Coded modulation with unequal error protection for fading channels

Information is transmitted in digital form over fading channels using DPSK coded modulation incorporating multi-level coding in order to provide unequal error protection for different classes of data such as generated by CELP or other speech encoders.

BACKGROUND OF THE INVENTION 
The present invention relates to the transmission of information in digital 
form over fading channels. 
The increasing prominence of wireless telecommunications--particularly in 
the realm of digital cellular mobile radio--has given rise to the demand 
for improvements in the bandwidth efficiency of such systems. To this end, 
efficient coded modulation schemes, such as the built-in time-diversity 
technique disclosed in U.S. Pat. No. 5,029,185, issued to L. F. Wei on 
Jul. 2, 1991 and entitled "Coded Modulation for Mobile Radio," have been 
developed. Increased bandwidth efficiency is also achieved in these 
systems via the use of low-bit-rate speech coders, such as the so-called 
code-excited linear predictive (CELP) coders, which operate in the range 
of about 4 to 8 kilobits per second (kbps). 
The low-bit-rate coders represent speech information in such a way that 
certain aspects of the coded information is of significantly greater 
importance than other aspects in terms of being able to recover 
intelligible speech at the receiver. In CELP coders, for example, that 
so-called "important information" may comprise a) the linear predictive 
coding (LPC) parameters, b) the pitch, and c) a bit of information which 
indicates whether the speech was voiced or unvoiced. It is thus desirable 
that the transmission scheme be able to communicate the "important 
information" with a high degree of reliability, even at the expense--if 
channel conditions make it necessary--of the other, "less important" 
information. Such transmission schemes are referred to herein generically 
as schemes which provide "unequal error protection." And it should also be 
noted at this point that, in general, there can be any desired number of 
classes of information, of varying importance, rather than being limited 
to, for example, two classes. 
Transmission schemes which provide unequal error protection are, in fact, 
known in the prior art. Such known technology is exemplified by, for 
example, in Carl-Erik Sundberg, "Optimum Weighted PCM for Speech Signals," 
IEEE Transactions on Communications, Vol. COM-26, No. 6, June 1978, pp. 
872-881; C.-E. W. Sundberg et al., "Logarithmic PCM weighted QAM 
transmission over Gaussian and Rayleigh fading channels," IEE Proceedings, 
Vol. 134, Pt. F, No. 6, October 1987, pp. 557-570; and in the commonly 
assigned co-pending patent applications of V. B. Lawrence et al., Ser. No. 
07/611,225 filed Nov. 7, 1990 (now U.S. Pat. No. 5,164,963, issued Nov. 
17, 1992) and entitled "Coding for Digital Transmission," and of L. F. 
Wei, Ser. No. 07/611,200 filed Nov. 7, 1990 (now U.S. Pat. No. 5,105,442, 
issued Apr. 14, 1992) and entitled "Coded Modulation with Unequal Error 
Protection." Wireless telecommunications of the type that the present 
invention is concerned with are typically carried out over so-called 
fading channels, by which is meant so-called Rayleigh or near-Rayleigh 
channels, where multiplicative Rayleigh noise is the predominant noise 
phenomenon. However, the prior art (for coded modulation) has generally 
addressed the unequal error protection problem in the context of 
transmission of the information over, for example, voiceband telephone 
channels and HDTV channels, where additive white Gaussian noise is the 
predominant noise phenomenon, and those schemes will not perform 
effectively if used for the fading environment. Moreover, although 
aforementioned coded modulation schemes as disclosed in the Wei patent 
application are, in fact, directed to fading channel applications, they 
provide equal error protection for the transmitted data rather than the 
unequal error protection that is so highly desirable for the 
aforementioned coded speech applications. It can also be noted that 
schemes which provide unequal error protection in conjunction with binary 
and quaternary phase shift keyed signals are known in the prior art. See 
"Rate-compatible punctured convolutional codes for digital mobile radio," 
by J. Hagenauer, N. Seshadri and C.-E. W. Sundberg in IEEE Transactions on 
Communications, Vol. 37, No. 7, July 1990. However, these schemes are 
limited to a maximum of two bits per symbol, irrespective of the 
signal-to-noise ratio (SNR) of the channel and are thus 
bandwidth-inefficient. Moreover, even when achieving two bits per symbol, 
these schemes are power-inefficient. 
There thus remains in the art the need for effective, bandwidth- and 
power-efficient transmission schemes which can provide unequal error 
protection in fading channel environments. 
