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Description  |
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RELATED APPLICATIONS
This application is related to commonly assigned U.S. patent application
Ser. No. 08/122,525 filed Dec. 1, 1993 entitled FRAME SYNCHRONISATION FOR
QAM and naming John D. Brownlie and Richard G. Willians as inventors.
FIELD OF THE INVENTION
The present invention relates to phase amplitude modulation particularly,
though not exclusively, using block coding.
BACKGROUND OF THE INVENTION
In digital phase amplitude modulation, the modulated signal consists of a
sequence of symbols in each of which a carrier has a selected phase and
amplitude. Only certain phase/amplitude combinations are permitted; these
combinations may be plotted on a diagram with in-phase and quadrature axes
to form a pattern; the set of allowable points in this pattern is commonly
referred to as a constellation. If for example, one has a 16 point
constellation, it is a simple matter to modulate the signal with a 4-bit
word to be transmitted by regarding each point as associated with a
respective one of the 16 possible combinations of four bits.
It has been shown however that by using a larger constellation (e.g. 32
points) and a suitable coding of the 4 bits, the resultant inherent
redundancy in the modulated symbol sequence can be exploited by a soft
decision decoder to improve the reliability of decoding in the presence of
noise to an extent which exceeds the degradation caused by the larger
numbers of points and results in a net coding gain. Coding gain is defined
as the difference (in dB) between the signal-to-noise ratio that a coded
scheme needs to operate at a particular error rate and that needed by the
equivalent uncoded system.
One method of achieving coding gain is by the use of convolutional coding;
here however we are concerned primarily with block coding, though the
synchronization arrangements to be described are not limited to such
cases.
It is inherent in block coding that output symbols are generated on a block
by block basis. Thus if a 16-point constellation is to be used for
modulation at a rate of 3 bits/symbol, then the coding process needs to
produce 4n bits (for selecting points in the constellation) for every 3n
data bits received (where n is the length of a block of symbols).
Consider now the concept of set partitioning: the signal constellation is
progressively partitioned into subsets having increasing minimum Euclidean
distance between the points of each subset; .DELTA..sub.0 <.DELTA..sub.1
<.DELTA..sub.2 . . . as illustrated in FIG. 1 for 16 point quadrature
amplitude modulation. The Euclidean distance is simply the linear distance
on the phase diagram between adjacent points of a subset; thus, assuming
the sixteen points are on a unit grid,
##EQU1##
This distance is significant in that it is a measure of the capability of a
hard decision decoder to discriminate between points in the subset in the
presence of noise. By labelling each partition with a binary digit as
shown we form a partition tree. In FIG. 1 the label for each point is
constructed from the bits labelling the partitions needed to reach it; it
is convenient to write the bit corresponding to the first partition level
as the rightmost bit of the point label and so on. We then see that points
whose labels first differ (when read from right to left) in the ith
position (where the rightmost bit is the first position) are a Euclidean
distance of at least .DELTA..sub.i-1 apart.
The concept of set partitioning in this manner is discussed in G.
Ungerboeck's paper "Channel coding with multilevel/phase signals", IEEE
Trans IT-28, pp 55-67, January 1982.
The other primary consideration in the coding process is the Hamming
distance of the code or codes employed. FIG. 2 illustrates the coding
process, in the form of an array. Of a total of .SIGMA.k.sub.i input bits,
k.sub.1 bits are coded by means of an (N, k.sub.1, d.sub.1) code to form a
first row of bits a.sub.11 . . . a.sub.1N, k.sub.2 bits are coded by means
of an (N, k.sub.2, d.sub.2) code to form the second row of bits a.sub.21 .
. . a.sub.2N, and so on. The array has N columns, the bits of each column
forming a point label L.sub.1 . . . L.sub.N.
An (n, k, d) code is one in which k input bits are coded into n bits, with
a minimum Hamming distance of d.
For the 16 point constellation of FIG. 1 one might choose codes as set out
below, with a block size of 8 symbols.
______________________________________
i code Euclidean Distance
d.sub.i .DELTA..sup.2.sub.i-1.sup.2
______________________________________
1 (8, 1, 8) 1 8
2 (8, 4, 4) 2 8
3 (8, 7, 2) 4 8
4 (8, 8, 1) 8 8
______________________________________
Total number of input bits=.SIGMA.k.sub.i =20.
