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Description  |
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FIELD OF THE INVENTION
This invention relates to systems that communicate signals representative
of digital information, and more particularly to systems that spectrally
shape said communicated signals.
BACKGROUND OF THE INVENTION
In a typical data transmission system, a physical channel may be
effectively modeled by utilizing filtration at the transmitter, channel
filtration, an additive white Gaussian noise source, and receiver
filtration. Certain methods have been developed for reliably transmitting
digital information over linear distorting channels using linear
modulation methods such as quadrature amplitude modulation (QAM) and phase
shift keying (PSK). Powerful coded modulation methods have been utilized
in a sufficiently high signal to noise ratio (SNR) environment to allow
approaching a capacity of a Gaussian channel with intersymbol interference
(ISI) if the system can attain ideal decision feedback equalizer (DFE)
performance followed by Maximum Likelihood decoding. However realization
of DFE in a coded system poses problems in obtaining reliable decision
feedback, and hence, enhances severity of error propagation.
In the early 1970's Tomlinson modulo-precoding was introduced as a means to
avoid error propagation in DFE for pulse amplitude modulation (PAM)
systems by implementing a feedback filter of a DFE in a transmitter where
a transmit symbol is utilized for feedback filtration. This method
completely precompensates for postcursor ISI without increasing a
transmitted power where moderate to high transmission rates are used.
Modulo arithmetic is used to bound a dynamics range and to recover power
loss implied by the filtration. More recently, the concept of precoding
has been generalized to coded systems on partial response channels, onto
higher dimensional signal sets such as QAM, and has been combined with
trellis shaping to achieve substantial shape gain without reducing coding
gain.
A precoding system may be realized using a noise predictive form of DFE
together with a training procedure. Under moderate to high rate of
operation, spectral properties of a precoded sequence remain statistically
white, preserving characteristics of an input scrambled sequence to the
precoding process.
In certain types of channel there is a need for a transmitted sequence to
achieve certain spectral properties. For example, when a severe nonlinear
distortion source is present in an output signal of a channel filtration,
it may be desirable to include pre-emphasis filtration on the transmitted
sequence such that a peak-to-average ratio of the channel output signal is
reduced. However, typically pre-emphasis filtration as a component of
linear equalization geared pre-emphasis spectrally shaping the transmit
sequence imposes a power penalty on a transmit power-limited system, that
penalty being independent of any previous coding, shaping and/or
equalization method utilized in the transmission system. Higher than
symbol-rate filtering is a convenient filtering rate for conventional
transmit filters. However, at the present time, symbol-rate spectral
shaping independent of the higher than symbol rate transmit filter is not
available.
Thus, there is a need for a device and method that provide at least a
substantially symbol-rate transmitter spectral shaping of signals
representative of digital information that is independent of the higher
than symbol-rate transmit filter.
SUMMARY OF THE INVENTION
A device and method of the present invention provide at least a
substantially symbol-rate transmitter spectral shaping of signals
representative of digital information, the digital information being
represented by at least an initial symbol sequence, comprising at least
one of: a modulation unit for at least modulating information; and a
demodulation unit for at least demodulating information; wherein: the
modulation unit comprises at least: a precoding unit, where desired,
operably coupled to the digital information input, for substantially
precoding the at least initial symbol sequence utilizing a predetermined
equivalent channel response; a spectral shaping unit, operably coupled to
one of: the digital information input and the precoding unit, for
substantially utilizing a spectral shaping filtering function and a first
scaling factor to provide a spectrally shaped sequence, the spectral
filtering function also being provided, where desired, to the precoding
unit; a transmission preparation unit, where desired, operably coupled to
the spectral shaping unit, for providing at least one of: preselected
filtering and preselected equalization, to obtain a spectrally shaped
transmission sequence for transmission on a selected channel of a channel
unit; and the demodulation unit comprises at least: an equalizing unit,
where desired, operably coupled to the channel unit, for receiving and
equalizing one of the spectrally shaped sequence and the spectrally shaped
transmission sequence, and a symbol-rate processing unit, operably coupled
to one of the equalizing unit and the channel unit, for receiving one of
the spectrally shaped sequence and the spectrally shaped transmission
sequence, equalized where desired, substantially determining a noise
prediction filtering function, and utilizing that noise prediction
filtering function and at least a second scaling factor to provide at
least a first symbol sequence for a symbol-rate spectrally shaped signal,
the noise prediction filtering function also being provided, where
desired, to the precoding unit.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a block diagram of a first embodiment of a device in accordance
with the present invention.