SUMMARY OF THE INVENTION 
The present invention meets that need. In particular, in accordance with 
the principles of the invention, the information is coded using a 
multi-level channel code, by which is meant that a) each class of 
information is redundancy coded using a different, respective channel code 
and that b) the resulting multi-level-coded words select for transmission 
signal points of a predetermined signal constellation. In preferred 
embodiments, the minimum Hamming distance (defined below) for the code 
used for any particular class of information is greater than the minimum 
Hamming distance for the code used for any less important class of 
information. The error probability for channels characterized by Rayleigh 
fading assuming adequate interleaving (as described below), and coherent 
or differential coherent detection, at high SNR is, to a first, and 
typically adequate, approximation, proportional to the reciprocal of the 
signal-to-noise ratio (SNR) raised to the power of the minimum Hamming 
distance (assuming the use of, for example, a maximum likelihood decoding 
strategy). That is, for the i.sup.th class of data, class i, 
EQU P.sub.e (i).apprxeq..sub..gamma.i [1/SNR].sup.d.sbsp.Hi, 
where d.sub.Hi is the minimum Hamming distance, .sub..gamma.i is a 
proportionality constant and P.sub.e (i) is the probability of error upon 
decoding. Different levels of error protection are thus provided for the 
different classes of data. 
As is explained in detail hereinbelow, the proportionality constant 
.sub..gamma.i depends primarily on the ratio of a) the average number of 
nearest neighbors for the i.sup.th class of data to b) the product 
distance for that class. These parameters are determined by a) the channel 
codes and b) the signal constellation design, the latter including, for 
example, the constellation geometry, the labelling of the signal points 
and the manner in which the outputs of the channel codes map into the 
labels. Thus, in accordance with a feature of the invention, attainment of 
particular desired error probabilities for the various different data 
classes can be facilitated by appropriate joint selection of channel codes 
and signal constellation design. 
The prior art does disclose the use of multi-level codes in a fading 
channel environment, but only in the context of providing equal error 
protection. Exemplary is N. Seshadri and C.-E. W. Sundberg, "Multi-level 
codes with large time-diversity for the Rayleigh fading channel," 
Conference on Information Sciences and Systems, Princeton, N.J., pp. 
853-857, March 1990. Additionally, co-pending, commonly assigned U.S. 
patent application Ser. No. 07/785,723 filed Oct. 31, 1991 discloses the 
use of multi-level codes to provide unequal error protection, but not in 
the context of fading channels.

DETAILED DESCRIPTION 
Before proceeding with a description of the illustrative embodiments, it 
should be noted that various of the digital signaling concepts described 
herein are all well known in, for example, the digital radio and voiceband 
data transmission (modem) arts and thus need not be described in detail 
herein. These include such concepts as multidimensional signaling using 
2N-dimensional channel symbol constellations, where N is some integer, 
trellis coding; scrambling; passband shaping; equalization; Viterbi, or 
maximum-likelihood, decoding; etc. These concepts are described in such 
U.S. patents as U.S. Pat. No. 3,810,021, issued May 7, 1974 to I. Kalet et 
al; U.S. Pat. No. 4,015,222, issued Mar. 29, 1977 to J. Werner; U.S. Pat. 
No. 4,170,764, issued Oct. 9, 1979 to J. Salz et al; U.S. Pat. No. 
4,247,940, issued Jan. 27, 1981 to K. H. Mueller et al; U.S. Pat. No. 
4,304,962, issued Dec. 8, 1981 to R. D. Fracassi et al; U.S. Pat. No. 
4,457,004, issued Jun. 26, 1984 to A. Gersho et al; U.S. Pat. No. 
4,489,418, issued Dec. 18, 1984 to J. E. Mazo; U.S. Pat. No. 4,520,490, 
issued May 28, 1985 to L. Wei; and U.S. Pat. No. 4,597,090, issued Jun. 
24, 1986 to G. D. Forney, Jr.--all of which are hereby incorporated by 
reference. 
It may also be noted before proceeding that various signal leads shown in 
the FIGS. may carry analog signals, serial bits or parallel bits, as will 
be clear from the context. 
Turning now to FIG. 1, which illustratively depicts a digital cellular 
mobile radio terminal such as might be installed in an automobile, speech 
signal source 101 generates an analog speech signal representing speech 
information or "intelligence," which is passed on to speech encoder 104, 
illustratively a CELP coder of the type described above. The latter 
generates a digital signal comprised of a stream of data, or data 
elements, in which at least one subset of the data elements represents a 
portion of the information, or intelligence, that is more important than 
the portion of the information, or intelligence, represented by the rest 
of the data elements. Illustratively, each data element is a data bit, 
with an average K=k.sub.1 +k.sub.2 +k.sub.3 information bits being 
generated for each of a succession of M symbol intervals. The symbol 
intervals are comprised of N signaling intervals, where 2N is the number 
of dimensions of the constellation (as described below). The signaling 
intervals have duration of T seconds and, accordingly, the symbol 
intervals each have a duration of NT seconds. The embodiments explicitly 
disclosed herein happen to use two-dimensional constellations, i.e., N=1. 
