Note: Descriptions are shown in the official language in which they were submitted.
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SYSTEM AND METHOD FOR SPECTRALLY SHAPING
TRANSMITTED DATA SIGNALS
Cross-Reference to Related Applications
This application is related to the following U.S. Patent Applications, all
of which are assigned to the assignee of this application and all of which are
incorporated by reference herein:
US Provisional App. No. 60/042,826, entitled Generalized Spectral
Shaping, filed April 8, 1997, having inventors M. Vedat Eyuboglu, Pierre A.
Humblet; Daeyoung Kim and David Tung; the present application is based on
this application and priority thereto for common subject matter is hereby
claimed;
US Patent App. No. 08/747,840, entitled Device, System and Method
for Spectrally Shaping Transmitted Data Signals, filed November 13, 1996,
having inventors Vedat Eyuboglu and Pierre A. Humblet; and
US Patent App., Attorney Docket No. CX09s044P02, entitled Device
and Method for Precoding Data Signals, filed December 29, 1997, having
inventors M. Vedat Eyubogiu, Pierre A. Humblet; and Daeyoung Kim.
Field Of Invention
This invention relates to high-speed data communications and more
particularly to a system and method for spectrally shaping transmitted data
signals.
Background Of invention
The public switched telephone network (PSTN) consists of a digital
backbone network and analog local loops that connect end users to this
backbone. In a typical telephone call, the analog signal sent by the local
user
is digitized at the local central office and converted into a 64 kbitls bit
stream
which is carried across the digital backbone network and then converted back
to analog at the remote central office for transmission to the end user over
the
remote local loop. Dial-up modems, e.g. V.34 modems, communicate over the
PSTN by modulating the digital information into an analog signal for
SUBSTITUTE SHEET (RULE 26)
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transmission. The digital-to-analog conversion process at the entry point to
the digital backbone introduces quantization noise which limits the data
transmission speed to around 30 kbitls.
A technique that enables transmission at speeds significantly higher
than 30 kbitls, potentially up to 56 kbitJs, when one user has a direct
connection to a digital network, for example, via 1SDN or Tt, has been
developed. Moreover, a standardized protocol for this type of transmission
exists, International Telecommunications Union (1TU) standard V.90, and is
expected to be ratified soon. With this technique, random digital information
is
encoded into p-law or A-law octets (depending on the region of the world) by a
digital poise code modulation (PCM) modern using a channel encoder. The
octets era mapped directly into symbols in the digital-to-analog (DIA)
converter
located in the end user's central office. (Unless indicated otherwise, a!I
discussions below pertain to p,-law: the extensions to A-law are
straightforward.) The mapping could use all or any subset of the 2fi5 levels
of
the D!A converter, subject to regulatory restrictions on average power.
Since information is carried across the digital network in the form of
octets, the encoded data is first mapped into octets for transmission at a
rate
of 8000 octets per second. Then, in the end user's central office, the octets
are converted into corresponding symbols in the DIA converter. The resulting
8 kHz sequence of symbols is passed through a low pass filter (l-PF) and
transmitted over the analog loop to the end user's analog PCM modem. The
output of the DlA converter can be viewed as a sequence of impulses each
having an amplitude corresponding to one of the D!A levels. The analog PCM
modem recovers the original information by first detecting which symbols were
transmitted, and then inverse mapping these symbols to obtain an estimate of
the original digital information.
When the information is transmitted randomly, a spectral analysis of the
signal alter the DlA conversion reveals that the spectrum of the sequence
output by the DIA converter is essentially flat. Therefore, when this sequence
is passed through the l-PF et the central office, the spectrum of the signal
takes on the shape of the spectrum of the LPF. Unfortunately, this spectrum
t , . ..
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has a significant amount of energy n~ar DC (f--0) which can drive transformers
in the system Into saturation and introduce unwanted non-Ilnear distortion on
the signal being transmuted, in this application, this type of distortion
cannot
be tolerated and therefore there is a need for 'rte elimination.
More generally, with PCM there is a need for a scheme that can shape
the spectrum of the signal transmitted from the DlA converter. Further, there
is a need for a spectral shaping scheme that is applicable to various types of
transmission technologies in addition to PCM.
