Multilevel modulator comprising a compact error correcting code producing unit

In a multilevel modulator for use in modulating an input digital signal of N levels into a multilevel modulated signal, the input digital signal is converted by a code converting unit into a major converted signal for the input digital signal and a minor converted signal corresponding to the major converted signal. The major converted signal is rearranged into groups each of which consists of a predetermined number of levels smaller than N and which is produced in a time division fashion together with with minor converted signal. A signal producing unit processes each group to produce a Lee-error correcting code sequence. Alternatively, major and minor converted signals are produced on quadrature-phase amplitude modulation of a circular signal arrangement of N-levels to divide the circular signal arrangement into a square signal arrangement and the remaining signal arrangement. In a counterpart multilevel demodulator, an inverse operation is carried out to reproduce the input digital signal.

BACKGROUND OF THE INVENTION 
This invention relates to a multilevel modulator which has an error 
correcting code producing unit and to a multilevel demodulator for use as 
a counterpart of the modulator. 
For the multilevel modulator of the type described, it is desirable that a 
modulating signal have an increased number of levels. This is because the 
increased number of levels makes it possible to effectively utilize a 
carrier level. Therefore, a large-capacity digital radio communication 
network ordinarily comprises the multilevel modulator. In such a digital 
radio communication network, a transmission error, namely, a code error, 
of transmission information is reduced by an error correcting system which 
makes use of an error correcting code. As the error correcting code, a 
Lee-error correcting code is well known in the art. The error correcting 
system is exemplified in an article contributed by Katsuhiro Nakamura of 
NEC Corporation, namely, the present assignee, to ICC Conference Record, 
Vol. 4-3 (June 1979), pages 45.4.1 to 45.4.5, under the title of "A Class 
of Error Correcting Codes for DPSK Channels." 
With an increase in the modulating signal levels, the error correcting code 
requires an increased number of bits. Accordingly, the error correcting 
code producing unit must carry out a large amount of logical operation on 
producing the error correcting code. As a result, the error correcting 
code producing unit becomes bulky and expensive. This applies to the 
multilevel demodulator. 
SUMMARY OF THE INVENTION 
It is therefore an object of this invention to provide a multilevel 
modulator which comprises a compact error correcting code producing unit. 
It is another object of this invention to provide a multilevel modulator 
which is suitable for high-speed operation. 
It is a still further object of this invention to provide a multilevel 
demodulator for use as a counterpart of the multilevel modulator of the 
type described. 
A multilevel modulator to which this invention is applicable, is for 
modulating a carrier signal into a multilevel modulated signal in response 
to an input digital signal having a plurality of levels. According to an 
aspect of this invention, the multilevel modulator comprises code 
converting means for converting the input digital signal into a major 
converted signal and a minor converted signal. The major converted signal 
has rearranged groups each of which consists of a first predetermined 
number of levels. The minor converted signal has a second predetermined 
number of levels related to the respective groups. The multilevel 
modulator further comprises signal producing means responsive to the major 
converted signal for producing a Lee-error correcting code sequence, 
multiplexing means for multiplexing the error correcting code sequence and 
the major converted signal into a major multiplexed signal and the error 
correcting code sequence and the minor converted signal into a minor 
multiplexed signal, and modulating means for modulating the carrier signal 
by the major and the minor multiplexed signals into the multilevel 
modulated signal. 
A multilevel demodulator to which this invention is applicable, is for 
demodulating a multilevel modulated signal into which a modulator carrier 
signal is modulated by a modulating signal which is converted from an 
input digital signal and which comprises an error correcting code 
sequence. According to another aspect of this invention, the demodulator 
comprises demodulating means responsive to a local carrier signal for 
demodulating the multilevel modulated signal into a major demodulated 
signal and a minor demodulated signal. The major demodulated signal has 
rearranged groups, each of which consists of a first predetermined number 
of levels. The minor demodulated signal has a second predetermined number 
of levels related to the respective groups. The demodulator further 
comprises signal producing means responsive to the major demodulated 
signal for producing an error correcting signal, error correcting means 
for correcting the major demodulated signal and the minor demodulated 
signal with reference to the error correcting signal to produce a major 
correction result signal and a minor correction result signal, 
respectively, and code converting means for converting the major 
correction result signal and the minor correction result signal into a 
reproduction of the input digital signal.

