`
`MINIMUM
`DSTANCE
`MEMORY STORAGE
`UNIT
`TIMING
`SIGNAL
`
`MINIMUM DISTANCE
`SIGNAL
`
`
`
`7
`
`TIMING MEMORY UNIT -- 17-10
`4ores
`PARALLELIOSERAL-DECODEDDATA
`CONVERSION UNIT
`SIGNAL
`17-11
`
`IPR2018-1556
`HTC EX1020, Page 19
`
`

`

`U.S. Patent
`
`Dec. 16, 2003
`
`Sheet 18 of 19
`
`US 6,665,831 B1
`
`FIG. 18A
`
`BER
`
`1.OE-03
`
`
`
`
`
`
`
`BER
`
`OE-05
`
`6
`8
`10 12 14
`S/N (dB)
`
`F.G. 18B
`
`CODE1(R
`1/2).
`CODE2(R 3/4)
`
`1.OE-O2
`
`- - - - - - - -
`
`- - - - - - -
`- - - - - - as
`A.--
`- - - - -es an -s as is a -
`-
`y---
`--------
`
`is a - N- - - - - -
`
`OE-O3
`
`-
`- - - - - - - - - -
`re is -
`- - - -- as - as as a - - - - - -w-
`an - - - - - - - as als
`w
`- - -Ye
`-------
`- - - - - - - - - -
`
`1.OE-04
`
`- - - - - - -
`- a - - - - - - -
`as - - - - - - - - - - - - - - -
`
`- - - - - - - - - - -
`- - - - - - - - - - -
`
`- - - - -r- - - - - - - - - - - - -
`-- r - - - - - - - - -
`
`- are - as are a s - as is is as a
`
`is as as as -
`
`a- - - - - - - -
`
`O
`
`15 20 25 30
`5 1 O
`S/N (dB)
`
`IPR2018-1556
`HTC EX1020, Page 20
`
`

`

`U.S. Patent
`
`Dec. 16, 2003
`
`Sheet 19 of 19
`
`US 6,665,831 B1
`
`FIG. 19A
`
`
`
`IPR2018-1556
`HTC EX1020, Page 21
`
`