Brief Description of the Drawings
FIG, 1 is a simplified block diagram of a typical telephone company
central office;
FiG. 2 is plot of the frequency spsotrum of the symbols, yk, output from
the p-law to linear converter of FlG, 7 and the spectral shape of the tow pass
filter of FIG. i;
FIG. 3 is a plot of a portion of two frequency spectrums each having a
null at DC, wherein one spectrum falls off to zero very abruptly at DC and the
other spectrum falls off more gradually;
FIG. 4 is schematic block diagram of a transmitter of a central site
digital PCM modem configured according to this invention;
FIG. 5 is a schematic block diagram of a receiver of an end user analog
PCM modem configured according to this invention;
FIG. 6 is a schematic block diagram of the sign tit encoder of the
transmitter depicted in FIG. 4;
FIG. 7 is a schematic block diagram of the coset representative
generator depicted in F1G. 6;
FIG. .8 is schematic block diagram of the symbol sign bit selector of FIG.
e;
F1G. 9 is a treNis diagram which represents a convolutional code;
FlG. 10 is a flow diagram illustrating the generalized logic for the
symbol sign bit selector as depicted in FIG. B;
3
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FIG. t 1 is a schematic block diagram of the sign bit decoder depicted in
F1G. 5; and
FIG. 12 is a schematic block diagram of tho present invention utilized as
a precoder in an upstream PCM transmitter.
Descrlptlon of a Prei°erred Embodiment
The present invention involves a system and method for spectrally
shaping transmitted data signals that is generally applicable to various data
transmission technologies. For purposes of explanation, the invention is
described herein with regard to a PCM transmission system. However,
persons having ordinary skill in the art will appreciate that the invention
may
be extended to other transmission technologies and that the PCM
implementation described herein may be readily extended to those
technologies.
FIGS, 1 and 2 illustrate the presence of energy near DC in the signals
transmitted to an end user's analog PCM modem over an analog loop, There
is shown in FlG. i a portion of a typical telephone central office 10 on a
PSTN
which receives at input 12 p.-law octets transmitted from a central site
digital
PCM modem (not shown) directly attached to the digital portion of the
telephone system. The ortets are converted by a DIA converter, also known
as a p-law to linear converter 14, to a sequence of symbols, yk. Each of the
symbols corresponds to one of 256 p-law levels. The symbols are output over
line 16 to a low pass filter (LPF) 18 which outputs over analog loop 20 to the
end user analog PCM modem's receiver a filtered analog signal s(t). The
analog signal is demodulated and decoded by the receiving modem, which
outputs a digital bit stream. The digital bit stream is an estimate of the
originally transmitted data.
The sequence of symbols, yK , on line 16 from w-law to linear converter
14 has a flat frequency response 22, FIG. 2. The spectral shape 24 of l_PF 18
contains a significant amount of energy near DG ~f=0) as illustrated at point
26.
Since the sequence y, has a flat frequency response, the spectrum of the
signal e(t) output by filter 18 has the same spectral shape 24 as the filter i
8
4
_.....,.,P~._~~ _._. ,....r.... r .>
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and therefore the signal s(t) also contains a significant amount of energy
near
DC, As described above, this energy near DG tends to saturate the
transfomners in the system, which produces unwanted non-linear distortion in
the signal s(t) transmitted to the receiving modem.
In applications such as PCM, this distortion must be reduced. This can
be accomplished by reducing the signal energy of the transmitted signal near
DC to produce a DC null. Such a DC null 28 is depicted in FIG. 3. As is
known in the state-of-the-art, in order to create this specttal null at DC in
the
transmitted signal, the running digital sum (RDS) of the transmitted symbols,
yK
(namely, the algebraic sum of all previously transmitted levels) must be
maintained near zero. The shape of the spectrum around DC null 28 can vary
from a relatively shallow sloped spectrum 30 to a spectrum 32 which lefts off
very abruptly at AC, The sharpness of the null depends on how tightly the
ROS is controlled.