DESCRIPTION OF THE PREFERRED EMBODIMENTS 
Referring to FIG. 1, a multilevel modulator according to a first embodiment 
of this invention is for use in modulating an input digital signal S.sub.1 
into a multilevel modulated signal S.sub.2. The multilevel modulator 
comprises a code converting unit 15 supplied with the input digital signal 
S.sub.1. The input digital signal S.sub.1 is capable of representing at 
most N levels where N is represented by (i.2.sup.n +m) where, in turn, n 
is an integer which is not smaller than two, m and i are integers which 
satisfy 0.ltoreq.m.ltoreq.2.sup.n and (m+i).gtoreq.2, respectively. The 
code converting unit 15 is for converting the input digital signal S.sub.1 
to a major converted signal S.sub.10 of 2.sup.n levels and a minor 
converted signal S.sub.20 which has (i+k) levels where k is equal to zero 
and one when m is equal to zero and is greater than zero, respectively. 
When the input digital signal S.sub.1 is a four-bit binary digital signal, 
it is capable of representing at most sixteen levels (=2.sup.4). The code 
converting unit 15 converts the input digital signal S.sub.1 to the major 
converted signal S.sub.10 of eight levels (=2.sup.3) and the minor 
converted signal S.sub.20 of two levels (=2.sup.1). In other words, the 
code converting unit 15 rearranges the levels of the input digital signal 
S.sub.1 as will later be described in detail. It is understood under the 
circumstances that n, m, i, and k are equal to three, zero, two, and zero, 
respectively. 
The major converted signal S.sub.10 is divided into two parts one of which 
is delivered to a multiplexer 16. The other part is supplied to a signal 
producing unit 17. Responsive to the major converted signal S.sub.10, the 
signal producing unit 17 produces a single Lee-error correcting code 
sequence S.sub.3 in the manner described in the conference record cited 
hereinabove. The multiplexer 16 multiplexes the error correcting signal 
S.sub.3 and the major converted signal S.sub.10 into a major multiplexed 
signal S.sub.11 and the error correcting signal S.sub.3 and the minor 
converted signals S.sub.20 into a minor multiplexed signal S.sub.21. 
A multilevel modulating unit 18 has a code converting function which is 
complementary to the code conversion of the code converting unit 15. 
Accordingly, the modulating unit 18 converts the major multiplexed signal 
S.sub.11 and the minor multiplexed signal S.sub.21 to a multilevel signal 
having sixteen levels. Furthermore, the modulating unit 18 modulates a 
carrier signal C.sub.1 by the multilevel signal and produces the 
multilevel modulated signal S.sub.2 of sixteen levels. The multilevel 
modulated signal S.sub.2 is transmitted to a multilevel demodulator 
through a transmission medium. 
Referring to FIG. 2, description will be made as regards the code 
conversion in the code converting unit 15. In the manner exemplified 
above, it will be assumed that the input digital signal S.sub.1 is capable 
of having one of zeroth through fifteenth levels 0 to 15. The major and 
the minor converted signals have zeroth through seventh levels 0 to 7 and 
zeroth and first levels 0 and 1, respectively. 
The code converting unit 15 converts the zeroth to the third levels 0 to 3 
and the twelfth to the fifteenth levels 12 to 15 of the input digital 
signal S.sub.1 into the major converted signal S.sub.10 of the fourth to 
the seventh levels 4 to 7 and the zeroth to the third levels 0 to 3, 
respectively. The code converting unit 15 further converts the fourth to 
the eleventh levels 4 to 11 of the input digital signal S.sub.1 into the 
major converted signal S.sub.10 of the zeroth to the seventh levels 0 to 
7. In other words, the input digital signal S.sub.1 of sixteen levels 0 to 
15 is rearranged in the major converted signal S.sub.10 by the code 
converting unit 15 into first and second groups, each of which consists of 
eight levels 0 to 7. Alternatively, the code converting unit 15 may 
convert the zeroth to the seventh levels 0 to 7 of the input digital 
signal S.sub.1 into the major converted signal S.sub.10 of the zeroth to 
the seventh levels 0 to 7 and the eighth to the fifteenth levels 8 to 15 
also to the major converted signal S.sub.10 of the zeroth through the 
seventh levels 0 to 7. 
