Note: Descriptions are shown in the official language in which they were submitted.
~'~CI 2~83
This invention relates to quadrature carrier
modulation communications systems.
Quadrature-carrier modulation (QC~I) communications
methods convey information as pairs of coorclinate signals
representing digital values, modulated on an "in phase" and
on a "quaclrature p}lase" carrier respectively.
At ~he transmitter a series of binary digital
signals is transformed in sequential groups into pairs of
coordinate signals which spatially represent in Cartesian
]0 coordinates of two dimensions a message point corresponding to
the binary number value of such group. Such pairs of coordinate
signals appear as modulations on the carriers. At the receiver
the received moclulated carrier signals are demodulated and the
digital group identified from the demodulated received coorclinate
signals. Durin~ transmission over the network or channel, the
transmitted modulated carrier is affected by noise and by many
other influences well known to those skilled in the art. Correct
detection of the received signals therefore involves determining,
on a balance of probabilities, whicll of two or more message
~20 points is represented by the coordinate signals received.
The most common ancl best known of the signalling
methocls is dollble side band-clundr.ltllre carrier modulation (otten
abbreviated DS~-QC~I), DSB-QC~ inclucles moclulntion techniques
such as phase - shift keying (PSK), quaclrature amplitude
moclul.ltion (Q~l), and combinecl nlnr)litucle and pll.lse moclulation
~hich have long been known in the art.
This invention is pnrticularly suitable for use
with DSB-QCM systems ~ith the elernents of thc? pairs of coordinates
61i33
being sent on the quadrature ~nd in phasc carriers respectively.
Prior developments for signalling such pairs of
coordinates include Canadian Patent 985,376 which issued
~arch 9, 1976 to Codex Corporation and U.S. Patent 3,955,141
which issued May ~, 1976 to Intertel Inc. Both such patents
show signalling systems where the message points spatially
representing the coordinate values display a square or
rectilinear pattern and have four-fold symmetry.
llowever> it has becn notcd that mcssage points
1() arranged in hexagons show better performance with regard to
.aussian noise or phase jitter than the rcctangular or four-
fold symmetry of the prior patents referred to herein. A
discussion of hexa~onal systems is contained in an article
; entitled "Hexagonal Multiple Phase-and-Amplitude-Shift-~eyed
Signals Sets" by Marvin K. Simon and Jocl (;. Smith, ap~earing
in IEEE Transactions on Communications Vol. COM-21, No. 10,
October 1973.
It is an object of this invention to provide
apparatus and a method of signall;ng using pairs of coordinates
2() modulated on in phase and quadrature pil.lse carriers, where the
message points represented by the coordinate pairs collectively
form a hexagonal pattern arrangecl on the intersections of an
etluilateral triangular gricl. In tllC invcntivc apparatus ancl
method it will be understootl that a series of binary signals,
are encoded in groups of n binary signals requiring a minimum
of 2n message points clefined by coorclinatc? pairs. In accord
with the invention there are made available, in the hexagonal
pattern K message points~ where K>2n. It will bc noted
-- 2
~c~v
that of the 2n possible values for the group of n digits, some
of such values will be in one-to-one correspondence with a
corresponding number of the K message points. The remainder
of such 2n values will have 2 or more message points corresponding
thereto. For K~2n it is not necessary but it is certainly
preferable if the points K are not only arranged in a hexagonal
relationship to one another but are arranged with 120 and
preferclbly 6() symmetry. Symmetry of any degree ten~s to reduce
and preferably substantially eliminate the carrier component of
the received signal. ~urther the higher degree of symmetry
renders easier the decision ancl decoding process at the receiver,
particularly when combined with differential encoding techniques.