FIGS. 2A, 2B, and 2C are block diagrams further illustrating exemplary
block diagram embodiments of the precoding unit, spectral shaping unit,
and symbol-rate processing unit block diagrams, respectively, of the first
embodiment of the device in accordance with the present invention.
FIG. 3 is an exemplary representation of a 128 point signal constellation S
that consists of two 64-point constellations S.sub.00 and S.sub.01 in
quadrants 1 and 2, respectively, utilized in an embodiment of the present
invention.
FIG. 4 illustrates an exemplary embodiment of a encoding unit together with
an information shaping bit insertion unit for encoding in accordance with
the present invention.
FIG. 5 illustrates an exemplary embodiment of an inverse syndrome former
unit of a device with trellis precoding in accordance with the present
invention.
FIG. 6 illustrates an exemplary embodiment of a Tomlinson precoding unit of
a device with precoding in accordance with the present invention.
FIG. 7 is a schematic representation of a 45.degree. rotated square region
(shaded) for a modulo determiner that reduces precoded symbols in
accordance with the present invention.
FIG. 8A illustrates an exemplary embodiment of a trellis decoding unit of a
device with precoding in accordance with the present invention; FIG. 8B is
a schematic representation of an exemplary trellis code T diagram showing
all sequences whose subset labels {b.sub.n } belong to a 4-state rate-1/2
convolutional code C.
FIG. 9 illustrates an embodiment of a device with a symbol-rate processing
unit with trellis precoding in accordance with the present invention.
FIG. 10 is an exemplary representation of a 256 point signal constellation
S' that consists of four-64 bit constellations S.sub.00, S.sub.01,
S.sub.10, and S.sub.11, utilized in an embodiment of the present
invention.
FIG. 11 illustrates an exemplary embodiment of a syndrome former unit of a
device with trellis precoding in accordance with the present invention.
FIG. 12, illustrates a system model utilized for determination of an
optimal spectral shaping function of the present invention.
FIG. 13 is a flow diagram of steps of a method in accordance with the
present invention.
DETAILED DESCRIPTION OF A PREFERRED EMBODIMENT
The device and method of the present invention provide for at least
substantially precoding and symbol-rate transmitter spectral shaping of
signals representative of digital information in addition to providing
flexibility in selection of operational modem modes and to improve
received signals in the presence of non-ideal channel noise. The
flexibility of the present invention allows selection of desired
equalization, typically linear, precoding without spectral shaping, and
precoding with spectral shaping.
FIG. 1, numeral 100, is a block diagram of a first embodiment of a device
in accordance with the present invention. The device provides for at least
a substantially symbol-rate transmitter spectral shaping of signals
representative of digital information, where the digital information is
typically represented by at least an initial symbol sequence, and
comprises at least one of: a modulation unit for at least modulating
information; and a demodulation unit for at least demodulating
information; wherein: the modulation unit comprises at least: a precoding
unit (102), where desired, operably coupled to the digital information
input, for substantially precoding the at least initial symbol sequence
utilizing a predetermined equivalent channel response; a spectral shaping
unit (104), operably coupled to one of: the digital information input and
the precoding unit (102), for substantially utilizing a spectral shaping
filtering function and a first scaling factor to provide a spectrally
shaped sequence, the spectral filtering function also being provided,
where desired, to the precoding unit (102); a transmission preparation
unit (106), where desired, operably coupled to the spectral shaping unit
(104), for providing at least one of: preselected filtering and
preselected equalization, to obtain a spectrally shaped transmission
sequence for transmission on a selected channel of a channel unit (108);
and the demodulation unit comprises at least: an equalizing unit (110),
where desired, operably coupled to the channel unit (108), for receiving
and equalizing one of the spectrally shaped sequence and the spectrally
shaped transmission sequence, and a symbol-rate processing unit (103),
operably coupled to one of the equalizing unit (110) and the channel unit
(108), for receiving one of the spectrally shaped sequence and the
spectrally shaped transmission sequence, equalized where desired,
substantially determining a noise prediction filtering function, and
utilizing that noise prediction filtering function and at least a second
scaling factor to provide at least a first symbol sequence for a
symbol-rate spectrally shaped signal, the noise prediction filtering
function also being provided, where desired, to the precoding unit (102).