For those embodiments, then, the signaling intervals and symbol intervals 
are the same. 
Of the aforementioned K information bits, the bits within the stream of 
k.sub.1 bits per M symbol intervals, appearing on lead 105, are more 
important than the k.sub.2 bits per M symbol intervals, appearing on lead 
106, and in turn these bits are more important than the k.sub.3 bits per M 
symbol intervals appearing on lead 107. The bits on these three leads are 
referred to herein as the class 1, and class 2 and class 3 bits, 
respectively. 
The bits on leads 105-107 are independently scrambled in scramblers 
110-112, which respectively output on leads 115-117 the same number of 
bits per M symbol intervals as appear on leads 105-107, respectively. (In 
particular specific embodiments, scrambling may not be required.) 
Scrambling is customarily carried out on a serial bit stream. Thus 
although not explicitly shown in FIG. 1, scramblers 110-112 may be assumed 
to perform a parallel-to-serial conversion on their respective input bits 
prior to scrambling and a serial-to-parallel conversion at their outputs. 
The signal is then channel encoded and mapped. In particular, the bits on 
leads 115-117 are extended to multi-level coder 120. As described in 
detail hereinbelow, the latter illustratively includes three channel 
encoders which respectively receive the bits on leads 115-117. These 
encoders generate, for each block of M symbol intervals, a block of M 
multibit (illustratively 3-bit), multi-level-coded, words. M is greater 
than (k.sub.1 +k.sub.2 +k.sub.3)/3 so that the multi-level encoder is a 
redundancy coder, i.e., more bits are output than are input. The 
multi-level code implemented by encoder 120 to generate the 
multi-level-coded words lead 121 has so-called built-in time-diversity. 
Those bits comprise a multi-level-coded word and their values jointly 
select, or identify, a particular channel symbol of a predetermined 
constellation of channel symbols (such as the constellation of FIG. 5 as 
described in detail hereinbelow). Complex plane coordinates of the 
identified channel symbols are output by constellation mapper 131, 
illustratively realized as a lookup table or as a straightforward 
combination of logic elements. The complex channel symbols are interleaved 
in standard fashion by an interleaver 141 in order to be able to take 
advantage of the built-in time-diversity of the multi-level code. Since 
such interleaving is standard, it suffices for present purposes simply to 
note that the function of the interleaver is to provide adequate 
time-separation between signal points which comprise a coded block to 
ensure that fading events associated with those signal points are, in 
general, independent. The output of interleaver 141 is applied to 
modulator 151 and the resultant analog signal is then broadcast via 
antenna 152 over a free space communication channel to a remote digital 
cellular mobile radio cell site. 
In order to understand the theoretical underpinnings of the invention, it 
will be useful at this point to digress to a consideration of FIG. 3. The 
latter depicts a standard two-dimensional data transmission constellation 
of the general type conventionally used in digital cellular mobile radio. 
In this standard scheme--conventionally referred to as differential phase 
shift keyed (DPSK) modulation--data words each comprised of two 
information bits are each mapped into one of four possible two-dimensional 
channel symbols. The phase angle of each signal point (measured from the 
positive X axis) indicates a change that the phase of the transmitted 
signal must undergo in order to transmit the bit pattern associated with 
that particular signal point. More particularly, so-called .pi./4-shifted 
DPSK, in which the entire constellation is rotated by 45 degrees in 
successive signaling intervals, can be used. (Non-differential (coherent) 
PSK, where each signal point represents the associated bit pattern 
directly, could alternatively be used in appropriate applications.) Each 
channel symbol has an in-phase, or I, coordinate on the horizontal axis 
and has a quadrature-phase, or Q, coordinate on the vertical axis. The 
signal points have equal amplitude--lying on a circle of radius 1--so 
that, on each axis, the channel symbol coordinates are 
##EQU1## 
Thus the distance between each symbol and each of the symbols that are 
nearest to it is the same for all symbols--that distance being .sqroot.2. 
As a result of this uniform spacing, essentially the same amount of noise 
immunity is provided for both information bits. 