As shown in FIG. 2, the first group serves to specify eight levels 
consisting of zeroth through third levels and twelfth through fifteenth 
levels while the second group serves to specify eight levels consisting of 
fifth through eleventh levels. In the example being illustrated, (i+k) is 
equal to two as mentioned before and can determine the number of groups of 
the major converted signal S.sub.10. Accordingly, the major converted 
signal S.sub.10 exemplified in FIG. 1 is rearranged into two groups. 
The minor converted signal S.sub.20 has two levels in correspondence to the 
two groups of the major converted signal S.sub.10. The code converting 
unit 15 produces the minor converted signal S.sub.20 of the zeroth level 
"0" together with the major converted signal S.sub.10 when the input 
digital signal S.sub.1 takes one of the fourth to the eleventh levels 4 to 
11. The code converting unit 15 produces the minor converted signal 
S.sub.20 of the first level "1" when the input digital signal S.sub.1 
takes one of the zeroth to the third levels 0 to 3 and the twelfth to the 
fifteenth levels 12 to 15. Thus, the input digital signal S.sub.1 of 
sixteen levels is converted into the major converted signal S.sub.10 of 
eight levels and the minor converted signal S.sub.20 which has two levels. 
Referring back to FIG. 1, the signal producing unit 17 carries out a 
predetermined operation on the major converted signal S.sub.10. The 
predetermined operation is for producing the single Lee-error correcting 
code sequence S.sub.3. The exemplified single Lee-error correcting code 
sequence is suitable for correcting a single Lee-error such that a change 
of either "+1" or "-1" takes place in a data signal of eight levels. Such 
a change of either "+1" or "-1" can be corrected by adding either "-1" or 
"+1" modulo 8 to the data signal. This is similar to a double Lee-error 
correcting code sequence, if the signal producing unit 17 produces the 
double Lee-error correcting code sequence. In this event, such a double 
Lee-error can be corrected by adding either "+2" or "-2" modulo 8 to the 
data signal. 
Code correction of the single and the double Lee-error correcting code 
sequences is described in the conference record cited before and has no 
direct concern with the present invention. Therefore, no description will 
be made as regards the Lee-error correcting code sequence and the signal 
producing unit 17 any longer. 
It may, however, be pointed out that the signal producing unit 17 processes 
the major converted signal S.sub.10 of eight levels rather than directly 
the input digital signals S.sub.1 of sixteen levels. Therefore, the signal 
producing unit 17 is operable with a reduced amount of logical operation. 
The signal producing unit 17 is compact and can carry out the logical 
operation at high speed. 
Referring to FIG. 3, a multilevel demodulator is for use as a counterpart 
of the multilevel modulator illustrated with reference to FIG. 1. The 
multilevel demodulator is supplied as a demodulator input signal with a 
multilevel modulated signal which is identical with that illustrated in 
FIG. 1 as long as no transmission or code error takes place and which is 
indicated at S.sub.2 '. Responsive to the multilevel modulated signal 
S.sub.2 ' and a local carrier signal C.sub.2, a demodulating unit 21 
carries out multilevel demodulation of the multilevel modulated signal 
S.sub.2 ' and code conversion which is complementary to the code 
conversion in the modulating unit 18 (FIG. 1). As a result, the 
demodulating unit 21 delivers a major demodulated signal S.sub.11 ' and a 
minor demodulated signal S.sub.21 ' to an error correcting unit 22. If the 
multilevel modulated signal S.sub.2 ' is free from the transmission error, 
the major demodulated signal S.sub.11 ' and the minor demodulated signal 
S.sub.21 ' are reproductions of the major multiplexed signal S.sub.11 and 
the minor multiplexed signal S.sub.21, respectively. 
The major demodulated signal S.sub.11 ' is divided into two parts, one of 
which is supplied to the error correcting unit 22. The other part is fed 
to a signal producing unit 23. The signal producing unit 23 successively 
deals with each major demodulated signal S.sub.11 ' as the data signal of 
eight levels ("0" to "7") to detect the single Lee-error. The signal 
producing unit 23 thereby produces an error correcting signal S.sub.4 on 
detection of the single Lee-error. The error correcting signal S.sub.4 
takes either "+1" or "-1" at a position of the major demodulated signal 
S.sub.11 ' at which such a single Lee-error occurs. The signal producing 
unit 23 is also described in detail in the above-referenced conference 
record and will not be described any longer. 
