United States Patent (19)
`Spruyt
`
`US005636253A
`Patent Number:
`11
`45) Date of Patent:
`
`5,636,253
`Jun. 3, 1997
`
`54 METHOD FOR DETECTING ERASURES IN
`RECEIVED DIGITAL DATA
`(75) Inventor: Paul Spruyt, Heverlee, Belgium
`(73) Assignee: Alcatel N.V., Rijswijk, Netherlands
`
`(21) Appl. No.: 435,205
`22 Filed:
`May 5, 1995
`(51) Int. Cl. ...................... H03D 1/06; HO3D 11/04;
`HO3K 5/01; H03K 6/04
`52) U.S. C. .......................... 375/348; 329/304; 371/37.1
`(58) Field of Search .................................... 375/317.340,
`375/261, 264,348; 371/6, 31, 57.1, 43,
`44, 37.1; 329/304,306; 455/296
`
`56)
`
`References Cited
`U.S. PATENT DOCUMENTS
`5.121.395 6/1992 Millar ..................................... 371/39.
`5,226,062 7/1993 Fluharty ......
`... 375/343
`5,323,424 6/1994 Fazel et al. ............................. 375/279
`OTHER PUBLICATIONS
`R. Blauhut, "Theory and Practice of Error Control Codes".
`Addison Wesley Publishing Co., Reading, 1983, pp. 6-15 &
`198-199.
`
`B. Sklar, "Digital Communications-Fundamentals and
`Applications". Prentice Hall Int'l Editions, 1988. pp.
`357-364. 412–417 & 738-743.
`Primary Examiner-Tesfaldet Bocure
`Assistant Examiner-Bryan Webster
`Attorney; Agent, or Firm-Ware, Fressola, Van Der Sluys &
`Adolphson LLP
`ABSTRACT
`57
`A method is described for detecting erasures in a stream of
`sets of digital signal values received at a receiver side after
`transmission from a transmission side. Subsets of these sets
`are modulated on distinct carrier signals, each transmitted
`and received thus modulated carrier signal corresponding to
`one of a number of predetermined subset related points and
`to a receipt point on a carrier dependent modulation repre
`senting map respectively. The method includes the steps of:
`selecting for each receipt point the nearest of the prede
`termined subset related points;
`calculating a distance between the receipt point and the
`nearest subset related point and multiplying this dis
`tance with a map dependent weight factor;
`summing the thus obtained weighted distances for all
`Subsets of a set; and
`marking the latter set as an erasure when the thus obtained
`result exceeds a predetermined threshold.
`7 Claims, 3 Drawing Sheets
`
`d
`
`
`
`SELECT FOREACH
`RECEIPT POINT THE
`NEAREST OF THE
`SUBSETRELATED
`PONTS
`
`CALCULATEA
`DISTANCE BETWEEN
`THE RECEPT POINT
`AND THE NEAREST
`SUBSET RELATED
`POINT
`
`CALCULATEA
`WEIGHTED DISTANCE
`BYMULTIPLYING THE
`CALCULATED DISTANCE
`WITHAMAP
`DEPENDENT WEIGHT
`FACTOR
`
`SUMTHE WEIGHTED
`DISTANCES FOR ALL
`SUBSETS OFASET
`
`MARKASETASAN
`ERASURE WHEN THE
`RESULTSUMEXCEEDS
`APREDETERMINED
`THRESHOLD
`
`ERICSSON v. UNILOC
`Ex. 1032 / Page 1 of 11
`
`

`

`U.S. Patent
`
`Jun. 3, 1997
`
`Sheet 1 of 3
`
`5,636,253
`
`FIG. 1
`(PRIOR ART)
`
`TL
`
`TR1
`
`TR2
`
`N
`
`- - - - - - T - - - - - -
`O
`)
`O
`
`(1,1,1,0) (1,0,1,0) (1,0,0,0) (1,1,0,0)
`- - - - - - - - - - - - -
`
`(0,1,1,0), (0,0,1,0) (0,0,0,0) (0,1,0,0)
`
`O
`
`O
`
`O
`
`O
`
`FIG. 3
`
`
`
`FIG. 4
`
`(0,1,1,1) (0,0,1,1) (0,0,0,1) (0.101)
`
`
`
`O
`
`O
`
`O
`
`O
`
`(1,1,1,1) (1,011) (1,0,0,1) (1,10,1)
`
`0.15 TOPT
`
`0.5
`
`ERICSSON v. UNILOC
`Ex. 1032 / Page 2 of 11
`
`