As described below, the present invention encodes the digital data
being transmitted in a manner that maintains the RDS near zero. This creates
a spectral null at DC thereby reducing the non-linear distortion caused by
transformer saturation. More generally, the invention may also be used to
encode digital data being transmitted to shape the spectrum of the transmitted
signal, as desired.
Transmitter 40, FIG. 4, in a digital PCM modem receives a serial digital
bit stream 42 from data temninal equipment (not shown), such as a personal
computer, and encodes the received bits into octets 44 for transmission over
digital network 4fi. Serial bit stream 42 is converted to parallel format by
serial
to parallel converter 48. The transrnittinglencoding scheme of this invention
is
based on an n-symbol data frame, where k represents the data frame (time)
index. For example, there may be 2, 3, 4, 5 or 6 symbols transmitted per data
frame. The symbols transmitted correspond to p-law constellation points
setacted to represent the information bits. Far each data frame, serial to
parallel converter 48 outputs (n-r~+m information bits, where ris the number
of
redundancy bits. The number of redundancy bits as specified in the V.90
standard may be 0, 1, 2 or 3.
s
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It should be noted that for the remainder of the description lowercase
variables denote scalar quani'>ties, white uppercase variables denote
matrices.
Also, row vectors are represented by a bold lowercase variables and all
indices start from 0, e.g., x = (x a, xt,~,..,).
The n-rbits, labeled bits v~, represent the infom~ation carried through
sign bits (the sign information bits) and the m bits, labeled bits a ,
represent
the information carried through the magnitudes (the magnitude information
bits). The number of bits, m, can be determined by choosing m to satisfy the
following:
n-t
(1 )
where M, is the number of positive constefiation points for the i-th symbol in
a
data frame. This process is more fully described in the V.90 standard.
The m magnitude infomZation bits, uk , are provided to magnitude
moppet 50 which maps the m bits to n symbol magnitudes, g~, by a mapping
scheme such as a shell mapping, as described in the ITU V.34 standard, or by
a rnodulus conversion, described in the ITU V.90 standard. The magnitudes
to which the magnitude information bits are mapped are the magnitudes of the
~-law paints used as constellation points in transmitting the information
bits.
These magnitude mapping schemes and the constellation point selection
process are understood by persons skilled in the art and further description
of
them need not be provided herein. Th~ remaining information bits in the data
frame, the sign information bits v, are provided to sign bit encoder 52 which
generates n sign bits, s,, (encoded symbol sign bits) as described in detail
below. The n symbol magnitudes, g,, and the n sign bits, ak, are provided to
signal point selector 54 and are combined to torrn n signed symbols yr, The n
signed symbols yk are then provided to octet converter 56 which selects an
octet corresponding to each of the signed symbols and transmits the octets to
digital network 46. With other transmission technologies the octet converter,
which converts the signed symbols to a form compatible with the digital
portion
6
~~.. . . .-...._~._.-........_ 4 . _ ~ .. ~ , ,
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of the PSTN, may not be used and the signal point selector would output the
signed symbols directly to the network.
The octets 44' ~xiting digital network 46 (possibly modified by digital
impairments in the network) are reoelved by central office (GO) 60. The octets
4a' are converted into symbols by a DIA converter in CO 60 and transmitted
as an 8 kHz sequence of levels over the analog loop s2 to receiver 84 of an
end user analog PCM modem. The analog levels are roceived by receiver
fronl end 86, which digitizes the analog levels, performs timing recovery,
equalization and symbol decision.
Receiver front end 66 outputs received symbols, yk, in serial format to
serial to parallel converter 68 which converts the serial symbols into frames
of
n parallel signed symbols yt The n parallel signed symbols yr are provided to
magnitude and sign extractor 70 which extracts symbol magnitudes gk and
sign bits sr from yr. Symbol magnitudes gt are provided to magnitude
demapper 72, e.g. a moduius conversion demapper, to recover the magnitude
information bits ut Since the demapping process is understood by persons
skilled in the art, it will not be explained her~in. The sign bits sK are
provided
to sign bit decoder 74 to recover the sign information bits vt, as described
below. The decoded information twits may then be further processed and
provided to data terminal equipment, such as a personal computer.