One advantage of the present invention is allowance of substantially
symbol-rate spectral shaping that is independent of a higher than
symbol-rate transmit filter.
Training for determining coefficients utilized in spectral shaping is
typically in accordance with training methods known in the art, for
example, least-mean-square (LMS) and Least-Square acquisition of
predictive coefficients. In one embodiment, for example, a combination of
a matched filter and a mean-square-error (MSE) linear equalizer are
implemented as a digital transversal equalizer that has a fractional
tap-spacing of T/M, where T is a symbol interval and M is a predetermined
value sufficiently large to avoid aliasing. A known training sequence is
typically transmitted, and a desired adaptive training algorithm, for
example, the LMS algorithm, is utilized to learn the equalizer. Then, an
adaptive minimum MSE linear predictor is typically determined such that it
has a tap-spacing of T and steady state coefficients that form a desired
channel response h(D). After the desired length of training, h(D)
information is transmitted back to the transmitter. Thus, once the
equivalent channel response h(D) is determined, h(D) information is
transmitted to the precoding unit (102) and, where desired, to the
spectral shaping unit (104), depending on a selected mode of operation.
For pure precoding, h(D) information is transmitted to the precoding unit
(102). For pure pre-emphasis, an optimal coefficient is transmitted to the
spectral shaping unit (104). For precoding with spectral shaping, h(D)
information is transmitted to the precoding unit (102) and the spectral
shaping unit (104) utilizes a(D), as described more fully below. As
desired, an adaptive algorithm may also adjust linear equalizer
coefficients to minimize variations in channel response, but the
symbol-rate processing unit (103) is typically fixed. Where updating of
the symbol-rate processing unit (103) is desired, such updating
information is also transmitted to the transmitter for synchronization.
Also, as is known in the art, a receiver may monitor values of symbol-rate
processing coefficients and, where such coefficients vary more than a
predetermined level, may initiate new training.
In a trellis precoding system information data input may be expressed
typically in terms of shaping bits and coding bits, where the coding bits
also include so-called scaling bits, bits that typically do not directly
enter a convolutional coding device. For example, in FIG. 4, described
more fully below, an 11 bits input into the encoding unit (402, 404, 404)
are coding bits.
Coding is selectable and may utilize, for example, a 4D (four dimensional)
16-state Wei code, (See L.-F. Wei, "Trellis coded modulation with
multi-dimensional constellations," I.E.E.E. Trans. Inform. Theory, Vol.
IT-33, pp. 483-501, 1987) to transmit 19.2 kbits at 2954 symbols/sec, such
that, for example, a total number of 7 coded bits per symbol, of which 1/2
bit per symbol represents a redundancy of coding, are transmitted. Other
selected symbol rates may be used.
FIG. 3, numeral 300, illustrates a 128 point signal constellation S that
consists of two 64-point constellations S.sub.00 and S.sub.01 in quadrants
1 and 2, respectively. S is partitioned into four subsets as indicated by
different markings, and two coded bits determine a subset. Selection
between S.sub.00 and S.sub.01 is accomplished by identifying a sign of a
first coordinate in two's complement representation, i.e., selecting
between a positive coordinate x and its complement x-1.
FIG. 4, numeral 400, depicts a block diagram of an exemplary generic
16-state, rate-3/4, convolutional encoder (402) suitable for utilizing as
a encoding unit for the present invention, configured such that two
symbols from the 64 point mapping, S.sub.00, are generated (at 404; at
406). Every two bauds, 3 information bits enter a rate-3/4, 16-state
trellis code whose 4 output bits select two subsets for two 2D (two
dimensional) points in S.sub.00. The 4 `uncoded` information bits select a
first point s.sub.2j, and another group of 4 `uncoded` information bits
select a second point s.sub.2j+1, both from the 64 point constellation
S.sub.00 and from the subsets chosen by the coded bits. Every baud, in the
case of trellis precoding, a desired information shaping bit(s) is
precoded, for example, in an inverse syndrome former (414). The
information shaping bit(s), precoded where desired (for example, precoded
as t.sub.n,0), is combined by an insertion unit (412) with the coded
sequence, s.sub.n, to form a coded, shaped sequence. Thus, the information
data encoding unit (402, 404, 406) is typically utilized for converting
information into a selected number of bits to provide coded symbols. In
one embodiment, trellis encoding, generally an efficient coding method,
may be utilized. Where desired, more than one bit may be utilized in
shaping.