`

`U.S. Patent
`
`Jun. 3, 1997
`
`Sheet 2 of 3
`
`5,636,253
`
`I
`L
`
`HOVAUSALNI
`
`"lOALNOD
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`ERICSSONv. UNILOC
`Ex. 1032 / Page 3 of 11
`
`ERICSSON v. UNILOC
`Ex. 1032 / Page 3 of 11
`
`
`
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`

`

`U.S. Patent
`
`Jun. 3, 1997
`
`Sheet 3 of 3
`
`5,636.253
`
`
`
`SELECT FOREACH
`RECEIPT POINT THE
`NEAREST OF THE
`SUBSET RELATED
`POINTS
`
`CALCULATEA
`DISTANCE BETWEEN
`THE RECEIPT POINT
`AND THE NEAREST
`SUBSET RELATED
`POINT
`
`CALCULATE A
`WEIGHTED DISTANCE
`BY MULTIPLYING THE
`CALCULATED DISTANCE
`WTHAMAP
`DEPENDENT WEIGHT
`FACTOR
`
`SUM THE WEIGHTED
`DISTANCES FOR ALL
`SUBSETS OF A SET
`
`MARKA SETASAN
`ERASURE WHEN THE
`RESULT SUM EXCEEDS
`A PREDETERMINED
`THRESHOLD
`
`FIG. 5
`
`ERICSSON v. UNILOC
`Ex. 1032 / Page 4 of 11
`
`

