United States Patent
`Nakamura et al.
`[45] Date of Patent:
`Dec. 1, 1992
`
`llllllllllllllIIIIIIIIIIIIIIlllllllllIllllllllllllllIllllllllllllllllllllll
`
`U8005168509A
`
`[11] Patent Number:
`
`5,168,509
`
`[19]
`
`[54] QUADRATURE AMPLITUDE
`MODULATION COMMUNICATION
`SYSTEM WITH TRANSPARENT ERROR
`CORRECTION
`
`[75]
`
`Inventors:
`
`Makoto Nakamura, Kanagawa;
`Tomoko Kodama, Yokohama, both of
`Japan
`
`[73] Assignee: Kabushiki Kaisha Toshiba, Kawasaki,
`Japan
`.
`
`[21] Appl. No.: 507,303
`
`[22] Filed:
`
`Apr. 10, 1990
`
`Foreign Application Priority Data
`[30]
`Apr. 12. 1989 [JP]
`Japan .................................... 1-90623
`Apr. 28. 1989 [JP]
`Japan ..
`............ I-Ill622
`
`[51]
`Int. Cl.5 ............... H04L 05/12
`
`[52] US. Cl. ........................ 375/39; 371/375
`[58] Field of Search ....................... 375/39, 27, 42, 27,
`375/39, 42; 371/37.l, 37.5, 43
`
`[56]
`
`References Cited
`U.S. PATENT DOCUMENTS
`
`4,553,237 11/1985 Nakamura ............................. 375/39
`
`FOREIGN PATENT DOCUMENTS
`
`0111349
`0219252
`
`Japan .................................. 371/375
`9/1981
`9/1988 Japan ..................................... 375/39
`
`OTHER PUBLICATIONS
`
`IEEE Transactions on Communication Technology,
`vol. COM—19, No. 5, pp. 8212—8835, “A High—Speed
`Sequential Decoder: Prototype Design and Test”, G.
`D. Forney, et 31.. Oct. 1971.
`Proceedings of International Conference on Communi-
`cations, pp. 1472-1477 (F24). “6GHz 135MBPS Digital
`
`Radio System With 64 QAM Modulation”, T. Noguchi,
`et al., 1983.
`Proceedings of International Conference on Communi-
`cations, pp. 1482-1486 (46.7), “6GHZ 140MBPS Digi-
`tal Radio Repeater With 256QAM Modulation", Y.
`Yoshida, et al., 1986.
`Lin, et al., Error Control Coding Fundamentals and Ap-
`plications, Prentice-Hall, Inc., N.J., 1983, pp. 34-39,
`85:93,.141-151, and 170-177.
`
`Primary Examiner—Curtis Kuntz
`Assistant Examiner—T. Ghebretinsae
`Attorney, Agent, or Firm—Foley & Lardner
`
`[57]
`
`ABSTRACT
`
`In a rnultI-level QAM communication system, Reed-
`Solomon encoders and Reed-Solomon decoders are
`employed foi error correction purposes. The phase
`ambiguity of the received signal is eliminated with dif-
`ferential coding The multi-level QAM communication
`system utilizing 11 bits (“n" being an integer) QAM
`signal having 2” signal points, comprises: a quadrature
`differential encoder/decoder unit for differentially en-
`coding/decoding 11 pieces of input digital signal series
`to produce 11 pieces of differentially coded signal series;
`an error correction unit
`including a Reed-Solomon
`encoder and a Reed-Solomon decoder, provided inside
`the quadrature differential encoder/decoder unit along
`a signal processing path of the input digital signal series,
`for error-correcting the 11 pieces of differentially-coded
`signal series by utilizing at least one of the digital signal
`series with employment of a Reed-Solomon code; and,
`a QAM modulator/demodulator unit
`for QAM-
`modulating/demodulating n pieces of error-corrected
`signal series so as to produce 2" QAM signals.