The illustrated error correcting unit 22 corrects at least the single 
Lee-error of the major demodulated signal S.sub.11 ' and the minor 
demodulated signal S.sub.21 ' with reference to the error correcting 
signal S.sub.4 as will later be described in detail. The error correcting 
unit 22 produces a major correction result signal S.sub.10 ' and a minor 
correction result signal S.sub.20 '. If the major demodulated signal 
S.sub.11 ' is free from the code error, the error correcting unit 22 
produces the major demodulated signal S.sub.11 ' and the minor demodulated 
signal S.sub.21 ' as they stand. Otherwise, the error correcting unit 22 
produces error corrected signals. At any rate, the error correcting unit 
22 sends major and minor correction result signals S.sub.10 ' and S.sub.20 
' to a code converting unit 24. 
The code converting unit 24 carries out code conversion complementary to 
the code conversion of the code converting unit 15 (FIG. 1) and converts 
the major correction result signal S.sub.10 ' and the minor correction 
result signal S.sub.20 ' to produce an output digital signal S.sub.1 ' of 
sixteen levels as a reproduction of the input digital signal S.sub.1 (FIG. 
1). 
Referring to FIG. 4, description will be made as regards the error 
correction in the error correcting unit 22. The major demodulated signal 
S.sub.11 ' has two rearranged groups, each of which specifies eight 
levels. The minor demodulated signal S.sub.21 ' has two levels in 
correspondence to the two groups of the major demodulated signal S.sub.11 
'. The error correcting unit 22, for example, converts the major 
demodulated signal S.sub.11 ' of the fourth level 4 to the major 
correction result signal S.sub.10 ' of the fifth level 5 when the error 
correcting unit 22 is supplied with the error correcting signal S.sub.4 of 
"+1." Generally speaking, the error correcting unit 22 produces the major 
correction result signal S.sub.10 ' of a level which is equal to one plus 
the level of the major demodulated signal S.sub.11 ' even when the error 
correcting unit 22 is supplied with the error correcting signal S.sub.4 of 
"+1." To the contrary, the error correcting unit 22 produces the major 
correction result signal S.sub.10 ' of another level which is equal to the 
level of the major demodulated signal S.sub.11 ' minus one whenever the 
error correcting unit 22 is supplied with the error correcting signal 
S.sub.4 of "-1." In this manner, the error correcting unit 22 corrects the 
single Lee-error of the major demodulated signal S.sub.11 ' and the minor 
demodulated signal S.sub.21 ' as shown in FIG. 4. If the multilevel 
modulation is carried out either by amplitude modulation or frequency 
modulation, specific levels of the major and the minor demodulated signals 
S.sub.11 ' and S.sub.21 ' are excepted from the error correction. Each of 
the specific level is enclosed with parentheses in FIG. 4. 
With regard to the minor demodulated signal S.sub.21 ', the error 
correcting unit 22 inverts the levels of the first minor demodulated 
signal S.sub.21 ' on error correcting the seventh level of the major 
demodulated signal S.sub.11 ' whenever the error correcting unit 22 is 
supplied with the error correcting signal S.sub.4 of "+1." The error 
correcting unit 22 further inverts the levels of the minor demodulated 
signal S.sub.21 ' on error correcting the zeroth level of the major 
demodulated signal S.sub.11 ' whenever the error correcting unit 22 is 
supplied with the error correcting signal S.sub.4 of "-1." 
In the meanwhile, the signal producing unit 23 does not discriminate the 
two rearranged groups of the major demodulated signal S.sub.11 '. This 
might bring about occurrence of any error such that the minor muItiplexed 
signal S.sub.21 alone is erroneously demodulated into the minor 
demodulated signal S.sub.21 ' despite the fact that the major multiplexed 
signal S.sub.11 is correctly reproduced into the major demodulated signal 
S.sub.11 '. But, such a code error occurs in a very low probability so far 
as the Lee-error correcting code sequence is used as the multilevel 
modulated signal. Therefore, the above-exemplified code error can be 
disregarded. 