We now define some useful terminology: "Hamming distance," "minimum Hamming 
distance," "number of nearest neighbors," and "product distance." In 
particular, the "Hamming distance" between any two distinct sequences of 
signal points selected from the constellation is the number of positions 
within the two sequences at which the signal points differ. The "minimum 
Hamming distance" is the minimum over all such Hamming distances, i.e., 
taking into account all possible pairs of sequences. Since we are assuming 
at this point an uncoded transmission scheme, all possible sequences of 
signal points are allowed. This being so, the minimum Hamming distance for 
an uncoded transmission scheme is "1". A code which has so-called built-in 
time-diversity has a minimum Hamming distance which is greater than "1", 
the measure of that time-diversity being, in fact, the minimum Hamming 
distance. The "product distance" is the product of all non-zero squared 
Euclidean distances between the corresponding signal points of the 
sequences that are at minimum Hamming distance from each other--known as 
the "nearest neighbor sequences." For the present case, the product 
distance is "2". The "number of nearest neighbors" is the average number 
of sequences that are at the minimum Hamming distance to any transmitted 
sequence with a product distance of 2 and, in this case, the "number of 
nearest neighbors" is "2". 
As is well known, it is possible to provide improved noise immunity without 
sacrificing bandwidth efficiency (information bits per signaling interval) 
using a coded modulation approach in which an "expanded" two-dimensional 
constellation having more than (in this example) four symbols is used in 
conjunction with a trellis or other channel code. For example, the 
above-cited U.S. Pat. No. 5,029,185 discloses the use of expanded PSK 
constellations in combination with trellis and block codes to provide 
enhanced noise immunity of more than 10 dB over the uncoded case of FIG. 3 
while providing approximately two bits per signaling interval. 
In the above-cited '185 patent as, indeed, in the case of FIG. 3 hereof, 
the same amount of noise immunity is provided for all information bits. 
Thus, as noted above, there remains in the art the need for effective, 
bandwidth- and power-efficient transmission schemes which can provide 
unequal error protection in fading channel environments--a need that is 
met by the present invention. 
In particular, in accordance with the principles of the invention, the 
information is coded using a multi-level channel code, by which is meant 
that a) each class of information is channel coded using a different, 
respective channel code and that b) the resulting coded outputs select for 
transmission signal points of a predetermined signal constellation. 
To this end, and referring to FIG. 4, there is shown an illustrative 
embodiment of multi-level--illustratively three-level--channel coder 120. 
As noted earlier, the three classes of data are received on leads 115-117, 
from most-to least-important. The bit streams for these three classes are 
denoted i.sub.1, i.sub.2 and i.sub.3 and are applied to respective channel 
encoders 40i, i=1, 2, 3, i.e., encoders 401, 402 and 403, which 
respectively implement redundancy codes C.sub.i, i=1, 2, 3, i.e., codes 
C.sub.1, C.sub.2 and C.sub.3. The output bit streams from the three 
channel encoders--which are buffered in buffers 411, 412 and 413, as 
described below--are denoted b.sub.1, b.sub.2 and b.sub.3 and appear on 
leads 122-124, respectively. The constituent elements of the output bit 
streams can be represented as follows, in which the superscripts denote 
time: 
EQU b.sub.3 =(b.sub.3.sup.1, b.sub.3.sup.2, . . . , b.sub.3.sup.M) 
EQU b.sub.2 =(b.sub.2.sup.1, b.sub.2.sup.2, . . . , b.sub.2.sup.M) 
EQU and b.sub.1 =(b.sub.1.sup.1, b.sub.2.sup.1, . . . , b.sub.1.sup.M). 
The multi-level encoder output is 
EQU b=(b.sup.1, b.sup.2, . . . , b.sup.M) 
EQU where 
EQU b.sup.j =4b.sub.3.sup.j +2b.sub.2.sup.j +b.sub.1.sup.j. 
The index b.sup.j then constitutes an address applied to constellation 
mapper 131 to select a particular signal point of an illustrative 8-PSK 
constellation which is shown in FIG. 5. Note, in particular, that each of 
the eight signal points of the constellation has an associated 
label--shown in both binary and, in parentheses, decimal form--which is 
used as the address. Various ways of assigning the signal point labels to 
achieve certain overall error probabilities for particular codes and 
particular constellations are discussed hereinbelow. 
The codes respectively implemented by encoders 40i, i=1, 2, 3, are codes 
which are characterized by the parameter set (M, k.sub.i and d.sub.Hi), 
i=1, 2, 3. Here, M, introduced above, is the block length of the code; 
k.sub.i, introduced above, is the number of information bits required to 
be applied to encoder 40i to generate the output block; and d.sub.Hi is 
the minimum Hamming distance (defined above) of code C.sub.i. The three 
codes are illustratively as follows: Code C.sub.1 is a (4,1,4) binary 
repetition code consisting of codewords 0000 and 1111; code C.sub.2 is a 
(4,3,2) binary parity check code with even parity; and code C.sub.3 is a 
(4,4,1) code, which means that, in this example, no redundancy is added. 