Typically, an information shaping bit inserting unit (410), for an
information shaping bit(s) input, performs a binary precoding, where
desired, of the information shaping bit(s) in the inverse syndrome former
(414) and utilizes an insertion unit (412) to combine the coded symbols
with the information shaping bit(s), altered by shaping bit precoding
where desired. When an embodiment in which precoding with a trellis code
is utilized, the inverse syndrome former (414), typically a binary
precoder, is utilized in the information shaping bit inserting unit (410).
In one embodiment, for Tomlinson precoding, described further below, there
is no shaping gain, allowing omission of the inverse syndrome former
(414).
In a preferred embodiment, the precoding unit (102) is typically operated
as a Tomlinson/generalized precoding unit, or alternatively, a trellis
precoding unit. In Tomlinson precoding a transmitted sequence
x(D)=i(D)-c(D), where x(D) is a discrete-time precoding unit response and
i(D) is typically an input sequence. For Tomlinson precoding, c(D)
corresponds typically to a member in a lattice MZ.sup.2 where M is a
scaling factor and Z.sup.2 is a 2 dimensional integer lattice. Other
lattices may be used. For trellis precoding, c(D) corresponds to a
sequence in a selected shaping trellis code T. It should be noted that the
precoding unit (102) may be selected to receive coded, or alternatively,
uncoded information bits as input. For a coded system, for example, where
a 4-dimensional 16 state Wei code is utilized, typically a 16 state,
rate-3/4 convolutional encoder suitable for use in an encoding unit is
then utilized.
Clearly, where a net transfer function of the precoding unit (102) is
substantially one, the precoding unit (102) may be omitted. Also, in
instances wherein no signal modification after spectral shaping is desired
prior to transmission, the transmission preparation unit (106) may be
omitted. The transmission preparation unit (106) typically implements at
least a transmit filter at a higher rate than the symbol-rate to allow
spectral shaping for excess bandwidth and the like. The spectral shaping
unit (104) and the precoding unit (102) together substantially comprise a
symbol-rate transmitter processing unit (101) that typically utilizes bits
at the symbol-rate. The noise prediction unit (112) also typically
utilizes the symbol-rate.
Utilization of the spectral shaping unit (102) in the present invention for
at least one of symbol-rate spectral shaping and precompensation typically
provides improvement over implementation of spectral shaping in the
transmission preparation unit (106) since the transmission preparation
unit (106) typically requires greater design intricacy, more computation
complexity and operation at a higher rate.
Generally the channel unit (108) comprises at least a first physical
channel, as is known in the art, having a channel unit response C(D).
T(D), a transmission preparation unit response, and L(D), an equalizer
unit response, are typically selected to provide a desired value for
T(D)C(D)L(D). The equalizing unit L(D) that is installed to compensate for
an effect of T(D) and C(D) is typically trained utilizing Minimum Mean
Square Error criterion (MMSE). In an absence of noise, an MMSE solution to
L(D) will be substantially 1/T(D)C(D). Hence, in that case, concatenation
of T(D)C(D)L(D) is substantially unity. In the presence of noise, the L(D)
will be trained so that the error or noise power at the output of L(D) is
minimized. However, T(D)C(D)L(D) in the latter case may not be exactly
unity. Since minimization of noise power by further processing of the L(D)
output sequence is desired, such an MMSE solution is acceptable. L(D) is
typically determined at a sampling rate that is higher than the
symbol-rate. Thus, a sampling rate equalizer is typically utilized to
compensate for the transmission preparation unit (106) and the channel
unit (108). Compensation for a symbol-rate pre-emphasis filter is usually
implemented in the symbol-rate processing unit (103). Hence, the
symbol-rate transmitter processing unit (101) may be added after training
without recomputation of a typical equalizer (110).