From this fact, it is seen that the signal producing unit 23 may logically 
process the major demodulated signal S.sub.11 ' of eight levels. Such 
logical processing may need only three (=log.sub.2 8) logical steps which 
are reduced in number in comparison with four (=log.sub.2 16) logical 
steps necessary for processing the multilevel modulated signal S.sub.2 ' 
of sixteen levels. Accordingly, the signal producing unit 23 may be small 
in size and can carry out logical operation at high speed. 
Referring to FIG. 5, a modulator according to a second embodiment of this 
invention is for use in a sixteen-level quadrature-phase amplitude 
modulation. The modulator modulates a first input digital signal SP.sub.1 
of a channel P and a second input digital signal SQ.sub.1 of another 
channel Q into a quadrature-phase amplitude modulated signal QAM. 
The modulator comprises a code converting unit 31 supplied with the first 
and the second input digital signals SP.sub.1 and SQ.sub.1. Each of the 
first and the second input digital signals SP.sub.1 and SQ.sub.1 is 
capable of representing at most N levels where N is equal to 2.sup.x 
where, in turn, x is an integer which is not less than four. The code 
converting unit 31 is for converting the first input digital signal 
SP.sub.1 to first major and first minor converted signals SP.sub.10 and 
SP.sub.20 and the second input digital signal SQ.sub.1 to second major and 
second minor converted signals SQ.sub.10 and SQ.sub.20, respectively. Each 
of the first and the second major converted signals SP.sub.10 and 
SQ.sub.10 has 2.sup.x levels. Each of the first and the second minor 
converted signals SP.sub.20 and SQ.sub.20 has 2 y levels where y 
represents a positive integer. 
Each of the first and the second input digital signals SP.sub.1 and 
SQ.sub.1 may be a four-bit binary digital signal and capable of 
representing at most sixteen levels (=2.sup.4). Accordingly, each of the 
first and the second major converted signals SP.sub.10 and SQ.sub.10 has 
sixteen levels (=2.sup.4). On the other hand, each of the first and the 
second minor converted signals SP.sub.20 and SQ.sub.20 has two levels 
(=2.sup.1). Under the circumstances, a combination of the first and the 
second input digital signals SP.sub.1 and SQ.sub.1 can represent 256 
different values. The 256 different values are produced as the 
quadrature-phase amplitude modulated signal QAM. 
Referring to FIG. 6, the 256 different values are depicted as 256 signal 
points on a phase plane of the quadrature-phase amplitude modulated signal 
QAM. When distributed on the phase plane in a usual manner, the 256 signal 
points form a square on the phase plane. 
Turning to FIG. 7, the code converting unit 31 (FIG. 5) is for arranging 
the 256 signal points into a nearly circular shape on the phase plane. In 
order to derive the nearly circular signal arrangement, twenty-four signal 
points in first to fourth corners A.sub.1 to A.sub.4 (FIG. 6) of the 
square are displaced to four sides of the square in the manner which will 
be described in the following. 
Comparison of FIGS. 5 and 7 will show that the first input digital signal 
SP.sub.1 is rearranged in the first major converted signal SP.sub.10 by 
the code converting unit 31 into a first and a second rearranged group. 
The first rearranged group consists of zeroth to fifteenth levels 0 to 15. 
The second rearranged group consists of zeroth level 0 and fifteenth level 
15. Similarly, the second input digital signal SQ.sub.1 is rearranged in 
the second major converted signal SQ.sub.10 into two groups which will 
again be called a first and a second rearranged group. The first 
rearranged group consists of zeroth to fifteenth levels 0 to 15. The 
second rearranged group consists of zeroth level 0 and fifteenth level 15. 
Such code conversion is exemplified in U.S. patent application Ser. No. 
779,217 filed Sept. 23, 1985 by Junichi Uchibori et al for assignment to 
NEC Corporation and have no direct concern with the present invention. 
Therefore, no description will be made about the code converting unit 31 
any longer. 
In FIG. 5, the first major converted signal SP.sub.10 is divided into two 
parts one of which is delivered to a first multiplexer 32p. The other part 
is supplied to a first signal producing unit 33p. Responsive to the first 
major converted signal SP.sub.10, the first signal producing unit 33p 
produces a first single Lee-error correcting code sequence SP.sub.2 in the 
manner described in connection with the signal producing unit 17 (FIG. 1). 