Moreover the power requirements of the communications system will
be less if the hexagonally arranged signal points are packed as
closely as pos.-ible to the origin or point corresponding to ~ero
signal amplitude for both coordinates on a Cartesian coordinate
system. That is, the hexagonally arranged message points may be
considered to be located on concentric rings about the origin
and where nli availahle points on il ring (with the possible
exception of several outer rings) are occupied. Although the
extra K-2n message points provicle advantages inclependent of the
symmetry and density of packing o~ the message poin~s, the
principal advantages of the invention accrue when the message
points are symmetrically arrangecl about the origin and densely
packed outward therefrom and the aclvantageous use of the K-2n extra
points will be principally discussed where such symmetry ancl dense
packing are present.
The encocling ancl transmitting apparatus ia
~ _
0~3
preferably designed so tha-t the inner message points relative
to ~he origin are in one-to-one correspondence with the values
of groups of n binary signals where 2 or more of the outer
of the K message points correspond to others of th0 group values.
In this way, there are a plurality of outcr message points which
are not used each time the corresponding binary value is to be
transmitted, points in such plur;llity of outer message points
may be usecl cyclically or in accord with anothcr rule. In any
event, the outer points are used with less frequency than the
inner and power savings are thus achieved; since in a optimally
designe~ system the ener~y required to signal when using the
outer points in the pattern will be greater than when using the
inner points. The alternate message points corresponding to a
digital value of a group of bina~y digits may be used cyclically to
improve the symmetry of the collective transmission of sequential
message points. The fact that alternate points are available
corresponding to some of the group values allows transmission of
extra lnformation since the method of selection of alternate
point.s may he usecl for signalling. rhuS in accord with a prc-
20 ferred arrangement of the invention a class of values comprising
K-2 (K-2n) of the group values will be in one-to-one relationship
with a corresponding number of the K message points but K-2n of
the group values will each have two alternate corresponding
message points. This allows the transmission of binary information
on a channel additional to that represented by the dclta conveyed
by the groups of n digits. Thus the additional binary information
will not be regularly transmitted but must be queued for
transmission whcnever onc o~ thc K-2 vallJcs outslde thc class is
v~
to be transmitted. There are no practical 1imits to the type
of binary information which may be sent on the additional channel
thus provided. Thus the information transmitted on the
additional channel may (for example) relate to the operation
of the communications system, to the high speed transmission
of the 2n groups or it may be indcpendcnt information.
It will be obvious that; while the advantages
specified in the previous paragraph are easier to demonstrate
where the hexagonally arranged points are densely packed about
the origin and arranged in hexagonal or triangular symmetry;
that some of these advantages (namely the provision of an
additional channel and low frequency use of some message points)
also accrue when the dense packing and symmetry are absent.
Moreover thc prcsent invention allows the provision
of novel message point distributions, determined by the
coordinates transmitted by QCM modulation which continue to
exhibit near optimum margins against both Gaussian noise and
phase jitter as additional points are aclded. Further advantages
of the invention are that the apparatus and method allows
suppression of carrier and provide 60 or 120 symmetry.
In the drawings which illustrate a preferred embodiment
of the invention :
~igure 1 is a schematic diagram having blocks
referring to the functional requirements of a transmitter and
a receiver for employment with the invention,
Figures 2a - 2h show prior art message points
mapped on a rectangular grid in the two dimensional Cartesian
plane,
-- 5
Figures 3a-3f show prior art message points
mapped (largely) on a triangular grid in the two dimensional
Cartesian plane. (It should be noted that other message point
distributions are known such as those described and compared
in an article, "Digital Amplitude-Phase Keying with M-ary
Alphabets" by Thomas, Weidner and Durrani, IEEE Transactions
on Communications, Vol. COM-22, No. 2, February 1974)l
Figures 4a-4j show signal structures of the
invention mapped on -the Cartesian plane,
Figure S is a schematic block diagram of the trarls~
mission end of a communications link including a signal
processorl Figure 5 is on the same sheet as Figure 1,
Figure 6 is a flow chart showing the opera-tions of
the signal processor and microprocessor of Figure 5,
Figure 7 is a schematic block diagram of the
receiver end of a communications link including a signal
processor, and microprocessor,
Figure 8 is a flow chart showing -the operations of
the signal processor and microprocessor of Figure 7, and
Figure 9 shows the decision areas for received
signals which were encoded in accord with the distribution of Figure 4c.