Also, the equalizing means (110) may be replaced by other known methods of
channel transmission deficiency adjusters such as adaptive algorithm
adjusters.
Utilizing D-transform symbol sequence notation, the precoding unit (102)
system utilizes an equivalent linear discrete-time channel response, h(D),
where h(D)=.SIGMA.h.sub.i D.sup.i, i=0, 1, 2, . . . in a presence of white
Gaussian noise. Without a loss of generality, h.sub.o is taken as one. An
inverse of h(D) is always defined, and is denoted as q(D)=1/h(d)=1+.sub.q1
D+.sub.q2 D.sup.2 + . . . An output sequence of the precoding unit (102)
is denoted x(D) and is generated according to x(D)=[i(D)-c(D)]q(D), where
c(D), in a case of general precoding, is a sequence with elements chosen
from an integer lattice MZ.sup.2, being modulo 2, to minimize an energy
.vertline.x(D).vertline..sup.2 of the output sequence. For trellis
precoding, c(D) corresponds to a valid code sequence in a shaping trellis
code C that attains energy minimization. It is clear that other integer
lattices may be utilized for other selected modulo operations.
In the present invention, the equivalent channel response h(D) is
represented by the combined response a(D)b(D), where a(D) typically
represents a monic, minimum phase spectral shaping filter at a transmitter
and b(D) typically denotes a monic, minimum-phase prediction filter in a
receiver. g(D) is defined to be 1/a(D). Thus, h(D) is substantially
b(D)/g(D). Thus h(D)=a(D)b(D) generally represents an equivalent channel
response seen by the precoding unit (102) that is present in data sequence
transmissions, but not in training transmissions. Thus, the transmitted
sequence, x(D), is substantially:
x(D)=i(D)-x(D)[b(D)-1]+[i(D)-x(D)][g(D)-1]-c(D),
where i(D) is an input sequence. Typically, b(D) is an all zero FIR filter,
and a(D) is an all pole filter. Thus, g(D) is typically an all zero
filter.
FIG. 2A, numeral 200, further illustrates a block diagram of an exemplary
embodiment of the precoding unit (102). In the exemplary embodiment, the
precoding unit (102) utilizes one simple feedback system (for a modulo
unit (206) having a transfer function mod) that utilizes a b(D)-1 transfer
function unit (202), and one combined system comprising i(D) summed at a
second summer (210) with the modulo unit (206) output, then implemented
with a g(D)-1 transfer function unit (208). Upon input of an initial
symbol sequence, i(D), the initial symbol sequence is input to a first
summer (204) and is fed forward to the second summer (210). The first
summer (204) sums i(D), an output from the simple feedback determination
unit (for feedback from the modulo unit) wherein the transfer function
b(D)-1 was utilized (202), and an output from the combined system that
implemented a g(D)-1 transfer function unit (208). An output of the first
summer (204) is input into the modulo unit (206), feedback is as described
above, and x(D) is the output of the modulo unit (206).
FIG. 2B, numeral 225, further illustrates a block diagram of an exemplary
embodiment of the spectral shaping unit (104). The precoding unit output
sequence x(D) is passed through a symbol-rate spectral shaping filter
(212) with response a(D) and is multiplied (214) by a first scaling
factor, 1/.sqroot.A (216) to generate transmit sequence x'(D), where
A=.SIGMA..vertline.a.sub.k .vertline..sup.2 is defined as a power
enhancement in the spectral shaping filter (212), where a.sub.k is a
coefficient of the D transform a(D) in the expression h(D)=a(D)b(D). This
scaling ensures that energy of x'(D) is equal to energy of x(D), thus
complying with a transmit power limit constraint typical in a data
transmission system. Determination of A is described more particularly
below.
In one embodiment, wherein a discrete equivalent channel is utilized for
the symbol-rate transmitter processing unit (101) and the symbol-rate
processing unit (103), the transmission preparation unit (106) typically
performs transmit filtering, digital to analog conversion filtering, and
the like. As noted above, a non-discrete equivalent channel implementation
may be utilized for the equalizing unit (110), the transmission
preparation unit (106) and the channel unit (108).