`

`1
`UNEQUAL ERROR PROTECTION IN
`MULTI-CARRIER TRANSMISSION
`
`US 6,665,831 B1
`
`BACKGROUND OF THE INVENTION
`1. Field of the Invention
`The present invention generally relates to a method of
`providing unequal error protection in a multi-carrier
`transmission, and relates to a coding device and a decoding
`device for performing Such a method. The present invention
`particularly relates to a method of providing unequal error
`protection by providing different channel qualities for dif
`ferent media in multimedia transmission using a plurality of
`carriers So as to achieve efficient transmission, and relates to
`a coding device and a decoding device for performing Such
`a method.
`2. Description of the Related Art
`In broadband wireleSS communication, multi-path fre
`quency Selective fading is a major factor to deteriorate
`channel quality, and multi-carrier transmission is a well
`known Scheme to cope with this problem.
`FIGS. 19A and 19B are illustrative drawings for explain
`ing the multi-carrier transmission.
`As shown in FIG. 19A, the multi-carrier transmission
`divides a transmission band into a plurality of carrier fre
`quencies f1 through fN (hereinafter called Sub-carriers), and
`each carrier frequency is modulated to transmit data. This
`produces a frequency diversity effect, which compensates
`for degradation of transmission quality caused by frequency
`Selective fading, thereby achieving a high-quality wireleSS
`communication.
`When sub-carriers f1 through fN are orthogonal to each
`other, each modulated Signal can be extracted on the receiver
`Side without any degradation even if carrier spectrums
`overlap with each other as shown in FIG. 19B. This makes
`it possible to make use of a narrower frequency band. Such
`a Scheme is called orthogonal frequency division multiplex
`(OFDM), and is one of the variations of the multi-carrier
`transmission.
`One of the problems of the multi-carrier transmission is
`an increase in a peak envelope power of a transmission
`Signal or an increase in a ratio of the peak to an average
`power. In a transmission System having a large peak power,
`a linear amplifier having a broad range of amplifying levels
`is necessary in order to maintain linearity of the System.
`Such a broad-range linear amplifier is generally expensive,
`and is not attractive in terms of power efficiency. When an
`inexpensive narrow-range linear amplifier is used, a non
`linearity distortion is generated in a Saturation region, result
`ing in a degradation of System performance. These problems
`impeded an effort to use the multi-carrier transmission in
`practice.
`Measures to SuppreSS the peak power mainly fall into
`either one of two different categories. One is to place a
`restriction on input-signal patterns used in the multi-carrier
`transmission, and the other is to limit the output level of
`modulated Signals of the multi-carrier transmission.
`The former measure eliminates an input signal pattern
`having large peak power due to coding. This insures that the
`peak power of a transmission Signal Stays below a certain
`threshold level. No degradation in performance occurs when
`this measure is taken. Further, when the minimum code
`distance is larger than the minimum distance between a
`Signal, a bit error rate can be reduced.
`The later measure utilizes the fact that there is only a
`Small probability of having a Signal pattern with Such a large
`
`1O
`
`15
`
`25
`
`35
`
`40
`
`45
`
`50
`
`55
`
`60
`
`65
`
`2
`peak power as to generate a non-linear distortion. By uti
`lizing this fact, when peak power exceeding a predetermined
`threshold is detected, an exceSS portion of the peak power is
`cut off or clipped off, for example. This measure inevitably
`result in an increase of a Side-robe level due to the non-linear
`distortion. That is, inter-carrier interference is generated.
`This measure thus entails a degradation in performance.
`Another method is to normalize a signal to a threshold
`level by lowering the level of an entire envelope of the
`transmission signal when peak power exceeding the thresh
`old value is detected. This method results in a decrease in the
`Signal-to-noise ratio of the received signal, thereby degrad
`ing the performance.
`In consideration of these, the former measure is preferable
`for the purpose of achieving broadband high-quality wire
`less transmission. In high-speed broadband wireless
`communication, further, multi-media mobile acceSS needs to
`be achieved So as to handle various media Such as image
`data and audio data.
`In multi-media communication, each data type requires
`different channel quality. In general, channel quality
`depends on an employed coding method. However, audio
`transmission requires a bit error rate in the order of 10°, for
`example, while the transmission of image data requires a bit
`error rate lower than 10.
`In packet communication, further, control data for the
`packets requires a higher quality than is required for the data
`information that contains the multi-media contents. This is
`because delivery of packets may fail if the control data
`contains error, and Such a failure may cause an unexpected
`increase in the traffic load on the entire network. In order to
`prevent this, the control information requires a significantly
`lower bit error rate.
`In order to meet these requirements, a plurality of coding
`methods having different levels of protection against bit
`errors may be employed So as to provide different channel
`qualities, thereby achieving efficient transmission. An
`unequal error protection method is known to be effective for
`this purpose.
`The unequal error protection method, however, is not
`directed to the multi-carrier transmission. In other words,
`there is no unequal error protection method known to date
`that is directed to a coding process treating a Set of multi
`carrier Symbols as one code word.
`Accordingly, there is a need for an unequal error protec
`tion method which can provide different channel qualities
`for different data types in the multi-carrier transmission So as
`to improve transmission efficiency, and, also, can reduce
`peak power in the multi-carrier transmission.
`SUMMARY OF THE INVENTION
`Accordingly, it is a general object of the present invention
`to provide an unequal error protection method which can
`satisfy the need described above.
`It is another and more specific object of the present
`invention to provide an unequal error protection method
`which can provide different channel qualities for different
`data types in the multi-carrier transmission So as to improve
`transmission efficiency, and, also, can reduce peak power in
`the multi-carrier transmission.
`In order to achieve the above objects according to the
`present invention, a method of providing unequal error
`protection in a multi-carrier transmission includes the Steps
`of coding data by a coding process of a given minimum code
`distance as measured in block codes comprised of
`
`IPR2018-1556
`HTC EX1020, Page 22
`
`