Figure 9 is on the same sheet as Figure.7.
Figure 1 schematically illustrates functional
operations perLo 171~U 1~ a ~O~ UiliCat ons systems which would
utilize the invention. The functional operations are not
intended -to imply particular hardware or choices between analog-
vs. digital modes, or hardware vs. software modes at any
particular stage,
~2~2~
Thus as functionally illustrated in Figure 1 where,
functionally, serial binary data is converted, at a serial to
parallel converter, into groups of n digits. Such groups of
n digits are encoded to provide the message point Cartesian
coordinates for QC~1 modulation. A coordinate signal generator
and a carrier generator provide the signals to create the modulated
carriers which are combined and transmitted over the channel.
At the receiver the received signal is demodulated, conditioned
and equalized and sent to the decision region selection device
which rnakes the decision as to the message point coordinates.
Such 'Idecision coordinates" are supplied to the decoder which
converts these coordinates into parallel data intended to
correspond to the parallel data entered at the transmitter. The
received parallel data is converted into serial data for trans-
mission to the user. Circuitry for performing the above
functions is well known to those skilled in the art and examples
are disclosed in the Canadian and U.S. patents referred to.
Applicant's circuitry (the preferred form of which is discussed
hereafter) provides a novel relationship between the n binary
digit groups and the message points, less vulnerable to noise
and phase jitter, and error and whicll allows symmetry, suppression
of carrier and, in one alternative, the ability to transmit
a~xiliary information. Applicant's preferred ernbodiment also
reflects the advances in technology since the dates of the
Canadian an{l U.S. patents referrecl to.
There is here discussed the relationship of the
message ~oint coordin.ltes to the encoded binary information. In
contrast with the prior art the total number of message points
-- 7
2C~2~13
K employed in a si~nal structure th.lt is in accord with the
invention will not be an integral power of 2 such as 8, 16,
32, etc., even though the number of bits to be transmitted per
Cartesian coordinate pair is an integer n re~uiring at most
~1=2 message points. In fact the value of K will always
; exceed the value of ~. In a simplc cmbodiment of the invention
at least one of the required M values will be identified with
more than one of the K message points of the signal structure.
The reasons behind thc seleclion of K>M are firstly,
that the total number of points lying on concentric rings is
not a power of 2 for either of our type A or B structures,
secondly, we desire the carrier signal be suppressed which is
accomplished when the centre of the concentric rings is the
centroid (centre of gravity) of the K signal points, and
thirdly, we will desire to have 60 symmetry for type A
structures and 120 symmetry for type B structures when we
anticipate the use of c1ifferential encoding in conjunction with
these signal structures. By 'A type structures' we refer to
an arrangement of message points having 60 symmetry and a
point at the origin7 thus in thc optimllm arran~ement K~6I + 1
where I is any integer nnd is excmpliEiecl by l~igllres ~ta) (c~
(e) ~g) ~ It will be notcd that 60 ~hexagonal) symmetry can
be achievecl ancl near optimum arrangement, by omitting thc ori~in
point so that K=6I. Ilowever, discussions of the preferred
embodiment refer to K=6I ~ 1 arrangements.) By 'B type
structures' we refer to 120 symmetry with no points at the
origin and K=3I as exemplified by Figures ~(b)(cl)(f)~h)~j).
-- 8
~Q~3
.~ote that differential encocling is very desirable
since techniques which derive a carrier from the received data
signal, the carrier being fully suppressed, are generally
ambiguous in phase and when there is substantial 60 or 120
symmetry of the signal structure there can be 60 or 120
ambiguity in the recovered carrier.
With differential encoding, information is trans-
mitted in terms of the possible transitions from past trans-
mitted signal points to now transmitted signal points. In
our case, with K>M, there are K possible transitions and at
least two different transitions can convey the same information.