`
`16 Claims, 14 Drawing Sheets
`
`ENCODER
`
`QUADRATURE
`DIFFERENTIAL
`DECODER
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`

`

`US. Patent
`
`Dec. 1, 1992
`
`Sheet 1 of 14
`
`5,168,509
`
`PRIOR ART
`FIG.1
`
`(GRAY MAPPING)
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`PRIOR ART
`
`FIG.2
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`

`US. Patent
`
`Dec. 1, 1992
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`5,168,509
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`US. Patent
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`Dec. 1, 1992
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`5,168,509
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`US. Patent
`
`Dec. 1, 1992
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`Sheet 6 of 14
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`5,168,509
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`US. Patent
`
`Dec. 1, 1992
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`5,168,509
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`US. Patent
`
`Dec. 1, 1992
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`5,168,509
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`US. Patent
`
`Dec. 1, 1992
`
`Sheet 9 of 14
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`5,168,509
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`US. Patent
`
`Dec. 1, 1992
`
`Sheet 11 of 14
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`5,168,509
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`US. Patent
`
`Dec. 1,1992
`
`Sheet 12 of 14
`
`5,168,509
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`US. Patent
`
`Dec. 1, 1992
`
`Sheet 13 of 14
`
`5,168,509
`
`PRIOR ART
`FIG.14
`(NATURAL BINARY MAPPING)
`
`
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`

`

`US. Patent
`
`Dec. 1, 1992
`
`Sheet 14 of 14
`
`5,168,509
`
`PRIOR ART
`
`FIG.15A
`
`NATURAL BINARY MAPPING
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`

`1
`
`5,168,509
`
`QUADRATURE AMPLITUDE MODULATION
`COMMUNICATION SYSTEM WITH
`TRANSPARENT ERROR CORRECTION
`
`BACKGROUND OF THE INVENTION
`
`1. Field of the Invention
`The present invention generally relates to a multi-
`level QAM (quadrature amplitude modulation) system
`for transferring a digital signal by utilizing multi-level
`quadrature amplitude modulation. More specifically,
`the present invention is directed to a QAM communica-
`tion system capable of increasing signal transmission
`reliability by employing a transparent error correcting
`method.
`2. Description of the Related Art
`In a multi-level quadrature amplitude modulation
`(QAM) communication system in which multi-bit data
`such as 4 bit data and 8 bit data are transferred with
`reference to one signal point on a phase plane coordi-
`nate including 2" (“n” being the data bit number) signal
`points and original data are reproduced based upon the
`relationship between the amplitude and phase, utiliza-
`tion efficiency for a frequency becomes high so that this
`QAM communication system has been widely utilized
`in digital microwave communications and digital mo-
`bile communications.
`As previously stated, the signal transmission of the
`multi-level QAM communication system is carried out
`by employing the QAM signals produced by synthesiz-
`ing two orthogonal
`I—channel and Q-channel signals
`corresponding to each m-level amplitude-modulated
`signal. Each of these multi-level QAM signals owns m2
`(=2”) pieces of signal points. For instance, if "m” is
`selected to be 16 (n=8), this multi-level QAM signal is
`equal to 256 pieces of QAM signals having 256 signal
`points.
`In a QAM type receiving system employing synchro-
`nous demodulation, a carrier wave is first_reproduced
`from this multi~level QAM signal, and ’then demodu-
`lated by utilizing 2 orthogonal-reproduced carrier
`waves having different phases with each other at 90°
`(degrees), and thereafter “n" pieces of digital signal
`series are obtained in total by way of the multi-level
`identification. In general, there is a drawback in this
`QAM receiving system in that the phases of the repro—
`duced carrier waves derived from the carrier wave
`reproducing circuit have a so-called “phase ambiguity",
`i.e., the phase becomes any of 0°, 90°, 180°, and 270°.
`Generally speaking. since a transmission signal series
`cannot be correctly reproduced if phase ambiguity ex-
`ists, it is required to employ same means for eliminating
`the adverse influences caused by this phase ambiguity.