`

`US 6,665,831 B1
`
`3
`modulated-Signal points of Sub-carriers, and changing the
`minimum code distance for each multi-carrier-Symbol dura
`tion by changing the coding process.
`According to one aspect of the present invention, the
`method as described above has the coding process thereof
`using a set of Such codes that multi-carrier-modulated Signal
`has a peak power lower than a predetermined threshold.
`It is yet another object of the present invention to provide
`an encoder and decoder which can implement the unequal
`error protection method of the present invention.
`In order to achieve the object described above according
`to the present invention, a coding device for providing
`unequal error protection in a multi-carrier transmission
`includes a plurality of coding units, each of which codes a
`corresponding data frame of an information bit Signal by a
`coding process of a given minimum code distance Specific to
`a corresponding coding unit So as to output a coded bit
`Signal, a Selector unit which Successively Selects one of Said
`plurality of coding units, and outputs the coded bit signal
`Supplied from the Selected one of Said plurality of coding
`units, and a mapping unit which maps the coded bit signal
`output from Said Selector unit to complex Signals corre
`sponding to the Sub-carriers.
`Further, a decoding device for decoding received signals
`corresponding to a plurality of Sub-carriers transmitted in a
`multi-carrier-transmission System includes a timing control
`unit which generates data control Signals. Such that each of
`the data control Signals varies over time to present various
`patterns within a corresponding multi-carrier-Symbol
`duration, a plurality of coding units, each of which codes a
`corresponding one of the data control Signals by a coding
`process of a given minimum code distance Specific to a
`corresponding coding unit So as to output a coded bit signal,
`a mapping unit which maps the coded bit signal output from
`a Selected one of Said plurality of coding units to complex
`Signals corresponding to the Sub-carriers, and a code
`distance-calculation unit which calculates a code distance
`between the complex Signals and the received signals with
`respect to each of the various patterns of the corresponding
`one of the data control Signals within a corresponding
`multi-carrier-Symbol duration, wherein one of the various
`patterns providing a Smallest code distance is Selected as a
`decoding result of the corresponding received signals.
`Other objects and further features of the present invention
`will be apparent from the following detailed description
`when read in conjunction with the accompanying drawings.
`BRIEF DESCRIPTION OF THE DRAWINGS
`FIG. 1 is an illustrative drawing showing a basic configu
`ration of an encoder according to the present invention;
`FIG. 2A is an illustrative drawing showing a data-frame
`format of an information bit Signal Supplied to coding units
`of FIG. 1;
`FIG. 2B is an illustrative drawing showing a code-frame
`format of coded bit signals generated by the coding units,
`FIG. 3 is an illustrative drawing showing a change in a
`minimum distance between signals in a M-ary modulation
`Scheme,
`FIG. 4 is a block diagram of a first embodiment of a
`coding device according to the present invention;
`FIG. 5 is a block diagram of a second embodiment of a
`coding device according to the present invention;
`FIG. 6 is an illustrative drawing showing a basic configu
`ration of a decoder according to the present invention;
`FIG. 7 is a block diagram of a first embodiment of a
`decoding device according to the present invention;
`
`5
`
`15
`
`25
`
`35
`
`40
`
`45
`
`50
`
`55
`
`60
`
`65
`
`4
`FIG. 8 is a block diagram of a second embodiment of a
`decoding device according to the present invention;
`FIG. 9 is a block diagram showing a simplified version of
`the first embodiment of a coding device according to the
`present invention;
`FIG. 10 is a table showing relations between inputs and
`outputs of a coding unit;
`FIG. 11 is a block diagram showing a simplified version
`of the Second embodiment of a coding device according to
`the present invention;
`FIG. 12 is a block diagram showing another simplified
`version of the first embodiment of a coding device according
`to the present invention;
`FIG. 13 is a block diagram showing another simplified
`version of the Second embodiment of a coding device
`according to the present invention;
`FIG. 14 is a simplified version of the first embodiment of
`a decoding device according to the present invention;
`FIG. 15 is a simplified version of the second embodiment
`of a decoding device according to the present invention;
`FIG. 16 is another simplified version of the first embodi
`ment of a decoding device according to the present inven
`tion;
`FIG. 17 is another simplified version of the second
`embodiment of a decoding device according to the present
`invention;
`FIGS. 18A and 18B are charts showing bit-error-rate
`performance in relation to a S/N ratio according to the
`present invention; and
`FIGS. 19A and 19B are illustrative drawings for explain
`ing a multi-carrier transmission in the related art.
`DESCRIPTION OF THE PREFERRED
`EMBODIMENTS
`In the following, a principle and embodiments of the
`present invention will be described with reference to the
`accompanying drawings.
`FIG. 1 is an illustrative drawing showing a basic configu
`ration of an encoder according to the present invention.
`The encoder of FIG. 1 includes a plurality of coding units
`1-1 and a mapping unit 1-2. The coding units 1-1 receive an
`information bit signal, and encode the information bit Signal
`to generate coded bit Signals. The mapping unit 1-2 receives
`the coded bit signals, and outputs mapping Signals to modu
`late respective Sub-carriers.
`We assume that transmission of the information bit Signal
`is performed by using m different channel qualities.
`FIG. 2A is an illustrative drawing showing a data-frame
`format of the information bit signal Supplied to the coding
`units.
`When the information bit signal is to be transmitted by
`using m different channel qualities, the information bit
`signal has m data sub-frames FD, through FD. In FIG. 2A,
`V through V, indicate the number of bits included in the
`data Sub-frames FD, through FD, respectively. A total
`number V of included bits is represented as:
`
`where X, "{ } indicates a Sum of the contents in the
`brackets with respect to the index i from 1 to m. The same
`notation will be used hereinafter in the Specification.
`The coding units 1-1 of FIG. 1 receive respective data
`Sub-frames of the information bit signal. Namely, an input to
`
`IPR2018-1556
`HTC EX1020, Page 23
`
`