Leaving aside likely use of differential encoding
and decoding, consider the signal structure shown in Figure 4a
which has a total of K = 13 signal points and where the locations
of the seven innermost points are shown by solicl dots and six
outer points are marked with small circles. In this case we
presume that M = 8 and that 7 of the M points are to be
; associated with the inner 7 points and the eighth of the M points
will be associated with any of the outmost 6 points. Indeed, in
successive occurrences of the neecl to transmit the 8th of the
~l points the fi outer points will be use(l in turn so that each
will occur with a frecluency th.lt is l/fi of the frequency of each
of the 7 inner points. Thus when calclll.lting the signal energy
only one outer point neecl be incluclecl in the calculation. (The
6 outer points may l)e usecl in turn in cyclic order but for many
applications the 6 outer points will be used in a pseuclo ranclom
manner due to the differential encoding).
_ ~ _
``` ~Z~ 33
Signal sets can be comparecl on the basis of the
average required energy, under the assumption that in each set
the minimum distance between points in the set is 2 units in
each case and further the rectangular system points are assumed
to have integral coordinates. A lower average energy for a
given minimum separation results in an improved signal -to noise
performance.
As a result the average energy E, for the signal
structure shown in Figure 4a will have the value 4.5 versus, for
example a value of 5.5 for the prior art structure of Figure 2b
where each signal point is chosen from a rectangular grid and
each signal point is assumed to occur with the same frequency.
In other figures such as Figure 4c the situation is
slightly more complicatcd. Ilere there are a total of K = 19
points and we assume M = 16. In this case a chosen 3 of the ~1
values will each be associated with pairs of the six outer
points. Each of the paired outer points will be used in turn
so that outer points will occur with 1/2 the frequency that
inner points occur, (in one ~lternatc of thc preferred cmbodiment
~he selection of alternates will be in accord with auxiliary
channel binary signals). Thus only 3 of the six outer points
will enter into the energy calculation giving the rcsult E = 9.
In contrast the 16 point signal structure of Figure 2d results in
E = 10 and the structure of Figure 2c in E a 13~5~
Although use of the invention provides for a "good"
selection of signal points, differential encoding becomes more
complex as does the detection and decoding processes. In the
Type A and Type B codes it is advantageous to use the extra
message points in a statistically cqu;ll manner tha~ preserves
- 10 -
83
the 120 and 60 symmetries respectively required. In accord
with preferred techniqucs using the invcntion, it may be notcd
that differential encoding may be uscd to providc the statisti-
cally equal usage. In the preferred embodiment~ the extra
message points are selected on a basis that provides an extra
signrllling channel.
Type A codes present with regard to differential
encoding a complication since there is no angle associated with
the central point. This case can be treated by "remembering"
in the encoder the last signal poin~ that was not a central point
that was transmitted, whenever a central point is transmitted.
There is also an advantage that can be derived when
K>~l. It is possible, through varying the pattern of the
statistically equal usage of the extra ~oints, to transmit
auxiliary information. This ability can be enhanced by delibe-
rately increasing K over the minimum value that would be
; necessary to provide symmetry.
It should be noted that the extra points need not
be chosen entirely or partly from an outer ring but can be any
of the K points. However, to minimize average energy requirements,
points which are less frequently used should be outer rather
thrln inncr l)oints.
It should be noted that none of the prior a-rt of
Figures 2 and Figures 3 employ signal points at the centre of the
signal structure and none employ extra signal points.
In summary as greater datrl transmission rates are
employed over telephone channels it becomes more and more
important to utilize better performing signal structures even
although they are more complex to irnplement.
In ~igure 5 it is shown that a scries of binary
signals, for transmission along the communications lin~, are
sent to the circuitry along line 10 to a serial-to-parallel
converter 12 which converts the infor~ation into output bauds
of n binary digits. After processing in the microprocessor 14
and high speed processor 16 as discusscd in connection with
Figure 6J the rcsultant signals arc convcrtcd at digital-~o-
analogue converter 17 for the transmitter channel interface
and transmission along the channel.