The square Euclidean distance .DELTA..sup.2.sub.i-1 increases down the
column, with the Hamming distance d decreasing down the column. The
minimum value of the product d.sub.i .DELTA..sup.2.sub.i-1 is preferably
large for good performance. Note that although the fourth row is actually
uncoded--i.e. the 8 bits are simply 8 of the input bits unaltered, it is
convenient to view this as an (n, n, 1) "code".
The codeword array concept is described in Imai & Hirakawa's paper "A new
multilevel coding method using error-correcting codes", IEEE Trans IT-23,
pp 371-377, May 1977, and in relation to Reed-Muller codes by E. Cusack,
"Error control codes for QAM signalling", Elec. Letts., 20, pp 62-63, Jan.
19th 1984.
It is worth noting at this point that the labelling of bits in FIG. 1 is
entirely systematic. Although in most cases this is the most convenient
way of proceeding, it is not essential in all cases. In particular, if two
rows of the array are coded with codes having the same Hamming distance
(or are uncoded) then the lower of these two rows can be allowed a larger
Euclidean distance without reducing the coding gain, and therefore the
meaning of the two bits from these rows for any one or more symbols can be
transposed with no effect, for example, if the bottom two rows are
uncoded, then the allocation of the corresponding label bits to the signal
points of the constellation can be entirely arbitrary (although this
allocation may be subject to other constraints; e.g. for the purpose of
achieving 90.degree. phase jump immunity, as will be discussed below). A
departure from structured partitioning which results in a reduction of the
minimum d.sub.i .DELTA..sup.2.sub.i-1 product will produce a degradation
of performance but may still provide a performance better than that of the
uncoded case. Indeed, random labelling does not necessarily preclude some
coding gain, but for good results then, if we define the Euclidean
significance of a label bit as being the smallest change of Euclidean
distance that changing that bit can produce, it is preferable that the
label bits do not all have the same Euclidean significance. In the
following description, the term "significance" is used to mean Euclidean
significance as defined above, and labels are written with the
significances of the bits increasing from right to left (analogously to
the conventional representation of binary numbers). This convention can
give rise to ambiguity in that two bits of a given label can have the same
significance, but no confusion arises since in this situation it generally
does not matter which bit is which.
A modification to this method has been proposed by RGC Williams and PG
Farrell in "Combined Coding and Modulation with decreased decoding
Complexity", IEEE ISIT '88, Kobe, Japan, June 1988. They regarded the
modulated signal as being the sum of two amplitude modulated signals in
phase-quadrature and coded separately in the two dimensions. Thus the
two-dimensional constellation was regarded as two one-dimensional
constellations transmitted in quadrature. It follows that the set
partitioning process discussed with reference to FIG. 1 is carried out in
the two dimensions separately. This is shown in FIG. 2A for the x
dimension. Note that the labels actually correspond to the x coordinate as
measured from the leftmost point; if different senses are chosen for the
0/1 division at any partition this simply results in one or more bits of
the label being inverted relative to the coordinate bit.
Coding is illustrated in FIG. 3 for the general case. Here the as and bs
are elements of codes as before. Now each dimension has its own codeword
array, producing labels L.sub.x1, . . . L.sub.xN ; L.sub.y1 . . .
L.sub.yN. In principle different codes could be used in each dimension's
array if quadrant phase immunity is not required.
FIG. 4 shows a specific example of such a scheme assuming we wish to send 3
bits/symbol over a 16-point QAM signal constellation, with a block size of
N=8. We require two bits per symbol in each dimension (=four bits/symbol);
for a block we generate 4N=32 bits from m=24 input bits (i.e. the rate of
the code is 24/32=3/4). The 24 input bits are divided into two groups of
12 (note that these schemes take no cognizance of the meaning of the input
bits and it is immaterial whether the 24 bits are eight 3-bit words or
three 8-bit words; thus the division into two groups is arbitrary). Of
each group of 12 bits, four are coded into the 8 bits of the first row of
the relevant array using the (8, 4, 4) Reed-Muller code, and the remaining
8 pass unmodified into the second row. Assuming the FIG. 2A partioning,
each column forms the x or y coordinate of a symbol to be transmitted.
Again, the top row forms the least significant bit.