Thus, as set forth in FIG. 2C, numeral 250, a block diagram illustrating an
exemplary embodiment of the noise prediction unit, x'(D) is the input to
the noise prediction unit (112) such that a noise prediction filter (218)
having function b(D) provides an output that is multiplied by a scaling
factor (222), .sqroot.A, at a symbol-rate, to provide an output sequence.
The output sequence is i(D)-c(D), and is decoded as is known. b(D) is
selected to minimize noise power as seen at the input to a decoder, while
a(D) is typically utilized to apply desired spectral shaping to a transmit
sequence x'(D), or alternatively, as a pre-emphasis filter in linear
equalization. Inclusion of an inverse of a(D) and b(D) in the precoding
unit (102) operation ensures that the output sequence is y(D)=i(D)-c(D),
and hence that i(D) is recoverable. It is clear that i(d) may be encoded
or unencoded sequences.
Where the predetermined equivalent channel response is selected to be
substantially one, and the spectral shaping filtering function is selected
to be substantially an inverse of the noise prediction filtering function,
an output sequence having suboptimal linear equalization with pre-emphasis
shaping is achieved. Further, in the preceding case, where the noise
prediction filtering function is also a first order function,
substantially b(D)=1+b.sub.1 z.sup.-1, a (D) can be formulated to obtain a
closed form expression for filter coefficients.
Where the predetermined equivalent channel response is selected to be
substantially equivalent to the noise prediction filtering function and
the spectral shaping filtering function is selected to be substantially
one, general precoding without spectral shaping is obtained.
Where the predetermined equivalent channel response is selected to be
substantially a product of the spectral shaping filtering function and the
noise prediction filtering function, and the spectral shaping filtering
function is a selected shaping response, an output sequence having
combined precoding with spectral shaping is obtained.
Where the spectral shaping filtering function and the noise prediction
filtering function substantially equal one, the system reduces to a
conventional PAM or QAM transmission, another case of suboptimal linear
equalization.
FIG. 5, numeral 500, illustrates an exemplary embodiment of an inverse
syndrome former unit (510) of a device in accordance with the present
invention. This exemplary embodiment utilizes a first summer (502) to add
input information shaping bit(s) to a sum of two immediately preceding
successive input information shaping bit(s)(504, 506) obtained utilizing a
second summer (508). Typically the summer is implemented with an exclusive
OR.
FIG. 6, numeral 600, illustrates an exemplary embodiment of a Tomlinson
precoding unit (608) of a device with precoding in accordance with the
present invention. Again, the transmitted sequence, x(D), is
substantially:
x(D)=i(D)-x(D)[b(D)-1]+[i(D)-x(D)][g(D)-1]-c(D),
where
x(D)[b(D)-1] corresponds to a feedback term and [i(D)-x(D)][g(D)-1)]
corresponds to a new "modified coupled feedforward feedback" term since it
involves foth feedforward symbol i(D) and the feedback symbol x(D) in the
filtering process g(D)-1. b(D) is typically of a form 1+b.sub.1 D+b.sub.2
D.sup.2 +. . . +b.sub.K1 D.sup.K1 and g(D) is typically of a form
1+.sub.g1 D+.sub.g2 D.sup.2 +. . . +b.sub.K2 D.sup.K2, where K1 is a
highest order of coefficients for the feedback filter (606) and K2 is a
highest order of coefficients for the feedforward/feedback filter (610).