The apparatus and procedures of Figures 5 and 6
are operable with n bits per baud where n is 2 or greater.
Figures 4a, 4c, 4e, 4g and 4i represent message point dis-
tributions which may be achieved with the apparatus and methods
of Figures 5 and 6 for n = 3,4,5,6 and 7 respectively.
The processors 14 and 16 and the flow chart of
Figure 6 are more easily discussed in detail using a specific
value of bits per baud. Before commencing such description it
is desired to set out certain constant values Cl, C2, C3, C4,
for n bits/baud where n = 4,5~6 or 7. The usage of these
'() constant values will be discllsscd herea~ter.
Thus thc table below givcs valucs for use of the
preferred processors and the flow chart of Figure 6 for
n = 4,5,6 and 7.
n M Cl C2 C3 C4 K (message Shown in
(hits/baud) points) Figure
~ 16 12 3 6 15 19 4c
32 26 5 8 31 37 4e
6 64 54 9 10 63 73 4g
7 128 116 11 14 127 139 4i
- 12 -
Figures 5 and 6 will now be described where n is
selected as 4 bits/baud. The 4 bits in each baud are provided
to the register 20 o a microprocessor 14.
It may be here noted that for bauds of four bits,
n=16 tl-at is each b.-ud or group represents one of 16 poss;hle
values. It should also be noted that the lowest value for
K hexagonally arranged message points (K>2n) is 19 where there
is a point at the origin and 60 symmetry (See Figure 4c).
With K=l9 and 2n = 16 it will be notecl that 13 of the 2n possible
1() baud or group values may be a class in one-to-one correspondence
with message points while the remaining 3 of the baud values
outside the class will each correspond to two of the K message
points, makin~ up a total of 19. In Figure 4c the 13 solicl ones
of the message points are those in one-to-one correspondence with
a class of values consisting of a corresponding number of baud or
group values while the 6 message points which are outlined only,
comprise 3 pairs with each pair corresponding to one of the
remaining 3 of the baud or group values.
Figure 6 is a flow chart showing the operations of
microprocessor 14 and high speed processor 16.
The four bits in the register 20 of Figure 6
re~resent a number ,`~I, the baud or group value ot which may have
16 values from 0-15. These bits are scramblecl at 22 to produce
another 4 bit value rls in accord with well known techniques.
Although such scrambler is commonly a hardware clevice, we prefer
to use the availahle capacity of the microprocessor. The output
o~ t1le scrambling provi~es at Register 24 Ms, a scramblecl binary
number having 2n group values 0-15.
- 1.~ --
2~
Cl is 12, and 13 (counting the ~ero position) is
the number of the 2 group values in one-to-one correspondence
to a message point.
The decision block 26 determines whether Ms is < 12
(i.e. whether it is in one-to-one correspondence with a message
point). If this is so tllc numhcr Ms is sul)pliccl dircctly to
decision block 36.
At decision block 26 if Ms > 12 then each group
value of Ms will correspond to a pair of alternate message points.
~or Ms > 12, Ms is supplied to the "auxiliarY channel enabled"
block 28. When it is clesircd to use the Auxiliary Channel a
switch (not shown) will usually enable the channel between blocks
30 and 31 and provide a signal 'Auxiliary Channel enabled' to
decision hlock 2~.
Data to be sent to the auxiliary channel is
supplied to storage 31 where it is retained in a queue for
transmission in single bits when the auxiliary channel becomes
~ available. It is not relevant to the present description
; whether the auxiliary data is related to the main data sent
along line lO or completely independent.