A 16-point constellation is shown in FIG. 5 with labels derived from the
FIG. 2A partioning. The method employed for decoding this array involves
decoding separately in the two dimensions. Imagine that a demodulator has
received the eight points (relative to the lower left point of the
constellation) of a block and the x-coordinates of the received points are
(1.02, 2.94, 0.23, 2.53, 3.23, 0.45, 2.03, 1.24)
The first step is to regenerate the first row of the coding matrix; these
bits indicate whether the coordinate is odd or even; thus the received
vector is converted into a vector with values between 0 and 1 indicating
the distance of the received x-coordinate from the nearest even number,
viz
(0.98, 0.94, 0.23, 0.53, 1.0, 0.45, 0.03, 0.76)
Note that 3.23 is given the value 1.0 since the largest even coordinate in
the constellation is 2.
Application of a soft-decision decoding algorithm gives information digits
1010, implying a transmitted top row codeword of 11001100. This type of
soft-decision decoding is well known; however for a more detailed
description in relation to decoding in the separate dimensions see R. G.
C. Williams, "Low Complexity Block Coded Modulation", Ph.D. Thesis,
Victoria University of Manchester, U.K., August 1988.
Knowing the least significant bit of each symbol (i.e. whether the symbol
is even (0) or odd (1)) an inspection of the received coordinates shows
that the transmitted vector is (1, 3, 0, 2, 3, 1, 2, 2) and the remaining
eight information bits are (0, 1, 0, 1, 1, 0, 1, 1). Clearly if more than
two rows were involved, then the algorithm could be applied progressively;
in a more sophisticated system the results of later decisions could be fed
back to modify earlier decisions (again discussed by Williams).
Note that if the same codes are chosen for each dimension's array then
there are fewer different decoders required for the decoding since each
array has only half the number of rows of the equivalent 2 dimensional
array. Another feature of this scheme is that the decoders work with
1-dimensional distances and are therefore not as complex as the decoders
used in the original scheme which worked with 2-dimensional distances due
to the nature of the signal constellations.
SUMMARY OF THE INVENTION
According to one aspect of the present invention there is provided an
apparatus for modulating digital signals onto a carrier, comprising:
means for receiving a block of bits to be transmitted;
coding and partition means for partitioning each block into groups of bits,
at least one group having been coded by a redundant code having a Hamming
distance greater than one, the partitioning and coding being such that
each group has the same number of bits;
means for assembling a plurality of digital words from the bits of the said
groups;
means for quadrature amplitude modulation of a carrier to form a plurality
of successive output symbols, the two quadrature components of each symbol
being determined by a respective pair of the digital words;
characterized in that each word contains a bit from each group, whereby the
or a single redundant code produces bits which control both quadrature
components of each symbol.
Preferably in the coding and partitioning means at least one other group is
either uncoded or is coded using a code having a smaller Hamming distance
than the said one group, and the modulation means is so arranged that each
bit supplied thereto as part of the pair of digital words which is derived
from the said other group produces a minimum Euclidean distance which is
greater than that produced by any bit derived from the said one group. In
particular it is preferred that at least one coded group is coded
employing a code which has a Hamming distance greater than that obtainable
by dividing the group into two subgroups and coding each subgroup
independently into the same total number of bits.
If desired, for improving resistance to 90.degree. phase jumps, the
apparatus may include means to examine bits determining a predetermined
symbol of a block and those of a predetermined symbol of the preceding
block to determine the angular difference between the quadrants occupied
by those symbols; means for rotating the phase of the transmitted symbols
of the block in question by the said angular difference, and means for
modulating the carrier with information representing .the angular
difference.
In another aspect the invention provides a modulation apparatus comprising
quadrature amplitude modulation means operable in a first mode to produce
one of a plurality of discrete output symbols each having a predetermined
phase and amplitude and operable in a second mode to produce one of a
second such plurality of discrete output symbols each of which has at
least one quadrature component with an amplitude greater than that of the
corresponding component of any of the first plurality of symbols, means
for supplying to the quadrature amplitude modulation means digital words
for selecting of output symbols, and block timing means operable to
produce a block synchronization signal during a predetermined symbol
period of a block of symbols, the quadrature amplitude modulation means
being responsive to receipt of the synchronization signal to operate in
the said second mode for production of a symbol during that period.
BRIEF DESCRIPTION OF THE DRAWINGS
Other preferred features of the invention are set out in the subclaims.