`To this end, there are some solutions to resolve such a
`phase ambiguity. That is, for instance, a known signal
`series is periodically transmitted, whereas the phases of
`the reproduced carrier waves are discriminated based
`upon the relationship between this known signal series
`and the signal which has been demodulated and judged
`by the reproduced carrier waves having the phase ambi-
`guity at the signal reception side. Otherwise, a transmis-
`sion information signal is differential-encoded so as to
`be transmitted, which does not directly correspond to
`the transmission phase, but corresponds to a relative
`phase difference of a continuous transmitting symbol.
`At a signal
`reception end, when this differential-
`encoded signal is differential-encoded after being de-
`modulated by the reproduced carrier waves, the phase
`
`10
`
`15
`
`20
`
`25
`
`30
`
`35
`
`45
`
`50
`
`55
`
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`
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`
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`
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`ambiguity in the reproduced carrier waves can be re-
`solved. In general, since a 1 bit error is expanded to a
`continuous 2-bit error, the differential encoding/decod- .
`ing method has the advantage that a circuit arrange-
`ment thereof is simple, although the bit error rate in the
`received signal series is increased as compared with that
`of the first—mentioned solution method for judging the
`absolute phase. Moreover, to suppress an increase of a
`bit error rate caused by a differential coding method,
`there is another method in which signal point mapping
`of a QAM signal is quadrant symmetry mapping. In
`accordance with the last-mentioned method, since the
`judgement concerning the upper 2 bits of the input
`digital signals which is determined by the orthogonal
`axes (i.e., I-axis and Q-axis) on the phase plane is ad-
`versely influenced by the phase ambiguity, the differen-
`tial coding operation is required. However, the judge-
`ment concerning other bits thereof which is determined
`by the respective amplitude levels of the I-axis and
`Q-axis, is not adversely influenced by the phase ambigu—
`ity, so that no differential coding operation is required.
`Although the QAM modulation method has the ad-
`vantage of higher frequency utilization, there is a draw-
`back in that when the number of the bits transmitted
`with l symbol, namely the value of T‘n”, is increased, the
`bit error rate is deteriorated even when the transmission
`power per 1 bit is selected to be equal. Under such a
`circumstance, it is required to improve the bit error rate
`in the multi-level QAM communication system by em—
`ploying an error correcting method. On the other hand,
`a QAM modulation system is originally employed so as
`to increase the frequency utilization efficiency, and
`accordingly, there is a severe restriction in the available
`frequency band in systems which employ the QAM
`modulation method, such as a digital microwave radio
`communication system. As a consequence, it is expected
`to utilize a higher coding rate having a less redundant
`bit to be added to the input digital signal in the error
`correcting method.
`Furthermore, various limitations are provided in ap-
`plying the‘ error correcting method to the QAM com-
`munication system with employment of the above-
`described differential coding system. First, when the
`error correcting encoder and decoder are provided
`outside the differential encoding/decoding processors,
`since the 1 bit error occurring on the signal transmission
`channel is expanded to the 2-bit error due to the differ-
`ential decoding process, the loads required for the error
`correcting encoder and decoder become large. In other
`words, error correction codes having greater correc-
`tion capability are required so as to achieve the same
`reliability as that of the other case where the error cor-
`recting encoder and decoder are provided inside the
`differential encoding/decoding processors. As a result,
`since the redundant bit number to be added to the input
`digital signal is increased, there are problems in that the
`resultant utilization efficiency of frequency is lowered
`and the circuit arrangement of the error correcting
`decoder becomes extensive.
`
`It should be understood that the expression “outside"
`and “inside" described above are defined as follows.
`That is, for instance, the error correcting encoder and
`decoder are positioned outside the differential en-
`coding/decoding circuits in a circuit arrangement pro—
`vided along the flow path of an input digital signal (i.e.,
`along a signal processing sequence).