`

`5,636,253
`
`1
`METHOD FOR DETECTING ERASURES IN
`RECEIVED DIGITAL DATA
`
`TECHNICAL FIELD
`The present invention relates to a method for detecting
`erasures in a stream of sets of digital signal values received
`at a receiverside after transmission from a transmission side.
`
`2
`an erasure. The above method provides a criterion for
`deciding whether impulse noise occurs or not. It is to be
`noted that modulation parameters such as power allocated to
`the various carrier signals and the modulation representing
`map, and encoding techniques for encoding the stream of
`digital signal values are chosen to cope with the additive
`white gaussian noise but not with the impulse noise.
`Indeed, when the transmitted stream is submitted to
`additive white gaussian noise before being received at the
`receiver side, the receipt point for each carrier is close to the
`one of the subset related points which corresponds to the
`respective transmitted modulated carrier signal. As a
`consequence, the nearest subset related point is most likely
`constituted by the latter subset related point. Thus, an
`interpretation of the receipt point as the nearest subset
`related point is most probably correct. Furthermore, the
`distance between the nearest subset related point and the
`receipt point, which is a measure of the noise to which the
`received stream has been submitted, is probably small. By
`weighing this distance or noise measure with the map
`dependent weight factor it is in fact normalized and has a
`probability distribution with a small mean distance. When
`the thus normalized distances or noise measures are then
`summed for all modulated carriers, an average normalized
`distance is obtained which has a gaussian probability dis
`tribution with a mean equal to the above small mean distance
`and a variance which is inversely proportional to N. N being
`the number of carriers over which the normalized distances
`are summed.
`On the other hand, when the transmitted stream is sub
`mitted to impulse noise, this impulse noise having a rela
`tively flat probability distribution characteristic compared to
`that of the additive white gaussian noise, the relation
`between the receipt point and the one of the subset related
`points which corresponds to the respective transmitted
`modulated carrier signal is fully corrupted for all carriers. As
`a consequence, an interpretation of the receipt point as the
`nearest subset related point is most probably wrong and each
`subset had best be marked as erased. Furthermore, the mean
`distance between the nearest subset related point and the
`receipt point is relatively large. By weighing this distance
`with the weight factor normalized distances are obtained
`which have a probability distribution with a relatively large
`mean distance. When these normalized distances are then
`summed for all modulated carriers, an average normalized
`distance is obtained which has a gaussian probability dis
`tribution with a mean equal to the above relatively large
`mean distance and a variance which is inversely propor
`tional to N, N being the number of carriers over which the
`normalized distances are summed.
`To be noted that both the additive white gaussian noise
`and the impulse noise have a relatively flat power spectrum
`whereby all carrier frequencies are equally affected by them.
`It may be appreciated from the above, and it will become
`apparent later, that the obtained sum has a gaussian prob
`ability distribution which in case of additive white gaussian
`noise has a lower mean value than in case of impulse noise,
`and that in both cases the variance on this value is low, Thus,
`by comparing the obtained sum with the predetermined
`threshold a criterion is provided for deciding whether the
`subsets of a set are only slightly corrupted (gaussian noise)
`or fully corrupted (impulse noise). This threshold is so
`chosen that the probability for an erroneous decision is
`minimized.
`Another characteristic feature of the present invention is
`that for each said carrier the transmit power and said carrier
`dependent modulation representing map are chosen such
`
`BACKGROUND OF THE INVENTION
`In this context, an erasure means a faulty set having a
`known position in the stream, and is thus different from an
`error which indicates a faulty set having an unknown
`position in the stream. Such a method is already known in
`the art, e.g. from the book "Theory and practice of error
`control codes', by R. E. Blahut, published by Addison
`Wesley Publishing Company, Reading, 1983, pp. 11 and
`199. Therein, it is used in a receiver which processes the
`stream of sets of digital signal values and declares a set
`erased either when it is received ambiguously (p. 11), or
`when presence of interference or a transient malfunction is
`detected(p. 11), or when various internal validity checks fail
`(p. 199). However, from this book it is not clear at all which
`criterion should be used to decide when a set is received
`ambiguously, or when interference or a transient malfunc
`tion is present, or which internal validity checks should be
`performed.
`The advantage of being able to detect whether a set is
`erased or not becomes apparent when the stream of digital
`signal values is encoded according to an error-correcting
`code having a so-called minimum distanced. Indeed, in that
`case, a number of R errors and E erasures in this bit stream
`may be corrected when 2xR+E+1sd. Thus, by detecting
`erasures the error correcting capability of the code is
`doubled for a given minimum distance d. This may be
`appreciated from the fact that half the error correcting work,
`specifically the work locating faulty digital signal values in
`the stream, is already performed when an erasure is detected.
`DISCLOSURE OF INVENTION
`An object of the present invention is to provide a method
`of the above known type, but which is fully elaborated.
`According to the invention, this object is achieved due to
`the fact that subsets of said sets of digital signal values are
`modulated on distinct carrier signals, each transmitted and
`received thus modulated carrier signal corresponding to one
`of a number of predetermined subset related points and to a
`receipt point on a carrier dependent modulation representing
`map respectively, and that said method includes the steps
`selecting for each said receipt point the nearest of said
`predetermined subset related points;
`calculating a distance between said receipt point and said
`nearest subset related point and multiplying this dis
`tance with a map dependent weight factor;
`summing the thus obtained weighted distances for all
`subsets of a set; and
`marking the latter set as an erasure when the thus obtained
`result exceeds a predetermined threshold.
`The invention is based on the insight that the transmitted
`stream is submitted to noise before being received at the
`receiverside, and that in general this noise is additive white
`gaussian noise corrupting only a limited number of digital
`signal values per set, whereas occasionally short bursts of
`so-called impulse noise may occur corrupting close to all
`digital signal values of a set. Thus, when during transmission
`of a set impulse noise occurs, this set had best be marked as
`
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`Ex. 1032 / Page 5 of 11
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`