Some embodiments of the invention will now be described, by way of example,
with reference to the accompanying drawings, in which:
FIG. 1 is a phase diagram showing a known way of partitioning a 16 point
QAM constellation;
FIG. 2 illustrates by means of an array one known method of block coding;
FIG. 2A is a diagram illustrating partitioning in one dimension;
FIG. 3 illustrates in similar fashion a second known method of block
coding;
FIG. 4 is an array illustrating a specific example of the array of FIG. 3;
FIG. 5 is a phase diagram showing the labelling of the points of a 16 point
QAM constellation as used in a first embodiment of the present invention;
FIG. 6 is an array illustrating the operation of the first embodiment of
the invention;
FIG. 7 is the known array of FIG. 4, redrawn for comparison purposes;
FIG. 8 is an array illustrating a second embodiment of the invention;
FIG. 9 is an array illustrating a third embodiment of the present
invention;
FIG. 10 is a block diagram of a coder operating in accordance with the
array of FIG. 9;
FIG. 11 is a block diagram of a corresponding decoder;
FIG. 12 is a block diagram of a modified form of coder and decoder;
FIG. 13 and 14 are phase diagrams showing enlarged constellations employed
in a further modification of the invention;
FIG. 15 is a block diagram of part of the coder of FIG. 10, modified to
provided synchronization;
FIG. 16 is a block diagram of a modified form the of the decoder of FIG.
11, with synchronization circuitry added; and
FIGS. 17 and 18 are block diagrams of, respectively a coder and decoder in
accordance with a further embodiment of the invention.
DETAILED DESCRIPTION OF THE DRAWINGS
The proposed modulation scheme uses only one array of 1-dimensional
components, the output information being shared between the two QAM signal
coordinates.
FIG. 6 shows an arrangement which is essentially FIG. 4 cut in half.
Although the number of columns in the array is still 8, the block size is
now 4 since two columns are required for the x and y coordinates of one
symbol. Thus the number of bits transmitted per symbol, and the coding
gain, are unchanged, but the block size is halved.
It is important to appreciate the fundamental difference between this
scheme and the earlier one-dimensional scheme, and that this appreciation
is not obscured by any particular way of drawing the diagrams used to
represent the schemes. Referring to FIGS. 7 and 8, FIG. 7 shows a scheme
similar to that shown in FIG. 4, (with eight symbols per block) but with a
rate of 1/2, thus accommodating only 16 input bits per block. FIG. 8 shows
a conjectural scheme as envisaged by the present invention, also with a
block size of 8.
Again we have to generate a total of 32 bits (16 in each row). If we
conjecture that, of 16 input bits, we code 2 bits into the first row with
a (16, 2, 8) code and fourteen in the second row using a (16, 14, 2) code
then we have achieved no advantage. However, a (16, 5, 8) code and a (16,
15, 2) code both exist (Reed-Muller codes) and if (as shown in FIG. 8) we
employ these then although the block size and coding gain are unchanged,
the scheme has an enhanced transmission capacity of 20 rather than 16
bits.
It may be noted that this example has the same performance as the
conventional 20-bit scheme discussed in the introduction; however it has
the advantage of reduced complexity of coding.
It is a known property of redundant codes that the maximum Hamming distance
d obtainable, for a code of a given rate, increases with the length of the
code. The invention thus exploits this fact by, for at least one array
row, coding the bits controlling the x and y coordinates of the
constellation symbols together using a single code.
The advantage of this is that one or more of the following (for a given
signal constellation) can be enhanced compared with using entirely
separate coding of the two dimensions
(a) the block size
(b) the coding rate (i.e. no. of bits/symbol)
(c) the coding gain.
Improvement (a) is exemplified by the comparison between FIGS. 4 and 6,
whilst that of (b) can be seen from FIGS. 7 and 8.
To illustrate meaningfully an improvement in coding gain by such a direct
comparison is more difficult since for a given coding scheme in accordance
with the invention this involves visualising an equivalent
decoupled-coding scheme having the same rate and block size. An
improvement in coding gain necessarily involves an improvement in the
Hamming distance d.sub.i for all rows having a minimum d.sub.i
.DELTA..sub.i.sup.2.sub.-1 product, so that for any scheme having such a
row with d.sub.i =1 a directly equivalent decoupled scheme does not exist
since this would need a Hamming distance of 1/2.