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`Conversely, in the case in which the error correcting
`encoder and decoder are provided inside the differential
`encoding/decoding circuits along the signal processing
`path, the adverse influence caused by the phase ambigu-
`ity in the reproduced carrier waves is not yet resolved
`at the input unit of the error correcting encoder. As a
`result, in such a case, it is required to employ such an
`error correcting code, namely a transparent error cor-
`recting code, even if the input signal is adversely influ-
`enced by the phase ambiguity in the reproduced carrier
`waves, e.g., there is bit inversion of the input signal, the
`error correction can be correctly performed with re-
`spect to the bit-inverted input signals.
`As an error correcting code, there are a binary error
`correcting code and a nonbinary error correcting code.
`When a transparent binary error correcting encoder is
`employed inside differential encoding/decoding cir-
`cuits, the transparency can be established by employing
`error correcting encoders/decoders in “n" pieces of a
`signal series. However, this system has a drawback in
`that when the multiple number of the QAM system is
`increased, the total number of the required error cor-
`recting encoders/decoders is also increased. In addi-
`tion, there is a drawback in the binary error correcting
`code such that it
`is very difficult
`to produce a code
`whose coding rate is extremely high. When the decod-
`ing delay time of the error correcting code is, for in-
`stance, 63 symbols, even the resultant coding rate of the
`binary BCH (Bose-Chaudhuri-Hocquenghem) .codes
`(63, 57) is 90.5%, by which a single error can be cor-
`rected, and thus the frequency band is expanded by
`approximately 10%. On the other hand, when the non-
`binary error correcting code is employed, many diffi-
`culties may occur in realizing the above—described
`transparent conditions. Although it has been proposed
`that the signal point mapping of the QAM signal is the
`natural binary mapping and the Lee error correcting
`code is employed, since only such a case that errors
`occur in the signal points near the transmission signal
`points can be corrected based upon the Lee error cor-
`recting code, the error correcting effect cannot be ex-
`pected in a communication channel or path which are
`subjected to a fading phenomenon.
`In addition,
`the
`coding rate of the Lee error correcting code is not
`always as good as other nonbinary codes.
`As previously described, in the conventional QAM
`communication system employing the binary error cor-
`recting code, there are problems since the coding rate
`cannot be high so that the efficiency in the frequency
`utilization is lowered and also the total number of the
`required error correcting encoders/decoders to per-
`form the differential encoding operation is necessarily
`increased. Furthermore,
`in accordance with the con-
`ventional QAM communication system employing the
`Lee error correcting code, there are drawbacks in that
`error correction can be executed limited only to the
`signal points having a small distance on signal point
`mapping.
`The above-described problems of the conventional
`multi-level QAM communication system will now be
`described in detail.
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`generally differential-encoded/decoded by employing
`the quadrant differential encoder/decoder.
`On the other hand, there exist a natural binary map- ,
`ping method, a Gray code mapping method and a quad-
`rant symmetry mapping method as a signal point map-
`ping method for mapping 2" pieces of signal points from
`the 11 bits of the digital signals.
`As typical examples, FIG. 1 represents signal point
`mapping for a l6-QAM communication system employ-
`ing the Gray mapping method, whereas FIG. 2 repre-
`sents another signal point mapping for a 16—QAM com-
`munication system employing quadrant symmetry map-
`ping. Further, FIG. 14 indicates signal point mapping
`employing natural binary mapping. As is apparent from
`FIG. 1, the respective signal points are symmetrically
`positioned with respect to the respective 1 and Q coor-
`dinate axes in Gray coded mapping. To the contrary.
`the signal points positioned in the respective quadrants
`are arranged in quadrant symmetry mapping in such a
`manner that these signal points are rotated with respect
`to those of the adjoining quadrants.
`In these mapping methods shown in FIGS. 1. 2 and
`14, the influences caused by the phase shifts of 11/2, 77.