I~ no data is to be sent from thc Auxiliary data
queue i.e. the Auxiliary Channel is not enabled, then the
number Ms is supplied to block 36. If auxiliary data is to be
sent the A~lxiliary Channel is enabled and a signal is sent to
block 30 causing it to receive and ac]~llowledge the 1 or 0 which
is the 'first-in-line' of the queued bits in Auxiliary Data
Queue 31. (Auxiliary Data Queue 31 is designcd to receive binary
data and to retain it in a queue and to supply it bit by bit to
- 14 -
~v~
operator block 30. The auciliary binary data may represent
any binary data whether inclependent, related to the main channel
data or to the transmission). The receipt by block 30 of the bit is
acknowledged to block 31 to ready the next bit in the queue for
subsequent transmission. By arbitrary convention it is decided
that a "1" on the auxiliary channel will not change Ms while a
0 on the auxiliary channel will require a change. Accordingly,
iE a "1" is present the decision block 32 sends the number Ms
unchanged to block 36. If the auxiliary channel digit is a "~"
then the number ~2 (here 3) is added to Ms. The new Ma = Ms + 3
is supplied to decision block 36. Notc that where the auxiliary
channel is disabled the transmitted data is equivalent to a
constant binary ~. Note also that Ma can exceed the ran~e 0
to 2n-1 and hence requires an additional bit in its representation.
Decision block 36 is inserted since differential
encoding is to be used to avoid the effects of phase ambiguities
during transmission and because logic is simplified if such
differential encoding is not carried out for Ms=0. ~ccordingly,
; decision block .~6~ if Ms=0 sends Ms forward to block 38. If
;20 Ms ~ 0 (and Ma ~ 0) Ms or Ma as the case may be is transmittecl
to block 40 for conversion to coordinates defining the hexagonal
message points.
Tllus, Eor example in Figure 4c the values of Ms
have been assigned to the message points 0-12. While the assign-
ment of a value for Ms to a message point could be arbitrary, the
assignment is here chosen to agree with the logic used in Figure 5
where the lower Ms values (0-t2) in one-to-one correspondence
with message points are assigned to message points on inner rings~
As will be noted, in the outer ring two message points (shown in
outline only) corresponcl to each MS Va1UC from 13-15. For
Ms>12 a "1" from Auxiliary Data Queue 15 leaves the number Ms
unchanged at 13, 14 or 15 while for a "0" from Queue 15 tlle
number MS will be augmented by 3 (C2) to be 16, 17 or 18. The
message points for 16, 17, 18 are therefore one set of message
points 13,14,15. ~igure 4c also shows sector divisions,
Section 0, Sector 1 etc. After conversion at block 40 the
message points are designated by sector and a number (1, 2 or 3
therein). Thus or the first two sectors in Figure 4c -the
conversion will be :
Ms or Ma R(Sector) Q(No. in Sector)
0 0
7 0
13 0 2
2 1 0
14 1 2
and so on, and where R is the sector number and Q is the position
in the sector. Differential encoding is used so that a sector
error in transmission will have no effect after 2 bauds.
~perations ~lock ~0 ;Ichicvcs:
Q + L(M-1)/6¦ de-termining a~ number corresponding
to the l)osition of the signal point
in the sector (wllere Q is the
integral part of the quotient
(M-1)/~))
R + tM-l) mod fi - determining the sector number
- 16 -
~z~
P + (P~R) mod 6 - where P is the sector number
from the previous baud
and MD ~ QX6tP~ giving a uniclue designation of
the message point.
In fact, of the operations designated in box 40 a
look up table is used to obtain the values QX6+1 and ~. P (where
0 < P < 6) is the sector number from the previous baud, allowing
the calculation P + (P~R) mod 6.
It will be noted that, due to the differential
encoding techniques used the sector locations of the message
points are signalled as transitions from one sector to the
next, for reconversion to locations at the receiver. In
general reference in the application and claims herein such
~` signalling of transitions is considered as a signalling of
locations since this is the information ultimately conveyed.