A more practical scheme, using a larger block size, will now be described,
together with particulars of its implementation. The scheme is set out in
FIG. 9, in the same manner as before.
This codes 4 bits/symbol onto a 64 point constellation, using a block size
of 16; the coding rate is 2/3. The first array row uses the (32, 6, 16)
Reed-Muller code, the (32, 26, 4) extended Hamming code and an uncoded
(32, 32, 1) row.
A suitable constellation is shown as the centre portion of FIG. 13, where
point labels (which are the same as the x, y coordinates) are indicated in
octal notation. The outer (underlined) 64 points will be discussed later.
A block diagram of a coder for implementing this scheme is shown in FIG.
10. An input 1 is assumed to receive serial data at 9.6 k bit/s which is
clocked into a 64-bit serial in parallel-out shift register 2 under
control of a 9.6 kHz clock signal ..phi..sub.1 from a master clock
generator 3 synchronized (by means not shown) to the input bit stream.
Every 64 bits, the parallel output is loaded by means of a second clock
signal (at 9600/64=150 Hz) into a register 4. Of the 64 bits in this
register, 6 bits are fed to a coder 5 which implements the (32, 6, 16)
Reed-Muller code and produces 32 bits a.sub.1,j whilst 26 bits are
supplied to a coder 6 which implements the (32, 26, 4) extended Hamming
code and produces 32 bits a.sub.2,j. The remaining 32 bits are uncoded and
form the 32 bits a.sub.3,j shown in FIG. 9. As mentioned previously the
allocation of which bits go to which coder is arbitrary.
The 96 bits a.sub.1j, a.sub.2j, a.sub.3j are now supplied to six 16-stage
shift registers 7-12. The registers 7, 8 and 9 are to contain the x
coordinates of the output symbols and the registers 11, 12 and 13 the y
coordinates. Sixteen of the heavily coded bits a.sub.1j from the coder 5
are loaded in parallel into the shift register 7 and the other 16 into the
register 10. Similarly the less heavily coded bits a.sub.2j from the coder
6 are loaded into the registers 8 and 11, sixteen into each, and the
uncoded bits a.sub.3j are equally divided between the registers 9 and 12.
The loading occurs under control of a 150 Hz clock signal .phi..sub.2 '
delayed with respect to the signal .phi..sub.2 to allow for delays in the
coders 5, 6.
The six registers 7-12 now contain the x and y coordinates of sixteen
symbols to be transmitted; once loaded their contents are clocked out
under control of a 2.4 kHz clock .phi..sub.3 (i.e. at a baud rate of
2400). Thus, every symbol period, a three-bit word representing the x
coordinate of the symbol to be transmitted is available at the output of
the registers 7, 8, 9 where register 9 supplies the most significant bit
and register 7 the least. Similarly the y coordinate is available at the
output of the registers 10, 11 and 12.
These outputs are used to control modulation of a carrier; this process is
illustrated in the diagram by a pair of amplitude modulators 13, 14
supplied respectively with carrier C.sub.l and carrier C.sub.Q in phase
quadrature to it, whose outputs are added in an adder 15 to provide a
modulated output at an output 16. Although not shown, any of the usual
techniques conventionally employed for avoiding phase or slope
discontinuities in the modulated signal may be employed. Note that
although coordinates here are expressed relative to the bottom left point
of the constellation, a symmetrical representation is more usual. This
simply represents a translation of (-3.5, -3.5) which is assumed to occur
in the modulators 13, 14.
Another scheme similar to that shown in FIG. 9 uses the following codes.
(32, 16, 8) Reed-Muller for a.sub.1j
(32, 31, 2) Parity Check for a.sub.2j
(32, 32, 1) Uncoded for a.sub.3j
This has an inferior noise immunity to that of FIG. 8 but has a higher
coding rate of 79/96, i.e. it carries an extra 15/16 bit/symbol. If a
fourth, uncoded, row is added and a 256 point signal constellation (e.g.
as shown in the inner portion of FIG. 14) is used, then it can carry 111
bits/block, i.e. 615/16 bits/symbol. If provision is made (as described
below) for carrying one extra bit per block, a bit rate of 19.2 kbit/s at
2743 baud can be achieved.