`and 37/2, which are given to the received signal series,
`are expressed in FIGS. 15A to 15C:
`In general, it is known that the transmission capacity
`and frequency utilization efficiency in such a multi-level
`QAM communication system can be increased by in-
`creasing the signal points. However, the more the bit
`numbers are increased, the more the bit error rate is
`increased due to imperfections in the systems. It is de-
`sired that the error correction encoding/decoding oper-
`ations be performed by slightly lowering the frequency
`utilization efficiency so as to improve the QAM com—
`munication quality.
`Thus, as previously stated, in the case that the error
`correction encoder and decoder are provided outside
`the differential encoding/decoding circuits along the
`signal processing path, since the continuous bit errors
`are produced by the differential encoding operation, the
`error correcting capability of the error correction code
`must be emphasized or an interleaver must be em-
`ployed.
`However, when the error correcting capability of the
`error correction code is increased, the frequency utiliza-
`tion efficiency is deteriorated. When the interleaver is
`newly employed, not only the circuit scale of the entire
`system becomes large, but also the decoding delay time
`is increased. As a consequence, it is generally accepted
`to arrange such an error correction encoder/decoder
`inside the differential encoder/decoder.
`
`It should be noted that when the error correcting
`encoder/decoder are arranged inside the differential
`encoder/decoder, error correction must be correctly
`performed even when the signal series are varied as
`represented in FIG. 14 due to the ambiguity of the
`capture phase in the reproduced carrier wave, and si-
`multaneously, the phase ambiguity must be preserved
`even when the error correction encoding/decoding
`operations are carried out. It should be also noted that
`the error correction code which can satisfy such a con-
`dition is called as a transparent code with respect to
`phase rotation in an input signal.
`Conventional circuit arrangements for the transpar-
`ent codes with respect to the phase rotations in the input
`signals, have been proposed in Japanese KOKAI (Dis-
`closure) patent application No. 63-219252, and “6GHZ
`140MBPS DIGITAL RADIO REPEATER WITH
`
`That is. while the original data is reproduced from
`the received signal
`in the conventional multi-level
`QAM communication system, since the capture phase
`of the reproduced carrier wave has phase ambiguity
`such as 0, 77/2, 77 or 377/2 radians, the two digital signal
`series to determine the quadrant of the phase plane are
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`5
`256QAM MODULATION" by Y. Yoshida et al., Pro-
`ceedings of International Conference on Communica-
`tions 1986, No. 46—7, pages 1482 to 1486.
`In the multi-level QAM communication system as
`disclosed in the above-described Japanese KOKAI pa-
`tent application No. 63-219252, there are various draw-
`backs. That is, since the error correction encoding/de-
`coding operations are independently performed with
`respect to each of "n" pieces of a digital signal series
`which constitute the in~phase channel and also the
`channel orthogonal to the in-phase channel, “n" pieces
`of encoders and decoders are required. As a result, the
`scale of the entire apparatus becomes large.
`On the other hand, in the multi-level QAM communi’
`cation system as described in the above publication, i.e.,
`ICC ’86, No. 46—7,
`there is employed such an en~
`coding/decoding method with employment of the Lee
`error correction code, for the respective signal series
`combinations between n/2 series combinations to con-
`stitute the in-phase channel and n/2 series combinations
`to constitute the orthogonal channel. However,
`this
`conventional communication system is limited to such a
`natural binary mapping method for mapping the 11 bits
`data to the signal points. Furthermore, there are many
`other limitations for the constituting methods of the
`error correction codes.
`
`SUMMARY OF THE INVENTION
`
`The present invention has been made in an attempt to
`solve the conventional problems, and therefore has a
`primary object to provide a QAM (quadrature ampli»
`tude modulation) communication system capable of
`realizing a higher coding rate and higher reliability.
`Moreover,
`the present
`invention has a secondary
`object to provide a multi-level QAM communication
`system in which both the error control code and map-
`ping methods are freely selected, a total quantity of
`encoders/decoders is smaller than a bit number of input
`digital data, and a transparent error correction coding
`for a phase rotation can be realized.