The first multiplexer 32p multiplexes the first single Lee-error 
correcting code sequence SP.sub.2 and the first major converted signal 
SP.sub.10 into a first major multiplexed signal SP.sub.11 and the first 
single Lee-error correcting code sequence SP.sub.2 and the first minor 
converted signal SP.sub.20 into a first minor multiplexed signal 
SP.sub.21. 
Similarly, a second multiplexer 32q is supplied with the second major 
converted signal SQ.sub.10 and a second single Lee-error correcting code 
sequence SQ.sub.2 which is produced by a signal producing unit 33q in 
response to the second major converted signal SQ.sub.10. The second 
multiplexer 32q multiplexes the second single Lee-error correcting signal 
SQ.sub.2 and the second major converted signal SQ.sub.10 into a second 
major multiplexed signal SQ.sub.11 and the second single Lee-error 
correcting signal SQ.sub.2 and the second minor converted signal SQ.sub.20 
into a second minor multiplexed signal SQ.sub.21. 
Responsive to the first major and the first minor multiplexed signals 
SP.sub.11 and SP.sub.21 and the second major and the second minor 
multiplexed signals SQ.sub.11 and SQ.sub.21, a multilevel modulating unit 
34 modulates a pair of quadrature-phase carrier signals C.sub.3 into the 
multilevel quadrature-phase amplitude modulated signal QAM. The multilevel 
quadrature-phase amplitude modulated signal QAM is transmitted to a 
multilevel quadrature-phase amplitude demodulator through a transmission 
medium. It is readily understood that the first and the second signal 
producing units 33p and 33q may produce a double Lee-error correcting code 
sequence as described in FIG. 1. 
As mentioned above, the first major converted signal SP.sub.10 is divided 
into the first group of sixteen levels and the second group of two levels 
placed outside of the sixteen levels and is subjected to error correction 
by the use of the first signal producing unit 33p for carrying out a 
logical operation of the sixteen levels. This is because the Lee-error 
correcting code sequence is used as the first major converted signal 
SP.sub.10. 
A conventional thought is that an error correcting code producing unit for 
thirty-two levels is indispensable for correcting such a first major 
converted signal of eighteen levels. From this fact, it is readily 
understood that the first signal producing unit 33p is small in size and 
operable at a high speed in comparison with the conventional error 
correcting code producing unit. 
This applies to the second signal producing unit 33q, although the 
above-mentioned description is restricted to the first signal producing 
unit 33p. 
Referring to FIG. 8, a multilevel quadrature-phase amplitude demodulator is 
for use as a counterpart of the sixteen-level quadrature-phase amplitude 
modulator illustrated with reference to FIG. 5. The demodulator is for 
demodulating the multilevel modulated signal illustrated with reference to 
FIG. 7. The demodulator comprises a multilevel demodulating unit 41 
supplied with the multilevel quadrature-phase amplitude modulated signal 
indicated at QAM'. Responsive to a pair of quadrature-phase local carrier 
signals C.sub.4, the demodulating unit 41 demodulates the multilevel 
quadrature-phase amplitude modulated signal QAM' into first major and 
first minor demodulated signals SP.sub.11 ' and SP.sub.21 ' of the channel 
P and second major and second minor demodulated signals SQ.sub.11 ' and 
SQ.sub.21 ' of the other channel Q. The first major demodulated signal 
SP.sub.11 ' is divided into two parts, one of which is delivered to a 
first error correcting unit 42p. The other part is supplied to a first 
signal producing unit 43p. Responsive to the first major demodulated 
signal SP.sub.11 ', the first signal producing unit 43p produces a first 
error correcting signal SP.sub.3 on detection of the single Lee-error in 
the manner described in conjunction with the signal producing unit 23 
(FIG. 3). 
The second major demodulated signal SQ.sub.11 ' is divided into two parts, 
one of which is delivered to a second error correcting unit 42q. The other 
part is supplied to a second signal producing unit 43q. Responsive to the 
second major demodulated signal SQ.sub.11 ', the second signal producing 
unit 43q produces a second error correcting signal SQ.sub.3 on detection 
of the single Lee-error. 
The first error correcting unit 42p corrects the single Lee-error of the 
first major demodulated signal SP.sub.11 ' and the first minor demodulated 
signal SP.sub.21 ' with reference to the first error correcting signal 
SP.sub.3 as will later be described in detail. The first error correcting 
unit 42p produces a first major correction result signal SP.sub.10 ' and a 
first minor correction result signal SP.sub.20 ' to a code converting unit 
44. On the other hand, the second error correcting unit 42q produces a 
first major correction result signal SQ.sub.10 ' and a second minor 
correction result signal SQ.sub.20 ' to the code converting unit 44. 