Note that the scheme described apparently requires an even length for the
codeword array, so that the columns of the matrix can be divided equally
between the two coordinate axes. However, if an odd length q is desired
this can be accommodated. One method of coping with this would be to carry
over one coordinate of alternate blocks to the next block, so that
alternate transmitted blocks contain (q-1)/2 and (q+1)/2 symbols
respectively.
Decoding of these signals is carried out in a manner analogous to that
described in the introduction for entirely separate decoding on the two
dimensions, the essential difference being of course that the x and y
coordinates obtained from the demodulator are assembled into a single
vector (in the same sequence, naturally as at the transmitter) and
processed together.
A block diagram of a decoder for the code of FIG. 9 is shown in FIG. 11. A
demodulator 20 receives the incoming signal and includes carrier
synchronization recovery and symbol synchronization; it demodulates the
signal to obtain x and y coordinates in digital form. Assuming, as is
conventional, that these coordinates are relative to the point of symmetry
of the constellation, adders 21, 22 add 3.5 to each coordinate to produce
the x, y coordinates relative to the lower left hand corner of the
constellation. As shown, the outputs of the adders are to 8-bit accuracy
(3 bits before the binary point, since the maximum coordinate is 7). The
demodulator also produces symbol clock signals .phi..sub.s.
The output coordinates are clocked into 16 state (16 being the block size)
shift registers 24, 25 under control of the symbol clock .phi..sub.s and,
each block period, loaded in parallel under control of a block
synchronization signal .phi..sub.B into a 32.times.8 bit buffer 26. The
least significant seven bits of each word pass via a unit 27 which derives
the distance of each coordinate from the nearest even number in the range
0 to 6 and supplies these to a soft decision decoder 28 for the (32, 6,
16) Reed-Muller Code. The output of this decoder is 6 data bits and the
valid 32-bit word which the decoder has judged the transmitter to have
used in the first row of the array.
The former are supplied to an output register 30, the latter to a unit 31
which adjusts the values of (the least significant seven bits of) the next
32 coordinates from the register 26 (i.e. constrains them to be the
nearest odd or even number according to the output of the decoder 28),
prior to passage to a soft decision decoder 32 for the (32, 26, 4)
extended Hamming code. This decoder supplies a further 26 data bits to the
output register 30. The decoder 32 also has an output for the 32 bits
which it has judged the transmitter to have sent; these are supplied,
along with the corresponding bits from the decoder 28, to a unit 33 which
makes any necessary adjustment to the remaining 32 (most significant) bits
from the register 26. As these bits are uncoded they then pass directly to
the output register 30. The total of 64 bits from the register 30 are
forwarded to the receiver's output 34. The 32-bit outputs from the
decoders 28, 32 are also conducted to an auxiliary output 35 along with
the adjusted uncoded bits from the unit 33.
When using signal constellations that contain rotational symmetries there
is a danger that they may suffer an undetected phase shift. If, during
transmission, there is something on the channel that rotates the
constellation points through one of its angles of symmetry then the
receiver's carrier tracking circuits will be fooled. The receiver will
think that it is receiving perfectly good points and will produce data but
this data will be based on the labels of the wrong points. For example, if
a QAM signal constellation is rotated through 90.degree. during
transmission then the receiver will produce data based on the labels of
points in the quadrant adjacent to those that the transmitted data had
selected. If we are not careful the data that we output will be wrong. It
is clearly necessary to take action to prevent catastrophic error
propagation. The problem has traditionally been overcome in the
convolutionally encoded case by using the process of differentially
encoding the data first.
In the case of block codes, it has been proposed by Brownlie and Williams
to apply a differential coding between blocks. A quadrant rotation is
determined by comparing the quadrant bits (i.e. the most significant x bit
and the most significant y bit) of the first symbol of the block and the
quadrant bits of the first symbol of the previous block. The first symbol
is chosen for convenience but any other consistent choice would be
satisfactory. This quadrant rotation is then applied to all symbols of the
block being transmitted.
This means that the quadrant bits of the first symbol becomes zero; these
are not transmitted: instead we substitute the difference.
After the decoder at the receiver the difference bits in the first symbol
are differentially decoded. The difference bits are also used to apply the
reverse rotation to all the symbols of the block and the differential
decoder's output replaces the block's quadrant bits. A systematic quadrant
phase error in the transmission path is thus cancelled since this affects
equally both the phase of the received difference and the phase of the
received symbols.