Accordingly, the number MD from block 40 (or
; Ms=0 from 36) is applied to look up table 38 to produce the X~M),
Y(M) being the coordinates of the differcntially encoded
message points for transmission. The X~r~l), Y~M) coordinates
define message points which correspond to the intended 60
symmetry and spatial clistribution. Illat is X~M), Y~M) for
P=0 will have counterpart points in the same relative position
within the sector for P=l, 2J3J4 or 5 and the outer points in
a sector will correspond to higher values of M.
The message points X~M), Y~M) may be converted to
analogue values and moclulatecl Oll a carrier in thc manner of
; the DSB-QCM systems shown in Canadian Patent 985J376 and U.S.
Patent 3,955,141 here-tofore referrcd to. However, it is
- 17 -
21~3
. ~
preferred, in the signal processor o~ the preferred embodiment
to calculate the values for the mocllllatecl 'in phase' and
'quadrature phase' carriers and convert the result in digital-
to-analogue converter 17 for transmission on the communications
link.
It will be notecl that all operations and decisions
depicted in Figure 6 may equally be performed by hardware.
However, cost and space limitations at this time suggest the
programming shown as the best mode.
Transmission on the transmission or communications
link takes place to the receiver shown in Figure 7.
It is now proposed to discuss the receiver in accord
with the invention. Before doing this it is noted that (excluding
the reference to the inventive message point distribution), it
is well known to provide receivers to convert message point
coordinates modulated on a QCM channel to provide the encoded
binary information from the transmitted coordinates. This is
evidenced by the receiver designs disclosed in U.S. Paten~
3,955,141 and Canadian Patent 985,356.
~20 It is proposed to discuss the receiver o~ this
invention operating with the novel message point arrangement
here proposed.
rn ~igure 7 signals receivecl along che communications
channel at interface 110 are sllppliecl to A/D converter 114 for
conversion to dlgital signals. These digital signals are
s~pplied to high speed signal processor 116 w}lere the signals
are treated to provide demodulation, equalization etc~, in accord
with well known techniques. Although it is within the scope of
- 18 -
~ ~ ~t~ ~
the invention for signc~ roce~sor llG to provide signals
of the encoded Cartesian coordinates for later conveIsion into
binary data, in this invention it is found preferable, because
of the triangular grid distril)ution of thc message points, to
provide zones (referred to as RGB coordinates in Figure 7) in
triangular coordinates to a microproccssor 118 for dctcction as
to the value of the n bit bauds or group transmitted. The
values of the n bit bauds or groups transmitted are then
converted from parallel to serial form in converter 120. The
]0 microprocessor 11~, as hereinafter explained, also extracts the
auxiliary channel data as part of its operation.
In thc higi~ speed sign.ll proccssor 116 demodulation,
equalization and conditioning are performed in a manner well
known to those skilled in the art.
The high speed signal processor 116 might have been
designed in accord with conventional techniques, as in the
apparatus in the Canadian and U.S. patents referred to, to
convert the quadrature code signals into Cartesian values. However
the signal processor, in accord with the invention is designed
to convert by a si~ple conversion formula Cartesian coordinates
into coordinates at 0, 60 and 120 clockwise from the Y axis
(called Red, Blue, Green, respectively) with each coordinate
reprcsenting a zone bcing the area bctwccn adjaccnt triangular
grid lines perpendicular to the respective Red, Blue or Green
axes. Figure 9 shows the decision areasl defined by the
dccision hound.lry lincs, corrosl~onding to thc mcssagc points
oP Figure ~c. A result from the high speed signal processor 116
that the coordinates received defined in the areas corresponding
- 19 -
~21~2~3
to zones Red 0, Green 0 and Blue 1 is indicated on Figure 9
as the shaded triangle of Figure 9 and one which the decision
apparatus (in the microprocessor) will decide is message point
1. It will also be noted that since it is zones rather than
lines which are defined, only the integral part of the con-
verted Red, Green, Blue values need be transmitted to the micro-
processor. It will further be noted that once any two of ~he
zones are defined - here Red 0 and Green 0 - the only remaining
ambiguity is between the two triangles comprising the rhombus
defined by the red and green zones so that the Blue information
may be confined to whether it is even or odd. This Red -
Blue - Green information is provided to the microprocessor.