That is, class 3 is not coded at all. Since M=4, and since each signal 
point is a two-dimensional signal point, the overall coded modulation 
scheme is 8-dimensional (8D). The class 1 bits--which are the most 
important--are encoded by code C.sub.1 ; the class 2 bits--which are the 
second-most important--are encoded by code C.sub.2 ; the class 3 
bits--which are the third-most important--are encoded by code C.sub.3. In 
order to provide three-bit addresses to constellation mapper 131 on an 
ongoing, regular basis, buffers 411, 412 and 413, each of length M=4, are 
provided, as already noted, to buffer the outputs of encoders 401, 402 and 
403. It is thus seen that K=k.sub.1 +k.sub.2 +k.sub.3 =8. That is, 8 
information bits are transmitted for each block of M=4 symbol intervals, 
yielding a bit rate of 2 bits per signaling interval. Note that 1/8=12.5% 
of the data is in class 1;3/8=37.5% of the data is in class 2; and 
4/8=50.0% of the data is in class 3. 
In order to advantageously use the minimum Hamming distance separation, 
i.e., the built-in time-diversity of a code, it is necessary that symbols 
within any one block of M signal points be subject to independent fading. 
In practice this is achieved by way of the interleaving provided by 
interleaver 141 as described above. 
We consider, now, specifically the error probability for each of the data 
classes in this example. We first note that the typical cellular mobile 
radio channel is a Rayleigh fading channel. The probability of error for 
such channels is, to a first, and typically adequate, approximation, 
proportional to the reciprocal of the signal-to-noise ratio (SNR) raised 
to the power of the minimum Hamming distance (assuming the use of, for 
example, a maximum likelihood decoding strategy). That is, for the 
i.sup.th class of data 
##EQU2## 
where d.sub.Hi is the minimum Hamming distance 
P.sub.e (i) is the probability of error upon decoding and 
.gamma..sub.i is a proportionality constant. 
(Hereinafter, for convenience, we will use "P.sub.e (i)=" rather than 
"P.sub.e (i).apprxeq.".) Therefore, since the minimum Hamming distance for 
class 1 is "4," which is greater than that for any less important class of 
data for which the minimum Hamming distance is "2", the bit error 
probability for the former is, in accordance with the invention, better 
(i.e., lower) than that for the latter, assuming some minimum SNR and 
ignoring, in the first instance, the contributions of the proportionality 
constants .gamma..sub.i. 
Of course, it is readily seen that the proportionality constants 
.gamma..sub.i do also make a contribution to P.sub.e (i). Each 
.gamma..sub.i, in particular, is proportional to is the ratio of a) the 
average number of nearest neighbors for the i.sup.th class of data to b) 
the so-called product distance for that class. (Hereinafter, for 
convenience, we will use ".gamma..sub.i =" rather than ".gamma..sub.i 
.apprxeq.".) These parameters are determined by codes chosen, as well as 
the signal constellation design, which includes, for example, the 
constellation geometry, the labelling of the signal points and the manner 
in which the outputs of the channel codes map into the labels. Thus, in 
accordance with a feature of the invention, attainment of particular 
desired error probabilities for the various different data classes can be 
facilitated by appropriate joint selection of channel codes and signal 
constellation design. In virtually all instances of practical interest, 
the code selection and constellation design will be such that the values 
of the .gamma..sub.i will not change the result that P.sub.e (i)&lt;P.sub.e 
(2)&lt;P.sub.e (3) . . . for d.sub.Hi &gt;d.sub.H2 &gt;d.sub.H3 . . . . 
The product distance for the class 1 data is 0.587.sup.4 =0.119, which can 
be verified by noting that the minimum Hamming distance of code C.sub.1 is 
"4" and that the squared Euclidean distance between nearest neighbors of 
the signal constellation which differ in the bit that is addressed by the 
output of code C.sub.1 --bit b.sub.1 --is 0.587. The number of nearest 
neighbors for this code is 8 since, corresponding to any transmitted 
multi-level-coded words, there are 8 other multi-level-coded words which 
are at a Hamming distance of 4 with a product distance of 0.119. Thus, 
EQU .gamma..sub.1 =8/0.119=67.23. 
For class 2 data, the product distance is 2.sup.2 =4, which can be verified 
by noting the minimum Hamming distance of code C.sub.2 is "2" and that the 
squared Euclidean distance between nearest neighbors of the signal 
constellation which differ in the bit that is addressed by the output of 
this code is 2.0. The number of nearest neighbors for this code is 6 since 
for each multi-level-coded word (assuming i.sub.1 has been decoded 
correctly), there are 6 multi-level-coded words that are at a Hamming 
distance of 2 that can result in an error in information sequence i.sub.2. 
Thus, 
EQU .gamma..sub.2 =6/4=1.5. 