SI,~,Bit Encodln4
Sign bit encoder 52 is depicted in more detail in FIG. 6. The sign
information bits vt are provided to cosec representative generator 80 which
generates for each frame n coset representative sign bits t,, and provides
them
to symbol sign bit selector 82. The n cosst representative sign bits iy during
each frame define a coset representative ~lement for a defined convotutional
code, G(D), used by symbol sign bit selector 82 and the entire sequence of
coset representative sign bits i(D) collectively define a coset repres~ntative
for
the convolutional code. The n coset representative sign bits tr also identify
a
coset of the convotutional code which contains candidates of encoded symbol
sign bits, as described in more detail below.
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Using the n coset representative sign bits tt, symbol sign bit selector 82
modifies cos~t representative sign bits tt by EXCLUSIVE OR'ing the bits with
valid convolutional cads sequences defined by a trellis diagram, such as the
trellis diagram depicted in FIG, 9 and d~scribed below, to form the candidates
of encoded symbol sign bits. These candidates are elements of the cosec
identified by the coset representative sign bits, With the symbol magnitudes,
symbol sign bit selector B2 selects for each frame the candidate of encoded
symbol sign bits,a~, from the candidates of encoded symbol sign bits that
produces the desired spectra! shape and provides those sign bits to signal
point selector 54, FIG. 4. The output of symbol sign bii selector B2 forthe
entire sequence, as oppos~d to on a per frame basis, may be represented as
s(D)=t(Dj ~ c(D), where s(D) is the sequence of encoded symbol sign bits,
t(Dj is the coset representative far the convalutional code and c(D) are the
code sequences which are elements of the convolutional code, G(D).
it should be noted that with this selection process any of the
candidates of encoded symbol sign bits may be used and will be decoded, as
described below, to the encoded sign information bits v,. Thus, the present
spectral shaping scheme has no affect on the symbol magnitudes and
therefore does net affect the transmit power. As a result, it is easy to
design a
systom to satisfy the transmitter power limitations imposed by the FCC and
still
accomplish spectral shaping.
Gaset representative generator 80 is depicted in more detail in FIG. ~
to include differential encoder 84 and matrix block 86. Noise on the data
channel might cause a polarity inversion by affecting the transmitted sign
bits.
By employing differential encoding, differential encoder 84, and decoding,
differential decoder t 32, F1G. 11, of the sign bits to certain bit positions,
e.g.,
even positions 0, 2 and 4 far the HT, H'T and G(D) given below, it is possible
to
achievo polarity inversion invariance. The differentially encoded sign
information bits v'are multiplied (in modulo 2) (i.e., filtered) in matrix
block 84
by matrix H~T ~,_~m to produce the n cosec representative sign bits rx which
are
provided to symbol sign bit selector 82.
r , . W.,.
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An example of this matrix when there are six (6) symbols transmitted
per frame and one redundancy bit, as specified in the (TU V.90 standard, is as
follows:
0 0 0 0 0 1 /(1
+ D)
4 0 0 0 1!(1+D)0
H'T 0 0 0 1 l(1 0 0 (2)
-. + D)
0 0 11(1 0 0 0
+ D)
0 11(1+D)0 0 0 0
where D is the frame delay, which is the delay based on the frame
(time) index k.
As shown in F1G. 8, symbol sign bit selector 82 includes selection
controller 88 which receives the n cosec represantativ~ sign bits t~ each
frame
from coset representative generator BO and n symbol magnitudes from
magnitude mapper 50, FIG. 4 and outputs encoded symbol sign bits,sk , for
each frame. Selection controller 88 combines the candidates of encodBd
symbol sign bits with the magnitudes to farm encoded signed symbol
candidates, which are provided to filter 90. Fitter 90 caloulstes a metric
referred to herein as a running filter sum (RFS), described below, for each
candidate and provides them to selection controller 88 which selects the
encoded symbol sign bias associated with the encoded sign~d symbol
candidate that minimizes RFS. The operation of symbol sign bit selector 82 is
described below with regard to FIGS. 9 and i0.