`In addition, a third object of the present invention is
`to provide a multi-level QAM communication system in
`which clock frequencies of the error correction en-
`coder/decoder can be lowered with respect to a modu»
`lation frequency of a quadrature amplitude modulator.
`A quadrature amplitude modulation system, accord-
`ing to the present invention, comprises:
`differential encoder/decoder means (12;17) for differ-
`entially encoding/decoding n pieces of input digital
`signal series to resolve phase ambiguity contained in the
`differentially encoded input signal series;
`error correction means including a Reed-Solomon
`encoder (13;83) and a Reed—Solomon decoder (16;87),
`provided inside
`said differential encoder/decoder
`means (12;17) along a signal processing path of said
`input
`digital
`signal
`series,
`for
`error-control—
`encoding/decoding said n pieces of differentially-coded
`signal series by utilizing at least one of said digital signal
`series to correct errors with employment of Reed-Solo-
`mon codes; and,
`means
`modulator/demodulator
`QAM
`(14;15;34;36;80;82) for QAM-modulating/demodulating
`n pieces of error-control-coded signal series so as to
`produce 2" QAM signals.
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`BRIEF DESCRIPTION OF THE DRAWINGS
`
`For a better understanding of the present invention,
`reference is made to the following detailed descriptions
`in conjunction with the drawings, in which:
`FIGS. 1 and 2 schematically illustrate known signal
`point mappings;
`FIG. _3 is a schematic block diagram of a QAM (quad-
`rature amplitude modulation) communication system
`100 employing a first basic idea, according to a first
`preferred embodiment of the present invention;
`FIG. 4 is a schematic block diagram of another QAM
`communication system 200 employing the first basic
`idea, according to a second preferred embodiment of
`the present invention;
`FIG, 5 is a schematic block diagram of an internal
`circuit of the Reed-Solomon encoder 13 employed in
`the second QAM system 200;
`FIG. 6 is a schematic block diagram of an internal
`circuit of the Reed~Solomon decoder 16 employed in
`the second QAM system 200;
`FIG. 7 is a schematic block diagram of an internal
`circuit of the syndrome generator 50 employed in the
`second QAM system 200;
`FIG. 8 is a schematic block diagram of a 256-QAM
`communication system 300 employing a second basic
`idea, according to a third preferred embodiment of the
`present invention;
`FIG. 9 is a schematic block diagram of another 256-
`QAM communication system 400 employing the second
`basic idea, according to a fourth preferred embodiment
`of the present invention;
`FIG. 10 is a schematic block diagram of a still further
`256-QAM communication system 500 arranged by uti-
`lizing the second basic idea, according to a fifth pre-
`ferred embodiment of the present invention;
`FIG. 11 is a schematic block diagram of a 64—QAM
`communication system 600 constructed by using the
`third basic idea, according to a sixth preferred embodi-
`ment of the present invention;
`FIG. 12 is a schematic block diagram of another
`64-QAM communication system 700 employing the first
`basic idea, according to a seventh preferred embodi-
`ment of the present invention;
`FIG. 13 is a schematic block diagram of another
`256-QAM communication system 800 employing a
`unique word adder/detector and no quadracture differ-
`ential encoder/decoder, according to an eighth pre-
`ferred embodiment of the present invention;
`FIG. 14 schematically illustrates natural binary map-
`ping; and,
`FIGS. 15A to 15C are tables for explaining phase
`reference error effects occurring" in the three typical
`mapping methods.
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`DETAILED DESCRIPTION OF THE
`PREFERRED EMBODIMENTS
`Basic Ideas
`
`Before describing various preferred embodiments,
`two basic ideas of the present invention will now be
`summarized.