`

`3
`that a required signal quality characteristic for a said subset
`modulated on the respective carrier is met.
`In this way, the probability distribution function of the
`receipt point around the one of said subset related points
`which corresponds to the respective transmitted modulated
`carrier signal, is equivalent for all carrier signals, i.e. the
`integral of the probability distribution function over the
`so-called decoding region associated to the latter subset
`related point is the same for all carrier signals, this integral
`indeed corresponding to the required signal quality charac
`teristic. Thus, by choosing the map dependent weight factor
`inversely proportional to the standard deviation of the
`respective probability distribution function, this standard
`deviation being function of the area of the respective decod
`ing regions, an effective normalization of the distances may
`be obtained.
`Another characteristic feature of the present invention
`providing a general criterion for choosing the map depen
`dent weight factor is that said map dependent weight factor
`is function of a distance between said nearest subset related
`point and those of said predetermined subset related points
`which therewith have a bisecting plane which forms part of
`a border of a decoding region associated to said nearest
`subset related point, said decoding region including all
`possible receipt points for which the latter nearest subset
`related point is the nearest subset related point.
`Thereby, the latter distance indeed being proportional to
`the standard deviation of the respective probability distri
`bution function when the above signal quality characteristic
`is met, a criterion is provided for choosing the map depen
`dent weight factor for arbitrary modulation representing
`maps.
`A further feature of the present invention providing a
`choice of the map dependent weight factor is that said carrier
`dependent modulation representing map corresponds to an
`M-ary quadrature amplitude modulation scheme, M being
`carrier dependent, and in that said map dependent weight
`factors are proportional to the square root of M.
`In this way, since the square root of M is inversely
`proportional to the distance referred to in the previous
`characteristic feature, an effective value for the map depen
`dent weight factor is provided.
`Still another feature of the invention is that said stream of
`sets of digital signal values is encoded according to a
`predetermined error correcting code, in that a said set is
`marked as erased by providing an associated mark signal
`indicative of such erasure, and in that said method includes
`additional step of decoding said stream according to said
`error correcting code and taking said mark signal into
`account.
`In this way, as is clear from the above, the method for
`detecting erasures leads to an increase of the error correcting
`capabilities of the error correcting code.
`Yet a further characteristic feature of the present invention
`is that said distance is the Manhattan distance between said
`receipt point and said nearest subset related point.
`In this way, a fair trade-off is reached between the
`effectiveness of the distance in providing a criterion for
`differentiating between additive white gaussian noise and
`impulse noise, and the complexity of calculating it. To be
`noted that the Manhattan distance refers to the sum of the
`positive distances between corresponding coordinates of the
`transmit and receipt points.
`These and other objects, features and advantages of the
`present invention will become more apparent in light of the
`detailed description of a best mode embodiment thereof, as
`illustrated in the accompanying drawing.
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`4
`BRIEF DESCRIPTION OF THE INVENTION
`FIG. 1 shows a known communication system in which a
`method for detecting erasures according to the invention
`may be used;
`FIG. 2 represents a transceiver TR used in FIG. 1;
`FIG.3 shows a modulation representing map for so-called
`16-QAM;
`FIG. 4 shows the probability distribution functions for an
`average normalized distance in case of both gaussian and
`impulse noise; and
`FIG. 5 is a logic flow diagram of the method for detecting
`erasures according to the invention.
`BEST MODE FOR CARRYING OUT THE
`INVENTION
`The communication system shown in FIG. 1 includes a
`transceiver TR1 coupled to a transceiver TR2 via a trans
`mission line TL. Digital signals exchanged between both
`transceivers TR1 and TR2 are submitted to noise N as
`schematically represented in FIG. 1. These digital signals
`are modulated on a plurality of carriers as described for
`instance in the U.S. Pat No. 4.679,227. Therein, bits of data
`to be transmitted and power are allocated to each of the
`carriers such that, given actual noise characteristics of the
`transmission line, a same bit error rate is obtained for all data
`modulated on the various carriers. In general, the transmis
`sion line TL may be described as a so-called additive
`gaussian channel wherein signals transferred therethrough
`are submitted to gaussian noise with zero mean value and
`standard deviation o. As will be explained later such gaus
`sian noise causes a received signal to have characteristics
`which with high probability are only slightly changed with
`respect to those of the transmitted signal. However, due to
`electromagnetic induction or interference of external
`sources, e.g. originating from neighbouring transmission
`lines carrying so-called telephone ringing currents, signals
`transferred via the transmission line TL may be submitted to
`impulse noise which has a flat probability distribution func
`tion up to relatively high noise values, and which fully
`corrupts the transmitted signal as will become clear later. To
`be noted that both the additive white gaussian noise and the
`impulse noise have a relatively flat power spectrum whereby
`they equally affect all carrier frequencies.
`The bits to be transmitted are arranged in sets of bits
`which in successive time intervals are modulated on the
`carrier signals. In each time interval respective subsets of the
`corresponding set are modulated on the respective carriers,
`the number of bits included in a subset and thus allocated to
`the corresponding carrier being so chosen that indeed a same
`bit error rate is obtained for all carrier modulated subsets.
`The bits allocated to a carrier are modulated thereon
`according to a so-called Quadrature Amplitude Modulation
`(QAM) scheme which may be represented by a modulation
`representing map constituted by a constellation of points in
`a signal space as shown for instance in FIG. 3 for case of
`so-called 16-QAM, this modulation representing map being
`applicable when 4 bits are allocated to the carrier. In this
`scheme each point corresponds to one 4-bit value, for
`instance as represented in FIG. 3, and represents a relative
`amplitude and the phase of the carrier to be transmitted. The
`4-bit value corresponding to each such point of the modu
`lation representing map may thus be transmitted by trans
`mitting a cosine wave having an amplitude proportional to
`the abscissa of this point, the so-called in-phase component,
`combined with a sine wave having an amplitude propor
`
`ERICSSON v. UNILOC
`Ex. 1032 / Page 6 of 11
`
`