Selection controller 88 modifies the n coset representative sign bits t,
per frame by EXCLUSIVE-4Ring the coset representative sign bits with valid
code sequences of the convolutional coda. The convotutional code is the set
of possible sequences defined by a trellis diagram and the valid code
sequences are the sequences that do not violate the constraints of the trellis
_ diagram. For purposes of description, selection controller 8B will use a
single
redundancy bit rend a convolutional code G(D) =
(1 + D 1 1 + D 1 1 t D 1~. Representing this in terms of a trellis diagram
9
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requires the use of a two-state trellis diagram, such as trellis diagram 100,
F1G. 9. The constraints of the trellis diagram are described as follows.
For a given frame k, selection controller i98 modifies the n coset
representative sign bits tr by EXCLUSIVE-UR'ing them with certain
convofutional code sequences according to the constraints of trellis diagram
100. The convolutional code sequences in this example are as follows:
A: 000000 (La, do nothing)
B: 111111 (i.e. invert al! sign bits in frame j)
C: 101010 (i.e. invert even-numbered sign bits in frame j}
A: 010101 (i.e. invert odd-numbered sign bits in frame j)
Thus, at the beginning of a frame k if the state, 4k , of selection
controller &8 is 0, only convolutional code sequences A 102 and B 104 are
valid sequences in frame k. Conversely, if the state , Qk , of selection
controller 88 is 1, only convolutionaf code sequences C 10B and D 108 are
valid sequences in frame k. As described above, the coset representative sign
bits are EXCt_USIVE-OR'ed with each of the valid code sequences, thereby
forming candidates of encoded symbol sign bits, e.g. { =r ~ A, tr ~ B}. Each
of the candidates is also an element of a coset of the convolutionai coda
identified by the coset repres~ntative sign bits (or the element of the coset
representative). Then, each candidate is combined with the symbol
magnitudes to form encoded signed symbol candidates which are provided to
fitter 90, FlG. 8, where the RFS for each is calculated and returned to
selection
controller B8. Selection controller 88 outputs the encoded symbol sign bits
for
frame j that minimize the RFS.
The current state Qk , together with the convolutional cads sequence of
the encoded symbol sign bits selected for frame k are used to determine the
next state by following the constraints of trellis diagram 100. For example,
if
candidate tk ~ 8 was selected for frame k, the state of selection controller
88
at the beginning of frame ~k+1 is 1.
~o
. . _.. ,. r ~ , _.,
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The spectral shaping achieved using the present Invention may be
improved by introducing look-ahead, That is, instead of selecting the encoded
symbol sign bits based solely on the current frame, symbol Sign bit selector
82
may use the symbol magnitudes produc~ad by the magnitude mapper 50, F1G,
4, and the coset representative sign bits for the current frame end for future
frames to decide which encoded symbol sign bits achieve the best spectrai
shaping. The V.90 standard specifies that up to three frames in the future may
be used depending on the amount of look-ahead delay negotiated during
startup.
The spectral shaping metric RFS, based on a filter transfer function
h(D), is computed for all possible paths (or candidate sequences) through the
trellis diagram up to the look-ahead delay or depth d by filter 80, and the
selection controller selects the encoded symbol sign bits associated with the
candidate sequence for frame k that produces the smallest RFS.
Referring again to trellis diagram 100, FIG. 9, the possible candidate
sequences for a look-ahead depth of 1 is described. At the beginning of a
frame k if the state, Clk , of selection controller BB is 0, convolutional
cads
sequences A 102 and B 104 are valid sequences far frame k. However, the
code sequenoes for frame k+1 must also be considered. Since in frame k
code sequences A 102 and B 104 are valid, then in frame k+1 the stale, Qk+1
could be 0 or 1 and therefore code sequences A 102', B 1(~', C 106' and D
108' are valid. As described above, the coset representative sign bits are
EXCLUSIVE-OR'ed with each of the valid code sequences to form candidates
of encoded symbol sign bits. With look-ahead, the coast representative sign
bits for each frame k and k+1 are EXCLUSIVE-OR'ed with the valid code
sequences in each path of the trellis diagram thereby forming candidate
sequences. The candidate sequences !n this example are the following four
sequences: { 1) ( t, s3 A, lk,r ~ A); 2) ( tr ff~ A, tt.r ~ B). 3) ( tk ~ 6,
r",r C~ C);
and 4) ( r~ ~ 8, t~~, ~ D)}. The RFS for each sequence is determined and the
candidate encoded symbol sign bits for frame k in the determined sequence is
chosen.