The information provided to the microprocessor
as lndicated in box 122 of Figure 8 is (Red Zone No. + C3) X-;
(C3 = 6 in the version using the message points of Figure 4c)
Green Zone No. + C3 and Blue Zone No. mod 2 (i.e. whether blue
is even or odd).
The result is comhined in box 124 to provide the
numher I which, in the microprocessor may be used in a look
up table to get the message point value M. For M=0, tlle
number is supplied directly to the unscrambler For M ~ 0
box 128 performs the operations indicated to perform the
differential de-encoding. The decodcd MJ correspondin~ to Ms
or Ma at the transmitter, is applied to decision box 130. For
M < Cl ~here Cl = 12) no auxiliary data is signalled and the Ms
- 20 -
~2~2~
value is supplied to the unscrambler 140. For M > Cl the
decision is macle at 132 whether M ~ (4 ~here 15). If M < C4
then a binary 1 is sent to the au~iliary binary data inter-
face (or channel) inclicated at 138. If M > C4 then a binary 0
is sent to the auxiliary binary data interface or channel and
M is reduced by C2. On either decision at block 132 the value
Ms or Ma is supplied to the unscrambler 140 to provide the
value M for the parallel to serial converter 120. The
unscrambler 140 of course reverses the scrambling performed at
the scrambler 22 of the transmitter so that the original
information is recovered.
As previously stated the table previously set out
For 4-7 bits/baud covers the values of M, K rmessage point~, Cl,
C2, C3 and C4.
It will be noted that although the drawings show
a single transmitter at one end of a transmission link and a
single receiver at the other, that in fact each end of the lin~
will customarily include a transmittcr and receiver in the
form of a MO~EM for two way transmission. Thus the high speed
~20 processor at the transmitter will typically be the same one acting,
at the same end as the high specd proccssor of the receiver.
It will be noted that the paired message points
~thosc shown in outline only) For thc altcrn;ltivcs in ligures
4e ancl ~i do not themsclves displ.ly 60 symmctry ~although the
collection of points as a whole does). Ilowever, this lack of
60 symmetry in the paired points does not affect the 60 symmetry
so far as transmission is concerned bcc.luse of the effect of the
differential encoding.
~ I _
~2C~
The specific embodiment deals with the use of the
excess K-2 points for signalling or providing an auxiliary
channel. As stated earlier the poir.ts may be used for other
purposes, for example merely to achieve lower frequency use of
outer message points requiring higl-er signalling power. Statisti-
cally even distribution is achieved to approximate symmetry and
elimination of carrier because of the differential encoding.
The examples in Figures 4a, c, e, g, i, show
message point distributions on a regular triangular grid having
symmetry.
The examples in ligures 4b, cl, f, h, j, show
message point distributions on a regular triangular grid having
120 symmetry. Although such symmetry may not be as advantageous
as 60 symmetry it does provicle the advantages of the invention
accuring from the superiority of use of points on a triangular
grid and the provision of K>2 points.
These message points distributed as illustrated in
Pigures 4b, 4d, 4f, 4h, 4j, show clistributions having only 120
symmetry and no point at the origin but having the advantages
discussed for signals representing the coordinates on an equilateral
triangular grid for K>2 . On the ligures last listed M=2n is set
Ollt as well as K.
It will be appreciated that it is wcll within the
abilities of those skilled in the art to convert binary signals
in groups of n into the coorclinates of the message points
illustrated in Figures 4b, 4d, 4f, 4h, 4j; and at the receiver
to convert them back to the hinary cligits encoded all in accord
with the techniques cliscussecl herein.
- 22 -
These distributions differ in that special
consideration of the point of ori~in may be omitted and that
there are only three sectors in ~lace of six and therefore
~dulo three calculations should replace the modulo six
calculations.
. 23 -