`

`5
`tional to the ordinate of this point, the so-called quadrature
`component. In this way, an M-ary QAM modulation repre
`senting map is allocated to each carrier, logM being at least
`equal to the number of bits included in the subset to be
`modulated on this carrier, and various choices of the modu
`lation representing map being possible as described for
`instance in the book "Digital Communications
`fundamentals and applications" by B. Sklar, published by
`Prentice-Hall International Editions, 1988, pp. 412-417. To
`be noted that in a preferred embodiment logM will be equal
`to the latter number of bits.
`Each of the transceivers TR1 and TR2 according to the
`invention is built as a transceiver TR shown in FIG. 2. This
`transceiver TR includes a transmission and a receipt branch
`both coupled to the transmission line TL via an interface
`INF. The transmission branch includes the cascaded con
`nection of a digital transmitter DTR, a coding device COD,
`an interleaving device INL, a modulation parameter genera
`tor MPG, a modulator MOD and a digital to analog con
`vertor DAC connected to INF, while the receipt branch
`includes connected to INF the cascaded connection of an
`analog to digital convertor ADC, a demodulator DEM, a
`digital data generator DDG, a de-interleaving device DIL, a
`decoding device DEC and a digital receiver DRE. The
`25
`transceiver TR furthermore includes a control unit CTR
`providing control signals NM and PM to the modulation
`parameter generator MPG and the modulator MOD
`respectively, as well as control signals ND and PD to the
`30
`digital data generator DDG and the demodulator DEM
`respectively.
`The transceiver TR transmits and receives digital signals
`via the transmission line TL. Such a digital signal to be
`transmitted via TL is constituted by a bit stream produced by
`the digital transmitter DTR and applied to the coding device
`COD. Therein the bits of this bit stream are encoded
`according to an error-correcting code whereby an encoded
`bit stream is produced. Such error-correcting codes are well
`known in the art and are described for instance in the above
`mentioned book by Blahut. The encoded bit stream is
`thereupon applied to the interleaving device INL where it is
`submitted to the technique of interleaving which is well
`known in the art and described e.g. in the above mentioned
`book by Sklar, pp. 357-364. The thus interleaved bit stream
`is then applied to the modulation parameter generator MPG.
`Therein, a subset of bits is allocated to each carrier and
`transformed into a point of the modulation representing map
`allocated to this carrier, the number of bits in this subset and
`this modulation representing map being indicated by the
`control signal NM provided by the control unit CTR to
`MPG. To be noted that in a preferred embodiment the
`number of bits included in the subset is uniquely related to
`an allocated modulation representing map so that only this
`number of bits needs to be indicated by the control signal
`NM. Thus, for each carrier a point of the modulation
`representing map, i.e. a relative amplitude for a cosine wave.
`i.e. the in-phase component, and a relative amplitude for a
`sine wave, i.e. the quadrature component, is applied to the
`modulator MOD wherein the respective carriers are accord
`ingly modulated. The thus modulated carrier is then ampli
`fied to a value corresponding to the power allocated to it as
`indicated by the control signal PM supplied by the control
`unit CTR to the modulator MOD. In a preferred embodiment
`
`6
`the modulator MOD performs an inverse FastFourier Trans
`form (FFT) with the points of the modulation representing
`maps applied to it as inputs. A modulated digital signal is
`then generated and thereupon converted to an analog signal
`by the digital to analog convertor DAC and applied to the
`transmission line TL via the interface DNF.
`A signal received via the transmission line TL is via the
`interface INF applied to the analog to digital convertor ADC
`where it is converted into a digital signal which is then
`demodulated in the demodulator DEM taking the power
`allocated to the various carriers into account, this power
`being indicated by the control signal PD provided by the
`control unit CTR to the demodulator DEM, thereby obtain
`ing for each carrier a receipt point of the corresponding
`modulation representing map, i.e. a relative amplitude for a
`cosine wave, i.e. the in-phase component, and a relative
`amplitude for a sine wave, i.e. the quadrature component. In
`a preferred embodiment the demodulator DEM performs a
`FFT on the digital signal thereby generating receipt points of
`the modulation representing maps for the various carriers.
`These points are then applied to the digital data generator
`DDG wherein they are converted to the bits corresponding
`thereto as indicated by the modulation representing map
`allocated to the respective carrier, this modulation represent
`ing map being indicated by the control signal ND supplied
`by the control unit CTR to DDG by indicating the number
`of bits included in the subsets modulated on the respective
`carriers. The thus obtained bit stream is then submitted to the
`technique of de-interleaving by the de-interleaving device
`DIL, this technique being the opposite of the above tech
`nique of interleaving, and thereupon decoded by the decod