Previously encoded symbols x.sub.n-k, k=1, 2, 3, . . . ,K, are passed
through a feedback filter (606) providing a feedback signal f.sub.n
=.SIGMA.x.sub.n-k b.sub.k, where b.sub.k corresponds to the
1.ltoreq.k.ltoreq.K1
coefficients of the D-transform b(D), typically with b.sub.0 normalized to
unity without loss of generality. When g(D).noteq.1, then a
feedforward/feedback term of substantially a form q.sub.n
=.SIGMA.[i.sub.n-k -x.sub.n-k ]g.sub.k is required, with g.sub.k
corresponding
1.ltoreq.k.ltoreq.K2
to the coefficients of the D-transform g(D), again typically with g.sub.0
normalized to unity without loss of generality. The precoder combiner
(602) subtracts f.sub.n and adds q.sub.n to i.sub.n to form p.sub.n
=i.sub.n-f.sub.n +q.sub.n. In the case of Tomlinson precoding the modulo
determiner (604) provides at its output x.sub.n =p.sub.n -c.sub.n where
c.sub.n is a symbol from lattice RZ.sup.2 that is closes (in Euclidean
distance) to p.sub.n, and so forth. In the case of trellis precoding, a
Viterbi algorithm is typically utilized. A precoder combiner (602),
typically an adder, subtracts the feedback signal f.sub.n from the input
symbol i.sub.n and adds the signal q.sub.n to form p.sub.n =i.sub.n
-f.sub.n +q.sub.n. A modulo determiner (604) provides encoded symbols
relative to a 2D lattice .LAMBDA.=RZ.sup.2 configured such that, for a
p.sub.n input to the modulo determiner (604), an output is substantially
x.sub.n =i.sub.n -f.sub.n +q.sub.n -c.sub.n =p.sub.n -c.sub.n, where
c.sub.n is a symbol from .LAMBDA.=RZ.sup.2 that is closest (in Euclidean
distance) to p.sub.n, minimizing an instantaneous energy .vertline.x.sub.n
.vertline..sup.2 of the precoded symbol without delay. A feedforward
feedback filter (610) is utilized where g(D).noteq.1, the previously
encoded symbols x.sub.n-k being fed back into the g(D)-1 block as further
described for FIG. 2A. a second combiner (612) is utilized to subtract
modulo determiner (604) output from input i.sub.n and provide input to the
feedforward feedback filter (610). The modulo determiner (604)
substantially reduces precoded symbols to a 45.degree. rotated square
region (shaded)(702), illustrated in FIG. 7, numeral 700, (where a larger
square (704) is a boundary in the case of shaping) to reduce signal peaks,
wherein a normalized average energy of the precoded symbol has
substantially the same energy as that of a 128-point quadrature amplitude
modulated (QAM) signal constellation with a square boundary (702). Trellis
coding is a method of increasing distances between symbols of a signal
constellation such that symbols likely to be confused are separated by
maximized distances, while substantially not increasing average power.
Shaping, a method of reducing the energy of coded symbols, may be utilized
to provide shaping gain such that more noise can be handled with a same
transmit power.
FIG. 8A, numeral 800, illustrates an exemplary embodiment of a trellis
precoding unit in accordance with the present invention. The trellis
precoding unit is configured to utilize a modulo determiner(604) on a
sequence basis with respect to a trellis code T to determine x.sub.n
=p.sub.n -c.sub.n, c.sub.n being a sequence in C such that the precoded
symbols x.sub.n have a small average energy. (Obtaining the sequence
c.sub.n necessarily invokes some delay.) For example, about 0.7-0.9
decibels of shaping gain may be obtained with a simple 4-state 2D
Ungerboeck code. Shaping gain depends on the response of the feedback
(prediction) filter h(D), but only slightly. Required delay in this
example is 6-10 symbols. The symbols of the trellis code T lie on an
integer lattice Z.sup.2, the symbols belonging to one of 4 subsets that
are represented by a two bit subset label b.sub.n. The exemplary trellis
code T consists of all sequences whose subset labels {b.sub.n } belong to
a 4-state rate-1/2 convolutional code C whose trellis diagram is set forth
in FIG. 8B, numeral 850.
In trellis precoding the modulo determination is implemented using a
Viterbi algorithm (VA), for example in a 4-state Viterbi decoding unit
(802), wherein inputs to the VA are encoded symbols, and outputs are
precoded symbols x.sub.n-D. The VA searches for a code sequence {c.sub.n }
from C such that an average energy of x.sub.n =p.sub.n -c.sub.n is
minimized. At any given time, the VA has in storage four path histories
(candidate paths) {x.sub.k (i)}, i=0,1,2,3, with k<n, where each path is
associated with a different state of the convolutional code. The VA also
has in storage, as path metrics, a total energy (E) of each path,
accumulated up to time n:
##EQU1##
When a new encoded symbol i.sub.n arrives, the VA extends each candidate
path into two possible directions according to the trellis diagram being
implemented (the trellis diagram set forth above for the exemplary
embodiment) and increments each path metric.
Specifically, for a branch (i->j) from state i | | |