n
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In FIG. 10. flow ch$rt 120 describes the operation of symbol sign bit
selector B2. In step 122, selection controller 8B generates the candidates (or
candidate sequences in the case of look-ahead) of encoded symbol sign bits
by modifying the coast representative sign bits according to the trellis
diagram.
Then, in step 124 selection controller combines the symbol magnitudes and
the candidates of encoded symbol sign bits to form encoded signed symbol
candidates (or candidate sequences) and provides them to fitter 90. In step
128, filter 9D determines the RFS for each candidate (or candidate sequence)
and provides the RFS for each candidate (or candidate sequenc$) to selection
controller 88. Finally, in step 126, selection controller 88 chooses the
candidate of encoded symbol sign bits (cr candidate secfuence) that minimizes
AFS and sends the encoded symbol sign bits.
It must be noted that this invention may utilize various convoiutional
codes, G(D), which are represented by different trellis diagrams and different
convolutional code sequences. The extension to various convolutianal codes
and code sequences in light of the description herein will be straighfforvvard
to
persons of ordinary skill In the art.
In general, with PCM, the spectral shaping scheme according to this
invention, shapes the spectrum of the analog signal transmuted from the DIA
converter in CO 60, FIG. 5, by setting the response of ~Iter 90, FIG. 8, to
achieve a desired spectral shape and by minimizing the RFS. The response,
h(d), of fitter 90, which defines the desired spectral shape, may be expressed
as follows;
~b,D''
11h(D)= 8(D)IA(D)= N° , ao~1 (3)
~arD_i
,_°
where A(D) and B(D) era functions and a and b are real numbers chosen to
achieve the desired spectral shape. And, N,, and NB are the number of
coefficients used for the numerator and denominator, respectively, to
represent h(D). The RFS on a symbol-by~symbol basis may be calculated as
follows:
12
....._-.._w-.~__ .~
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RFS~= ~b,Y~r -~,arRFS,-r (a)
r~o m
and the RFS on a frame basis for the kth frame may be calculated as
follows:
RFSk= ~~ Rh5 t,; (b)
where j is the symbol (time) index.
When using the sign bit encoder of the present invention to create a
spectral null at DC, the RFS is the running digital sum (RDS) and the
response, h(A), of filter 90 Is expressed as follows:
h(D) =1-D (g)
From the transmitted signed symbols yK filter 90 calculates the RDS of
transmitted signed symbols y~ at symbol time i as follows:
RDS, = ~ y ~
(7)
;.o
where j is the symbol (time) index and the RDS on a frame basis for
the kth frame may be calculated as follows:
RDSt= ~ RDS;~, J (g)
~w
where j is the symbol (time) index.
For look-ahead, with a look-ahead depth O, the RDS is calculated as
follows:
a
LRDSK ~ RDS~,; (g)
13
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where LRDS is the look-ahead RDS. We can similarly introduce look-ahead to
generally minimize RFS as follows:
LRFS~= ~ RFSk,., f 1 O)
Sign Blt DecodJ~~a
Sign bit decoder 74 in receiver 64, FIG. 5, is shown in FIG 11 to include
a matrix block 17 0. in matrix black 110 the sign bits er are multiplied (in
modufo 2) (i.e., filtered) by matrix HT~"~,~, to recover the differentially
encoded
sign information bits v~ '.
An example of matrix HT when there are six symbols transmitted per
frame (rr_6) and one redundancy bit (r=1) is shown in equation (11) as
falfows:
1 1+D 1 1+D Z
0 0 0 0 1+D
_ 0 0 0 1tD 0
0 0 1+D 0 0
0 1+D 0 0 0
1+D 0 0 0 0
Tha matrix HT is designed so that the decision error in vt due to error in the
received sign signal sk will not propagate more than one frame, Thls is
because HT is a finite impulse response (F1R) type of matrix and there is only
a
single delay.