`ing device DEC according to the above error-correcting
`code whereafter it is processed in the digital receiver DRE.
`Thus, a block of bits modulated on a carrier corresponds
`to a point of a modulation representing map as for instance
`represented in FIG. 3 for 6-QAM. Due to noise on the
`transmission line TL a transmitted signal thus corresponding
`to one of these points, henceforth referred to as transmit
`point, and transmitted for instance by TR1 is received in
`TR2 and then corresponds to a receipt point which may also
`be represented in the modulation representing map but is
`probably distinct from the transmit point. Having been
`submitted to additive white gaussian noise on the transmis
`sion line TL, the in-phase and quadrature components of the
`receipt point have a gaussian probability distribution
`
`N 2
`
`c.
`
`with a mean value m equal to the in-phase and quadrature
`components of the transmit point respectively, and with a
`standard deviation O. Since power and data have been
`allocated to each carrier such that the data modulated
`thereon is received in TR2 with a same bit error rate for all
`carriers, this standard deviation o is inversely proportional
`to VM for the case of M-ary QAM. Indeed, this bit error rate
`is equal to the volume under the associated gauss clock
`outside the so-called decoding region associated to a trans
`mit point, the decoding region being shown in FIG. 3 as
`bisecting planes shown by the dashed squares around each
`possible transmit point. Thus, it may be appreciated that this
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`Ex. 1032 / Page 7 of 11
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`5,636.253
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`7
`volume is equal for all carriers when the standard deviation
`o is proportional to the length of a side of a square of the
`corresponding modulation representing map, this length
`indeed being inversely proportional to VM. For both the
`in-phase and quadrature components this error probability is
`approximately equal to
`
`8
`impulse noise on the transmission line, this average distance
`may be calculated to be 0.50. Thus, in both cases (gaussian
`noise and impulse noise) a distance is obtained with an
`average value as given above and with a gaussian probabil
`ity distribution thereabout whose standard deviation is given
`by
`
`Pr=
`
`CX
`
`O.
`
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`
`15
`
`For gaussian noise this standard deviation may be calculated
`to be
`
`2
`
`o?
`-
`{ W2. O
`
`o
`1 + (1-e 2c ) )e(
`---
`e 2c
`(
`
`-- 2
`
`O
`
`--
`)- (1 - e 2c
`
`half the length of a side of the square, erf(x)=1-erf(x) is the
`complementary error function, erf(x) being the error
`function, and where
`
`25
`
`which for the above value of
`
`e
`O
`
`9.
`o
`
`is the same for all carriers due to the said proportionality.
`Thus, when for instance an error probability of the modu
`lated QAM signal less than 2x10" is imposed which
`corresponds to Ps. 10, then it may be verified that
`
`0.
`
`W2 o 23.77.
`
`When the transmitted signal is submitted to impulse noise
`the probability distribution function of the receipt point is
`almost flat over the entire modulation representing map, i.e.
`the receipt point may with equal probability be found to be
`anywhere on this modulation representing map.
`The average distance of the in-phase and quadrature.
`components of the receipt point from the transmit point is
`equal to
`
`C.
`
`a
`
`-0.
`
`O
`
`p(x) d,
`
`wherein p(x) is the probability distribution function of the
`receipt point around the corresponding transmit point which
`without loss of generality is located at x equal to 0. For
`gaussian noise this average distance may be calculated to be
`approximately equal to
`
`2
`
`---
`o(1-e 2c
`).
`
`For the above value of
`
`O
`O
`
`65
`this may be calculated to be less than or equal to 0.15o. On
`the other hand, when the signal has been submitted to
`
`may be shown to be less or equal to 0.013of, whereas for
`impulse noise it may be shown to be
`
`30
`
`12
`amomum
`
`0.083 02.
`2
`
`35
`
`By now calculating the weighted sum
`
`l
`2N i
`
`irl+y
`C.
`
`y
`
`where x is the above distance between the in-phase
`components, Y, is the above distance between the quadrature
`components, and ot, is the above half length of a square side,
`both for carrier i, and N is the total number of modulated
`carriers over which the sum is calculated, a parameter is
`obtained with a gaussian probability distribution whose
`standard deviation is inversely proportional to VN. In case of
`gaussian Noise the mean and standard deviation of this
`distribution are found to be less than or equal to m=0.15 and
`
`oc= 93
`
`respectively, whereas in case of impulse noise they are found
`to be m=0.5 and
`
`1
`Way
`
`45
`
`50
`
`55
`
`respectively. Both distributions for this parameter for N
`equal to 100 are shown in FIG. 4. From this FIG. 4 it is
`intuitively clear that when the above weighted sum is
`calculated and compared to a threshold in between both
`average values 0.15 and 0.5, a fairly good decision may be
`made as to whether the signal has been submitted to gaussian
`noise or to impulse noise.
`An optimal value TOPT for this threshold may be chosen
`in accordance with the so-called maximum likelihood cri
`
`ERICSSON v. UNILOC
`Ex. 1032 / Page 8 of 11
`
`