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`A multi-level QAM (quadrature amplitude modula-
`tion) communication system according to the first basic
`idea of the present invention, is featured by employing
`error correcting means for performing both encoding
`and decoding operations of the Reed—Solomon code
`under the condition that all or a portion of “n“ pieces of
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`an input signal series for determining signal point map-
`ping is used as a symbol. Also, in case the differential
`coding operation is performed by employing natural
`code mapping, such an error correcting means is em-
`ployed to independently perform both encoding and
`decoding operations for the Reed-Solomon code with
`respect to two “I" and “Q" channels orthogonal to each
`other. Although there are many generator polynomials
`for constructing the Reed-Solomon code, such a Reed-
`Solomon code so that codeword polynomials are not
`divisible by x—l (namely, the generator polynomial is
`not divisible by “x—l”) is utilized so as to establish
`transparency.
`In the above-described first QAM communication
`system, when (u,k) linear block codes are employed, a
`frequency band width expanding rate for influencing
`the QAM communication system is determined by the
`coding rate of the block codes. To correct a t-symbol,
`all of the linear block codes must satisfy a limit formula
`of t§(u-k)/2. In other words, a redundant symbol num-
`ber (u-k) cannot be reduced by twice the correction
`capability. A Reed-Solomon code can satisfy this limit
`formula. so that the frequency expanding rate can be
`suppressed to a minimum value in such a QAM commu-
`nication system employing a Reed-Solomon code.
`Due to the phase ambiguity of the reproduced carrier
`waves, the respective “I" and “Q" channels cause signal
`changes different from each other. However, this ad-
`verse influence can be eliminated by independently
`performing both the encoding and decoding operations
`of the Reed-Solomon code with respect to two “I” and
`“Q" channels orthogonal to each other.
`Furthermore, even when the signals are inverted in
`the QAM communication circuit due to the phase ambi-
`guity of the reproduced carrier waves, the transparency
`can be established by utilizing such a Reed-Solomon
`code in which a generator polynomial is not divisible by
`x—- I. That is, in case signal point mapping corresponds
`to natural code mapping, a necessary/satisfactory con-
`dition such that a Reed-Solomon code is equal to a
`transparent code, is as follows: Any codeword polyno-
`mial of the code is not divisible by x— 1. Another multi-
`level QAM communication system according to a sec-
`ond basic idea, has the following features:
`In a multi-level QAM communication system in
`which a bit number of transmitted/received data is
`equal to “n" and there are provided 2” pieces of signal
`points, an error correction coding operation is sepa-
`rately carried out with respect to each of signal series
`used for determining a quadrant of a phase plane, and
`also with respect to to other signal series among “n"
`pieces of signal series for determining a signal.
`As represented in FIG. 15C, in a multi-level differen-
`tial QAM communication system in which signal point
`mapping is determined based upon quadrant symmetry
`mapping, a bit inversion and a signal series substitution
`may occur with respect the signal series (11, Q1) for
`determining quadrants of a phase plane when the cap-
`ture phases of the reproduced carrier waves are shifted
`by 17/2, 7r, or 31r/2. However, such a phase ambiguity
`of the reproduced carrier wave does not influence other
`signal series (13, - - - , In/z; Q2, - - - , Qn/z). Therefore, if
`an error correction coding operation has been per-
`formed for the signal series (11, Q1) separately, whereby
`data bits which have been inverted can be decoded,
`even when an arbitrary error correction coding opera-
`tion is carried out for other signal series (12, - - - , I,,/2;
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`Q2, - - - , Qn/z), the transparency of this arbitrary error
`correction coding operation can be compensated.
`Furthermore in another multi-level difference QAM ,
`communication system in which signal point mapping is
`determined by the Gray coding operation, as repre-
`sented in FIG. 15B, a bit inversion and a signal series
`substitution may occur similar to the previous QAM
`communication system with respect to the signal series
`(11, Q1) used for determining quadrants of a phase plane
`if the phases of the reproduced carrier waves are
`shifted. To the contrary, in other signal series, only a
`signal series substitution may occur between the signal
`series of the I-channel (12, - - - , Inn) and the signal series
`of the Q-channel (Q2, - - — , Qn/z). Therefore, such an
`error correction coding operation by which data whose
`bit has been inverted can be decoded is independently
`performed as to