In order to demonstrate how the each of the candidates of encoded
symbol sign bits generated by sign bit encoder 52, FIG. 4, for each frame of
symbols to be transmitted are decoded to the same sign information bits, the
encoding and decoding processes must be expressed mathematically. The
information bits recovered, 'v~, (decoding) can be expressed mathematically
as follows:
Gt = sir t 12)
!4
r ~. ,
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and the sign bits rr (encoding) can be expressed mathematioally s follows;
8" = vw H~T + rrG ( 13)
tf the right hand side of equation (13) is subst'ttuted into equation (12) far
s~,
then the following equation is derived:
vt ~ v~H~TH~ + rxGHT (14)
8y selecting G, HT and H'T so that the following conditions are satisfied: (1)
HT
H'T= ! (whets I is the identity matrix ); and (2) GHT= 0, then G, = vk
regardless
of the value of rt.
In the above example, trellis diagram 100, FIG. 9, a single redundancy
bit, rr, is and convolutional code G(D)= (1+D 1 1+d 1 i+D 1). Since 1 "rk=r,
and D'r~-rte, then rkG(D) is equivalent to r~ (1 1 1 1 1 1) + rw, (1 0 1 01
0).
Here, r~., represents the states, C)~ , of the trellis diagram and
rrrepresents the
branches or paths taken through the trellis diagram. The four convoiutlanal
code sequences A-D can be mapped to the rk_,, r, representation as follows:
A: 000000 - r,,,=0, rr ~
B. 111111 - r,,,=0, r, =t
G: 1 O 1 O10 - rh,=1, r~ ~0
D: 010101 - r~,,=7 , r, =1
where code sequences A-D can be thought of as rrG(D).
Since the value of r, does not affect how the information bits are
decoded, each set of n sign bits generated by the different valid code
sequences rnay be used to produce the same decoded information. As a
result, the set of n sign bits that minimize the RFSIRDS can be selected to
perform spectral shaping as desired.
Cfhatream PCM Tra smicclon
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The spectral shaping scheme according to this invention can also be
used in an equalization context as in the transmitter of an analog PCM modem
used for upstream PCM transmission to perform precodlng. In this case, the
response h(D) represents the channel response betwe~n the transmitting
modem and the analog-to-digital (AID) canverter in the central office (CO)
line
card, and typically includes the effects of filtering in the transmitting
modem
front-end, th~ analog local loop and the CO fine card.
By using the principles of this invention a channel output sequence x(n)
(z(n) with prefiltering) can be generated that produces a sequence y(D) at the
AID converter input whose signal paints mimic the AID quantization levels. In
this case, the objective is to minimize the energy of the transmitted signal
x(D)
= y(D)Ih(D) while maintaining a low cansteliation expansion at the AID
converter input. Constellation expansion is undesirable in this case as waif
because larger constellation expansion may lead to increased echo-induced
quantization noise and other impairments.
In this application, usually the channel response h(D) wlll be determined
either by the receiving modem or jointly by the transmitting and receiving
modems based on channel measurements made during modem start-up, and
then during data transmission the transmitting modem will map the incoming
bits into the transmission sequence x(D), which ~.fter passing through the
channel are converted to the channel output sequence y(D). The channel
response h(D) is usually chosen to be minimum phase, which is easily
accomplished, for example through additional filtering in the transmitter,
Transmitter 40', FIG. 10, is a transmitter in an analog PCM madam
which is capable of upstream PCM transmission. Transmitter 40' uses the
spectral shaping scheme of this invention to precode, using precader i40, the
incoming data bit stream 42'. One type of PCM upstream precoding (referred
to as one-dimensional precoding which precodes on a per symbol Basis) is
described in detail in US Patent App., Attorney Docket No. CXOA6C44P02,
entitled Device and Method for Precoding Data Signals, flied December 29,
t 997, having inventors M. Vedat Eyubogiu, Pierre A. Hurnbiet; and Daeyoung
Kim. Precoder 140 perfQm~s multi-dimensional preceding, i.e, it precodes
symbols on a per frame basis. The present implementation differs from one-
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dimensional precodlng, but the concept Is analogous to the ons-dimensional
case and reference may be made to the above co-pending application for
further detail.