`

`5,636,253
`
`terion described for instance in the above book by Sklar on
`pp. 738-743. This optimal value TOPT of the threshold is
`such that the probability of an erroneous decision in case of
`gaussian noise is equal to the probability of an erroneous
`decision in case of impulse noise. These probabilities are
`
`5
`
`10
`marking a set as an erasure when the result sum exceeds
`a predetermined threshold.
`2. Method according to claim 1, characterized in that said
`carrier dependent modulation representing map corresponds
`to an M-ary quadrature amplitude modulation scheme, M
`being carrier dependent, and in that each said map dependent
`weight is proportional to the square root of M.
`3. Method for detecting erasures in a stream of sets of
`digital signal values received at a receiver side after trans
`mission from a transmission side, each set in said stream of
`sets representing one symbol, characterized in that a subset
`of each of said sets of digital signal values is modulated on
`a distinct carrier signal corresponding to one of a number of
`predetermined subset related points and to a receipt point on
`a carrier dependent modulation representing map
`respectively, and that said method includes the steps of:
`selecting for each said receipt point a nearest point of said
`predetermined subset related points;
`calculating a weighted distance between said receipt point
`and said nearest of said predetermined subset related
`points by multiplying the distance between said receipt
`and said nearest of said predetermined subset related
`points by a map dependent weight factor having a value
`that depends on the receipt point;
`summing, to obtain a result sum, the weighted distance
`calculated for each said receipt point for all subsets of
`a Set,
`marking a set as an erasure when the result sum exceeds
`a predetermined threshold,
`wherein for each said error a transmit power and said
`carrier dependent modulation representing map are
`chosen such that a required signal quality characteristic
`for a said subset modulated on a respective carrier is
`met; and
`wherein said signal quality characteristic is an error
`probability of said digital signal values included in said
`subsets.
`4. Method for detecting erasures in a stream of sets of
`digital signal values received at a receiver side after trans
`mission from a transmission side, each set in said stream of
`sets representing one symbol, characterized in that a subset
`of each of said sets of digital signal values is modulated on
`a distinct carrier signal. each transmitted and received thus
`modulated carrier signal corresponding to one of a number
`of predetermined subset related points and to a receipt point
`on a carrier dependent modulation representing map
`respectively, and that said method includes the step of:
`selecting for each said receipt point nearest point of said
`predetermined subset related points;
`calculating weighted distance between said receipt point
`and said nearest of said predetermined subset related
`points by multiplying the distance between said receipt
`point and said nearest of said predetermined subset
`related points by a map dependent weight factor having
`a value that depends