Note that this procedure requires that the most significant bits of the
first symbol also indicate the quadrant: this is true for the partioning
of FIG. 1, but care needs to be taken if less systematic bit
allocations--or constellations other than those having 2.sup.n points in a
square array--are used.
A coder and decoder implementing this procedure for the code of FIG. 9 are
shown in FIG. 12. Items 2 to 6 of FIG. 10 are shown as an encoder 50. The
most significant bits a.sub.3, 1 and a.sub.3, 17 of the first encoded
symbol of the block are separated and supplied to a differential phase
unit which takes the difference between its output one block previously
(via a delay 52) and its input. Note that this unit does not take the
differences between the bits, but provides an output indicating the phase
difference (for example by means of a look-up table). All the bits are
supplied to a rotator 53 which applies a phase shift of 0.degree.,
90.degree., 180.degree. or 270.degree. as indicated by the output of the
differential unit 51. This involves complementing the bits and/or
transposing x and y values, thus:
______________________________________
Phase (clockwise)
______________________________________
0.degree. x out = x in y out = y in
90.degree.
x out = y in y out = .sup.----x in
180.degree.
x out = .sup.----x in
y out = .sup.----y in
270.degree.
x out = .sup.----y in
y out = x in
______________________________________
The differentially encoded quadrant bits of the first symbol are
substituted for the quadrant bits of the output from the rotator. These
are then fed to a modulator 54 which contains items 7 to 16 of FIG. 10.
After transmission over a link 55, the inputs are demodulated in a
demodulator 56 containing units 20 to 26 of FIG. 11, and then pass to a
decoder 57. This contains units 27 to 32 of FIG. 11; however the output
that is required from the decoders 30, 32 is not the data bits but the
bits deemed by the decoder to have been received by the transmitter--i.e.
the auxiliary output 35 of FIG. 11.
The differentially encoded quadrant bits from the first symbols are
supplied to a differential decoder comprising a one-block delay 58 and
phase difference unit 59 (e.g. a look-up table similar to that used for
the unit 51) to produce received bits (a'.sub.3, 1, a'.sub.3, 17); it also
controls a rotator 60 which receives the remaining bits from the decoder
57 and applies (assuming no phase shift on the link 55) the opposite phase
rotation to that applied in the transmitter rotator 53. In the event of a
clockwise phase shift of n.times.90.degree. on the link, the amount of
rotation (anti clockwise) in the rotator 60 is, increased by n, thereby
compensating for the n.times.90.degree. clockwise rotation of the received
symbols (other than the quadrant bits of the first symbol which are
compensated by the differential coding).
The bits output from the units 59 and rotator 60 are now correct, and a
relatively simple data extractor unit 61 derives the data bits from the
Reed-Muller and Extended Hamming--coded bits and passes these, along with
the uncoded bits, to an output 62.
This method of achieving 90.degree. phase jump immunity has a number of
implications for the codes used. Since the phase rotations introduced at
the transmitter cannot be removed until after the soft-decision decoder
57, it is essential that the changes which these rotations make to the
bits of the transmitted array are such that each coded row of the array
remains a valid codeword--for example the changes made to the bits
a.sub.1, j must not generate a codeword which the Reed-Muller code cannot
produce.
The same phase rotation is applied to all bits except for the quadrant bits
of the first symbol. Therefore it is necessary that (as here) these bits
are derived from an uncoded row.
In the coded rows, in the case of the codes described in the Williams
thesis referred to, the transposition of x and y places no constraint on
the codes since the two coordinates are coded separately, whilst the fact
that x or y may be complemented means that the code used must be such that
if it contains a codeword A it also must contain its complement A.
In the case of the present embodiment, two things may occur, viz,
complementing x and y; or transposition of x and y and the complementing
of one of them. The first situation is met by the constraint just
mentioned. The second means that (given, as shown in FIG. 9 that the x
coordinates are taken from the first half of the codeword and the y from
the second), if BC is a valid codeword, where B and C are its two halves,
then CB and CB are also valid codewords. Both the Reed-Muller and extended
Hamming codes possess this property.
The foregoing description of the coder and decoder has assumed that a
coordinate (relative to the lower left point) and a point label are
synonymous, though--as has already been pointed out in the discussion of
FIG. 2A--this is not essential; but the only change that can occur to the
coded bits is that one or more label bits are complemented relative to the
coordinate bits. In the coder of FIG. 10, this | | |