Precoder 140 includes a serial to parallel aonvertar 48', magnitude
rnapper 50', sign bit encoder 52' and a signal point selector 64'. These
components are configured and operate as do the components with tike
numbers tr. FIG. 4 with minor modifications. For example, the operation of the
sign bit encoder is modified to perform precoding, as described below, and the
signal point selector outputs n precoded levels, x" per frame corresponding to
the signed symbols, y,, instead of the signed symbols themselves. The n
precoded levels, x,, are provided to parallel to serial converter 142 which
outputs the precoded levels in serial form to prefilter 144. Prefilter 144
fitters
the levels and outputs the filtered levels to digital to anatog converter 146
which in tum transmits precoded analog levels over analog channel 149. The
channel modifies the precoded levels , x~, and ideally produces levels
corresponding to the signed symbols, y" at the quantizer in central office
(CO) 150. In other words, the precodsr selects precoded levels, x" that
produce levels corresponding to the desired signed symbols, y,, at the
quantizer by accounting far the response of analog channel 148, or more
precisely a target channel response, h(n).
The target channel response, h(n) is equal to g(n), the response of
prefilter 144, convoived with c(n), the response of analog channel 148, where
n is the symbol time index and h(0)=1 . That relationship can be expressed as
follows:
y(n) = h(~)x(n) + h(1)x(n-1 ) + ... h(Nh)x(n-Nh) (15)
Since h(0) is designed to equal 1, then equation (15) can be simplified as
follows:
,N~,,~
x~n) = y(n) _ ~(t7~n-t7 , ( 1 s)
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The value for h(n) at a given time is known and the past values of x(n)
are also known. Fitt~r 90, F1G, e, calculates the summation term of equation
(16) as the RFS and provides it to selection controller BB. The past values of
x(n) are determined from the previous symbols y(n) by the known relationship,
x(D)=y(D)Ih(D) and stored in filter 90 and the selection controller 88
operates
according to flow diagram 120, FIG. 1 Q, by selecting the encoded symbol sign
bits that minimize x(n). Instead of sending signed symbols y(n), precoded
levels era transmitted.
In addition to the mapping operations described above, one needs to
include modules for echo cancellation which separates the tv~o directions of
transmission, a timing interpolation fitter which ensures that the symbols are
transmitted in synchronism with the network clock. This timing interpolation
fitter will typically be driven by the clock recovery circuit used in the
downstream receiver. The transmitter may also include a linear filter which is
primarily responsible far limiting the transmission bandwidth to about 4 kHz
and to provide the necessary prsfittering which would make the overall
channel response h(D) minimum phase.
Further, in a practical system one could also include a form of trellis
coding to increase noise immunity. For example, the trellis coding techniques
described in the application referred to above, entitled System and Device
far,
and Method of, Communicating According to a Trellis Code of Baseband
Signals Chosen from a Fixed Set of Baseband Signal Points, filed November
14. 1996, US Apl. Ser. No. OBl749040 (Attomay pocket No CX096050) can be
used. That application is incorporated herein in its entirety by reference.
The
operation of the system is essentially unaffected by trellis coding.
It should be noted that this invention may be embodied in software
and/or firmware, which may be stored on a computer useable medium, such
as a computer disk or memory chip. The invention may also take the form of a
computer data signal embodied in a carrier wave, such as when the invention
is embodied in softwarelfirrnware, which is electrically transmitted, for
example, over the Internet.
The present invention may bs embodied in other specific forms without
departing from the spirit or essential characteristics. The described
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embodiments are to be considered in all respects only as illustrative and not
restrictive. The scop~ of the invention is, therefore, indicated by the
appended
claims rather than by the foregoing description. All changes, which come
within the meaning and range within the equivalency of the claims, are to be
embraced within their scope.
What is claimed is:
I9