For class 3 data, the product distance is 2.0, which can be verified by 
noting the minimum Hamming distance for an uncoded case--which is what 
code C.sub.3 is in this example--is "1" since the squared Euclidean 
distance between nearest neighbors of the signal constellation which 
differ in the bit that is addressed by the output of this code is 2.0. The 
number of nearest neighbors for this code is "1" since there is only one 
neighbor at squared Euclidean distance "2.0" (assuming that the bits 
encoded by codes C.sub.2 and C.sub.1 have been decoded correctly). Thus, 
EQU .gamma..sub.3 =1/2=0.5. 
Overall, then, 
EQU .gamma..sub.1 =8/0.119=67.2, 
EQU .gamma..sub.2 =6/4=1.5, 
EQU .gamma..sub.3 =1.0/2.0=0.5, 
so that data classes 1, 2 and 3 have the following error probabilities: 
EQU P.sub.e (1)=67.2[1/SNR].sup.4, 
EQU P.sub.e (2)=1.5[1/SNR].sup.2, 
EQU P.sub.e (3)=0.15[1/SNR].sup.1, 
Note that as desired--at least when the SNR is greater than some 
minimum--the greatest level of error protection (lowest error probability) 
is provided to class 1; the second-greatest level of error protection is 
provided to class 2; and the third-greatest level of error protection is 
provided to class 3. 
(In this example, as well as all the other examples given herein, it is 
assumed that the interleaver provides sufficient separation in time 
between the signal points within a block of M signal points to ensure that 
fading events associated with those signal points are, in general, 
independent.) 
It will be immediately apparent, then, that using different codes--to 
provide different minimum Hamming distances--and different 
constellations--to provide different proportionality constants--various 
different sets of levels of protection can be provided. A few different 
possibilities--which are, of course, illustrative and not in any sense 
exhaustive--will now be presented. We begin by changing the codes while 
continuing to use the constellation and signal point labelling of FIG. 5. 
Consider, for example, a 16-D block coded modulation scheme which uses the 
following set of codes: 
EQU C.sub.1 is an (8,4,4) extended Hamming code; 
EQU C.sub.2 is an (8,7,2) binary parity check code with even parity; 
EQU C.sub.3 is an (8,7,2) binary parity check code with even parity. 
It is thus seen that K=k.sub.1 +k.sub.2 +k.sub.3 =18. That is, 18 
information bits are transmitted for each block of M=8 symbol intervals, 
yielding a bit rate of 2.25 bits per signaling interval. Note that 
4/18=22.2% of the data is in class 1; 7/18=39.9% of the data is in class 
2; and 7/18=39.9% of the data is in class 3. 
Overall, then, 
EQU .gamma..sub.1 =224/0.119=1882.35, 
EQU .gamma..sub.2 =28/4.0=7.0, 
EQU .gamma..sub.3 =28/4.0=7.0, 
so that data classes 1, 2 and 3 have the following error probabilities: 
EQU P.sub.e (1)=1882.35[1/SNR].sup.4, 
EQU P.sub.e (2)=7[1/SNR].sup.2, 
EQU P.sub.e (3)=7[1/SNR].sup.2. 
It will be readily seen that, in this case, the same level of error 
protection is provided to classes 2 and 3, yielding, in effect, a 
two-rather than a three-level unequal error protection scheme. However, as 
will be seen later, using a different constellation design--while not 
affecting the minimum Hamming distance--can result in a change of the 
proportionality constants, thereby providing different levels of error 
protection for classes 2 and 3. 
Now we consider a 32-D block coded modulation scheme which uses the 
following set of codes: 
EQU C.sub.1 is an (16,11,4) extended Hamming code; 
EQU C.sub.2 is an (16,15,2) binary parity check code with even parity; 
EQU C.sub.3 is an (16,15,2) binary parity check code with even parity. 
It is thus seen that K=k.sub.1 +k.sub.2 +k.sub.3 =41. That is, 41 
information bits are transmitted for each block of M=16 symbol intervals, 
yielding a bit rate of 2.56 bits per signaling interval. Note that 
11/41=26.8% of the data is in class 1; 15/41=36.6% of the data is in class 
2, and 15/41=36.6% of the data is in class 3. 
Overall, then, 
EQU .gamma..sub.1 =2240/0.119=18823.5, 
EQU .gamma..sub.2 =120/4=30, 
EQU .gamma..sub.3 =120/4=30, 
so that data classes 1, 2 and 3 have the following error probabilities: 
EQU P.sub.e (1)=18823.5[1/SNR].sup.4, 
EQU P.sub.e (2)=30[1/SNR].sup.2, 
EQU P.sub.e (3)=30[1/SNR].sup.2. 
Note that in this case, the error probabilities are approximately the same 
as in the previous example. However, the bits per symbol are different. 