`

`S
`the coding units 1-1 is Switched So as to Selectively Supply
`the data sub-frames FD, through FD, to the respective
`coding units 1-1. Each of the coding units 1-1 encodes the
`Supplied data according to the required channel quality, So
`that the coding units 1-1 accord the data sub-frames FD
`through FD, with unequal error protection against bit errors.
`The coding units 1-1 attend to the coding of data by a unit
`of multi-carrier Symbol, and outputs the coded bit signals
`with respect to n Sub-carriers. In response, the mapping unit
`1-2 generates mapping Signals for modulating the n Sub
`carriers according to modulation Schemes predetermined for
`the respective data sub-frames FD, through FD. Here, the
`mapping signals are complex signals (I ch/Q ch).
`FIG. 2B is an illustrative drawing showing a code-frame
`format of the coded bit Signals generated by the coding units.
`The code-frame format includes m code sub-frames FC,
`through FC.
`In FIG. 2B, w through w, indicate the number of bits
`included in the code Sub-frames FC through F.C.,
`respectively, and W indicates a total number of the bits. A
`number of bits w of a code sub-frame FC, and the total
`number W of the bits are represented as:
`
`15
`
`US 6,665,831 B1
`
`6
`Where a minimum distance (power) between signals in each
`carrier is denoted as d, use of all the codes {C} as
`transmission codes results in dif=d.
`The present invention uses m different partial Sets of the
`code Space C, as output codes generated in one symbol
`duration, thereby producing Symbols having different mini
`mum code distances.
`Namely, where the minimum code distance in the entire
`code space Cn is denoted as d(Cn) and the minimum
`code distance in a partial set C of C, is denoted as
`da, (C), the present invention Selects a partial code Space
`C for each input information Such that dif(Cn)sda,
`(Cp) is Satisfied, thereby providing different channel quali
`ties.
`Where a coding rate when the entire code Space C is used
`is denoted as R(C) and a coding rate when the partial set C.
`is employed is denoted as R(C), it inevitably ensues that
`R(C.)2R(C).
`A coding rate R of a given Sub-frame is represented by a
`ratio of the number D, of input bits to the number C. of
`output bits in one multi-carrier Symbol duration.
`
`(2)
`(3)
`where B, indicates a sub-carrier modulation level (bits/
`symbol) of the coded sub-frame FC, and 8, indicates a
`number of symbols constituting the coded sub-frame FC.
`When a coding rate of the i-th coding unit 1-1 is R, the
`number of bits w of the code sub-frame FC, and the number
`of bits V of a data sub-frame FD, are related as:
`
`(4)
`The multi-carrier transmission System using in Sub
`carriers has n channels, each of which has a transmission
`rate that is 1/n of the transmission rate of the Single-carrier
`transmission. The n channels together achieve parallel trans
`mission of data. Such a multi-carrier transmission System
`treats a n-dimensioinal signal Space as one codeword where
`the n-dimensional Signal Space is generated for one symbol
`duration (such a duration is referred to as a 1 FFT symbol
`duration in the case of the OFDM method).
`A n-dimensional code space C, represented by a code c(i)
`is mapped onto an output-code-Sequence vector S(c(i)) in
`the Signal Space vector S generated by one multi-carrier
`Symbol. Here, the output-code-Sequence vector S(c(i)) is
`represented as:
`
`where S(c(i)) is a complex signal point of a k-th carrier
`(1sksn) with respect to the code c(i), and i corresponds to
`input information.
`When Mindicates a modulation level of each carrier, each
`carrier represents 2' bit patterns of information. For n
`carriers, information i represents a total of 2" bit patterns
`(i.e., codewords).
`In this case, a code distance d between two different
`codes is represented as:
`
`25
`
`35
`
`40
`
`45
`
`50
`
`55
`
`60
`
`Accordingly, a minimum code distance (power) do
`between codes is represented as:
`
`65
`
`(7)
`
`Assuming that the i-th coding unit 1-1 of FIG. 1 has a
`minimum code distance dif(i) and a coding rate R,
`(1sism), then, an average coding rate R is represented as:
`R*=V/W=(1/W)-X,"{wR}
`(9)
`With regard to the coding units 1-1, it should be noted that
`there are no rules or restrictions on a number of coding units
`that do not attend to error corrections as well as on positions
`of Su

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