The code converting unit 44 carries out code conversion which is 
complementary to the code conversion of the code converting unit 31 (FIG. 
5). The code converting unit 44 converts the first major correction result 
signal S.sub.10 ' and the first minor correction result signal S.sub.20 ' 
to produce a first output digital signal SP.sub.1 ' of sixteen levels as a 
reproduction of the first input digital signal SP.sub.1 (FIG. 5). The code 
converting unit 44 further converts the second major correction result 
signal SQ.sub.10 ' and the second minor correction result signal SQ.sub.20 
' to produce a second output digital signal SQ.sub.1 ' of sixteen levels 
as a reproduction of the second input digital signal SQ.sub.1 (FIG. 5). 
Referring to FIG. 9, description will be made as regards the error 
correction in the first error correcting unit 42p. Although restricted to 
the first error correcting unit 42p, the description applies to the second 
error correcting unit 42q. The first major demodulated signal SP.sub.11 ' 
has first and second rearranged groups. The first rearranged group 
consists of zeroth to fifteenth levels 0 to 15. The second rearranged 
group consists of zeroth level 0 and fifteenth level 15. The first error 
correcting unit 42p produces the first major correction result signal 
SP.sub.10 ' of a level which is equal to one plus the level of the first 
major demodulated signal SP.sub.11 ' whenever the first error correcting 
unit 42p is supplied with the first error correcting signal SP.sub.3 of 
"+1." To the contrary, the first error correcting unit 42p produces the 
first major correction result signal SP.sub.10 ' of another level which is 
equal to the level of the first major demodulated signal SP.sub. 11 ' 
minus one whenever the first error correcting unit 42p is supplied with 
the first error correcting signal SP.sub.3 of "+1." In this manner, the 
first error correcting unit 42p corrects the single Lee-error of the first 
major demodulated signal SP.sub.11 ' as shown in FIG. 9. With regard to 
the first minor demodulated signal SP.sub.21 ', the first error correcting 
unit 42p inverts the level of the first minor demodulated signal SP.sub.21 
' on error correcting the fifteenth level of the first major demodulated 
signal SP.sub.11 ' whenever the first error correcting unit 42p is 
supplied with the first error correcting signal SP.sub.3 of "+1.". The 
first error correcting unit 42p inverts the level of the first minor 
demodulated signal SP.sub.21 ' on error correcting the zeroth level of the 
first major demodulated signal SP.sub.11 ' whenever the first error 
correcting unit 42p is supplied with the first error correcting signal 
SP.sub.3 of "-1." 
In the meanwhile, the first signal producing unit 43p does not discriminate 
the two rearranged groups of the first major demodulated signal SP.sub.11 
'. This might bring about occurrence of any error such that the first 
minor multiplexed signal SP.sub.21 alone is erroneously demodulated into 
the minor demodulated signal SP.sub.21 ' despite the fact that the first 
major multiplexed signal SP.sub.11 is correctly reproduced into the first 
major demodulated signal SP.sub.11 '. But, such a code error can be 
disregarded for the reasons described in conjunction with FIGS. 3 and 4. 
As mentioned above, the first major demodulated signal SP.sub.11 ' is 
divided into the first rearranged group of sixteen levels and the second 
rearranged group of two levels placed outside of the sixteen levels. The 
first signal producing unit 43p carries out a logical operation for 
detecting the Lee-error of the first major demodulated signal SP.sub.11 ' 
of the sixteen levels. It is readily understood that the first signal 
producing unit 43p is small in size and operable at a high speed for the 
reasons described in connection with the first signal producing unit 33p 
illustrated in FIG. 5. This applies to the second signal producing unit 
43q. 
While this invention has thus far been described in conjunction with two 
preferred embodiments thereof, it will readily be possible for those 
skilled in the art to put this invention into practice in various other 
manners. For example, the number N may be 32 or 64. The major converted 
signal may be rearranged into three or more groups. The minor converted 
signal has three levels in correspondence to the respective groups when 
the major converted signal is rearranged into three groups.