Now we consider a coded modulation scheme affording two, rather than three, 
levels of error protection and in which a binary convolutional code is 
used for protecting the class 1 data and a block code is used for 
protecting the class 2 data. The codes, in particular, are: 
EQU C.sub.1 is a rate R=1/2 convolutional code; 
EQU C.sub.2 is a (L, L-1,2) binary parity check code with even parity. 
Code C.sub.1, more particularly, is a maximum free distance (d.sub.free) 
code for any memory of the code that is desirable and is of the type 
described, for example, in J. G. Proakis, Digital Communications, 2nd Ed., 
McGraw-Hill, 1989. The two bits output by code C.sub.1 determine bits 
b.sub.1 and b.sub.2 and the output from code C.sub.2 determines b.sub.3. 
In this case, the total number of bits transmitted in a block of length L 
is K=(2L-1), yielding a bit rate of 2-(1/L) bits per signaling interval. 
Approximately 50% of the bits are in each of the classes 1 and 2, for 
reasonably large L. For example, if code C.sub.1 is a memory 2 
convolutional code, and L=10, then 
EQU .gamma..sub.1 =1/2.25=0.44, 
EQU .gamma..sub.2 =45/16=2.81. 
Moreover, as is well known, the parameter for convolutional codes which 
corresponds to the role of the minimum Hamming distance for block codes 
is, in this case, (d.sub.free -2)=3. In general, an upper bound on the 
value of time diversity for convolutional codes used in the manner 
described here is d.sub.free -2. For memory 2 code, this upper bound is 
achieved. Overall, then, data classes 1 and 2 have the following error 
probabilities: 
EQU P.sub.e (1)=1.0/2.25[1/SNR].sup.3. 
EQU P.sub.e (2)=45/16[1/SNR].sup.2. 
(For this example, in order to achieve the above error probabilities, and, 
in particular, the product distances indicated, the labeling assignment 
shown in FIG. 5 should be changed. The 000 label is assigned to the same 
signal point of the constellation. The other labels, reading 
counter-clockwise, are then, for this case, 001, 011, 010, 100, 101, 111 
and 110.) 
The foregoing examples thus illustrate that by using codes having various 
a) minimum Hamming distances (or convolutional code free distance) and b) 
block code lengths, one can obtain various levels of error protection, 
overall bits per signaling interval, and/or the fraction of bits allocated 
to the various classes. As noted earlier, yet further flexibility is 
provided by using various different constellations, thereby changing the 
proportionality constants .gamma..sub.i. 
FIGS. 6 and 7 show respective 8-point PSK constellations in which the 
signal points are non-uniformly spaced and for which, as a result one can 
provide a) numbers of nearest neighbors and/or b) product distances that 
are different from those obtained for the constellation of FIG. 5. In this 
way, different proportionality constants .gamma..sub.i can, 
advantageously, be obtained. 
Consider the use of these constellations in conjunction with the first set 
of codes described above for the 8-dimensional block code. 
In the constellation of FIG. 6, in particular, the squared minimum 
Euclidean distance between any two signal points that differ in bit 
b.sub.1 --that is the bit that is output by encoder 401--is 2.0. Hence 
using this constellation in place of the constellation of FIG. 5 increases 
the product distance from 0.119 to 16 for class 1. However, the product 
distance for class 2 decrease from 4 to 0.43, while the product distance 
for class 3 decrease from 2.0 to 1.0. The number of nearest neighbors for 
class 1 decreases from 8 to 1, while for classes 2 and 3 it remains the 
same as it was, at 6 and 1, respectively. The proportionality constants 
thus have the values 
EQU .gamma..sub.1 =1/16=0.0625, 
EQU .gamma..sub.2 =6/0.43=13.95, 
EQU .gamma..sub.3 =1.0/0.43=2.33, 
Note, then, that the overall result is to provide even greater error 
protection (lower error probability) for class 1 at the expense of less 
error protection for classes 2 and 3. Thus, the minimum SNR at which class 
1 data bits are subject to a better error probability is strictly lower 
with the constellation of FIG. 6 than with that of FIG. 5. 
In the constellation of FIG. 7, in particular, the squared minimum 
Euclidean distance between any two signal points that differ in either of 
bits b.sub.1 or b.sub.2 --that is the bits that are output by encoders 401 
and 402--is 1.0. Hence using this constellation in place of the 
constellation of FIG. 5 increases the product distance from 0.119 to 1.0 
for class 1. However, the product distance for class 2 decreases from 4.0 
to 1.0, while the product distance for class 3 decreases from 4 to 0.43. 
The number of nearest neighbors for class 1 decreases from 8 to 1; for 
class 2, it remains at 6; and for class 3, it remains the same as it was 
at 1. The proportionality constants thus have the values 
EQU .gamma..sub.1 =1/1=1, 
EQU .gamma..sub.2 =6/1=6, 
EQU .gamma..sub.3 =1/0.43=2.32. 
Here, the overall result is to provide a greater separation, in terms of 
level of error protection between classes 2 and 3 than with either of the 
other two constellations. Class 1 still has more protection than when the 
constellation of FIG. 5 is used, but not as much as when the constellation 
of FIG. 6 is used. 
It may also be possible to use codes which have the same minimum Hamming 
distance, in which case unequal error protection can nonetheless be 
obtained by having different values of .gamma..sub.i via, for example, the 
use of non-uniform signal constellations such as those of FIGS. 6 and 7. 
We turn, now, to the receiver of FIG. 2. 
In particular, the analog cellular mobile radio signal broadcast from 
antenna 152 is received by antenna 201 and is thereupon subjected to 
conventional front-end processing, which includes at a minimum, 
demodulation and A/D conversion. Demodulation can be carried out by any of 
the known techniques, such as coherent demodulation, differentially 
coherent demodulation, non-coherent demodulation, etc. The front-end 
processing may also include such other processing as equalization, timing 
recovery, automatic gain control, etc., as is well known in the art. The 
output of front-end processing 211 is applied to de-interleaver 221, which 
performs the inverse task of interleaver 141 in the transmitter, thereby 
restoring the signal points to their original order. The de-interleaver 
output is passed on to multi-level decoder 231, which performs the task of 
recovering the information bits that were encoded by multi-level encoder 
120. In the general case, a maximum-likelihood decoding algorithm is used. 
In particular, if the multi-level code is sufficiently simple, an 
exhaustive table-lookup approach can be used. For more complex codes, then 
the Viterbi algorithm could be used if the constituent codes of the 
multi-level code allow for a finite-state decoder realization. If the 
number of states of the multi-level code is too great to permit a 
practical implementation of a maximum-likelihood decoder, then multi-stage 
decoding can be used, this approach being described, for example, in A. R. 
Calderbank, "Multilevel codes and multi-stage decoding," IEEE Transactions 
on Communications, Vol. 37, pp. 222-229, March 1989. Enhanced multi-stage 
decoding as described in N. Seshadri and C.-E. W. Sundberg, "Multi-level 
codes with large time-diversity for the Rayleigh fading channel," 
Conference on Information Sciences and Systems, Princeton, N.J., pp. 
853-857, March 1990, can also be used. More specifically in that case, if 
any of the constituent codes are complex, e.g. Reed-Solomon, block codes, 
then any of the known decoding techniques that approximate the performance 
of the maximum-likelihood decoder for such a code can be used to deal with 
that code within the multi-stage decoder. 
The bits output by multi-level decoder 231 are provided in three parallel 
streams--corresponding to the three streams on leads 115-117--to 
respective descramblers 241-243, which perform the inverse function to 
scramblers 110-112 in the transmitter. Speech decoder 253 then performs 
the inverse function of speech encoder 104 of the transmitter, yielding a 
reconstructed speech signal that is passed on to the telephone network, 
including, typically, a cellular mobile radio switching system with which 
the receiver is co-located. 
A transmitter and a receiver similar to those of FIGS. 1 and 2 would, of 
course, be provided at the cell site and mobile (automobile) site, 
respectively, to support communication in the other direction of 
transmission. 
The foregoing merely illustrates the principles of the invention. For 
example, the various codes and constellations, including their 
dimensionalities are all illustrative. Any desired codes and 
constellations can be used. With respect to the codes, in particular, it 
should be noted that a data stream which is not actually redundancy coded, 
as is the case for code C.sub.3 the first example hereinabove, may 
nonetheless be said to be coded with a rate R=1 redundancy code. That is, 
"no coding" can be regarded--and, for definitional purposes herein, is 
regarded--as being a form of coding. With the respect to the 
constellations, in particular, any of various uniform or non-uniform 
configurations which have any desired number of signal points may be used 
advantageously to provide different proportionality constants. 
Moreover, any desired number of levels of error protection can be supported 
by using multiple multi-level codes to encode respective sets of data 
streams and time-multiplexing the signal points addressed by the various 
multi-level codes. 
The invention can be used to advantage in conjunction with any type of 
source coder (such as image, facsimile) that needs unequal error 
protection--not just speech coders. 
It will also be appreciated that although the various functional elements 
of the transmitter and receiver are depicted as discrete elements, the 
functions of those elements will typically be carried out using 
appropriately programmed processors, digital signal processing (DSP) 
chips, etc. 
Thus it will be appreciated that those skilled in the art will be able to 
devise numerous arrangements which, although not explicitly shown or 
described herein, embodying the principles of the invention and thus are 
within its spirit and scope.