Int’l J. of Communications, Network and System Sciences, 2011, 4, 388-394
doi:10.4236/ijcns.2011.46046 Published Online June 2011 (http://www.SciRP.org/journal/ijcns)
Performance Study of the Association TCM-UGM/STBC to
Reduce Transmission Errors of JPEG Images
Mohamed Benaissa1*, Abdesselam Bassou2, Mohammed Beladgham1, Abdelmounaim Moulay Lakhdar1
1University of Bechar, Bechar, Algeria
2Telecommunication and Digital signal Processing Laboratory, Djillali Lia bes University, Sidi Bel Abbes, Algeria
Received February 24 , 20 11; revised March 20, 201 1; accepted March 31, 2011
Abstract
The purpose of this work is to associate the channel encoder called ‘trellis-coded modulation with Unger-
boeck-Gray mapping’ (TCM-UGM) to ‘space-time block code’ (STBC), in order to study its performance to
correct the transmission errors of a JPEG image. The performance of the proposed scheme is evaluated in
senses of bit error rate (BER), frame error rate (FER) and peak signal-to-noise ratio (PSNR) of the recon-
structed image. Compared to the association TCM/STBC for a throughput of 2 bits/s/Hz, TCM-UGM/STBC
permits to obtain a PSNR gain up to 2 dB.
Keywords: Trellis-Coded Modulation, Trellis Coded Modulation with Ungerboeck-Gary Mapping,
Logarithm of Maximum a Posteriori, Space-Time Block Code, JPEG
1. Introduction
In future wireless communication systems, high data
rates need to be reliably transmitted over time-varying
band limited channels. The wireless channel mainly suf-
fers from time-varying fading due to multipath propaga-
tion and destructive superposition of signal received over
different paths. Fortunately, the effects of fading can be
substantially mitigated by the use of diversity. Different
transmit diversity techniques have been introduced. In
[1], Tarokh et al. proposed space-time trellis coding by
jointly designing the channel coding, modulation, trans-
mit diversity and the optional receiver diversity. The
proposed sp ace-time trellis co des perform extremely well
at the cost of high complexity. In addressing the issue of
decoding complexity, Alamouti [2] discovered a re-
markable scheme for transmissions using two transmit
antennas. A simple decoding algorithm was introduced,
which can be generalised to an arbitrary number of re-
ceive antennas. This scheme is significantly less complex,
than space-time trellis coding using two transmit anten-
nas, although there is a loss in performance [3]. Despite
the associated performance penalty, Alamouti’s scheme
is appealing in terms of simplicity and performance. This
proposal motivated Tarokh et al. [3,4] to generalise the
scheme to an arbitrary number of transmit antennas,
leading to the concept of sp ace time block codes. Space-
time block codes were designed for achieving the maxi-
mum diversity order of n × m for n transmit and m re-
ceive antennas. However, they were not designed for
achieving addit i onal coding gain.
Hence, in this contribution, we combine space-time
block codes with Trellis Cod ed Modulation (TCM) [5,6],
and TCM-UGM [7] in order to achieve additional coding
gains. The simulation results showed that the TCM-
UGM outperforms the original TCM scheme proposed
by Ungerboeck by 2.59 dB over Rayleigh fading channel
[7]. The comparison is do ne at a Bit Erro r Rate (BER) of
10 - 5. Visual signals such as compressed still images are
very vulnerable to chann el noise.
Usually, channel coding is utilized to protect the
transmitted visual signals. The Joint Photograph Experts
Group (JPEG) standard [8] proposed in 1992 is widely
used for still image compressio n and transmission. JPEG
has 4 distinct modes of operation: sequential DCT-based,
progressive DCT-based, lossless, and hierarchical [9].
JPEG, a DCT-based image compression algorithm [10],
is the current ISO standard for the encoding of still im-
ages. The JPEG algorithm follows a block-based com-
pression approach. It divides the input image into 8 × 8
pixel blocks, transforms each block using DCT, and then
codes the DC and AC coefficients. In this paper, we pro-
vide an efficient scheme for transmitting JPEG com-
pressed images using the concatenation of STBC with

M. BENAISSA ET AL.
389
TCM-UGM system (TCM-UGM/STBC). The considered
image is compressed using JPEG compression algorithm
then coded with TCM-UGM/STBC or TCM/STBC. At
the receiver, symbol-by-symbol MAP TCM-UGM or
TCM decoding algorithm is applied, and the image is
reconstructed by decompression algorithm.
2. Space-Time Block Codes
A Space Time Block Code describing the relationship
between the original transmitted signal and the signal
replicas artificially created at the transmitter for trans-
mission over various diversity channels is defined by an
nTxp dimensional transmission matrix. The entries of the
matrix are constituted of linear combinations of the
k-airy input symbols 12
, ,,
k
x
x
1
i
x and their conjug ates.
The k-airy input symbols
x
ik

are used to repre-
sent the information-bearing binary b its to be transmitted
over the transmit diversity channels. In a signal constel-
lation having 2m constellation points, a number m of bi-
nary bits are used to represent a symbol xi. Hence, a
block of kxm binary bits are entered into the STB en-
coder at a time and it is, therefore, referred to as a STB
code. The number of transmitter antennas is nT and p
represents the number of time slots used to transmit k
input symbols. Hence, a general form of the transmission
matrix of a STBC is written as
11 211
12 222
12
p
p
nn pn
gg g
gg g
gg g











(1)
where the entries gij represent linear combinations of the
symbols 12
, ,,
k
x
x
1, 
xn and their conjugates. More spe-
cifically, the entries gij, where xi, are trans-
mitted simultaneously fro m transmit antennas in
each time slot.
1,,T i
1,, T n
,jp
The transmission matrix in Equation (1) (which de-
fines the STBC) is based on a complex generalized or-
thogonal design, as defined in [3]. Since there are k
symbols transmitted over p time slots, the code rate of
the STBC is given by
k
Rate p  (2)
At the receiving end, one can have an arbitrary num-
ber of nR receivers. A simple transmit diversity scheme
for two transmit antenn as was introduced by Alamouti in
[2]. The transmission matrix is
12
221
x
x
G
x
x

 


It can be seen in the transmission matrix G2 that there
are nT = 2 (number of columns in the matrix G2) trans-
mitters, k = 2 possible input symbols, namely, x1, x2 and
the code spans over p = 2 (number of rows in the matrix
G2) time slots. Since k = 2 and p = 2, the code rate is
unity. The associated encoding and transmission process
is shown in Table 1. At any given time instant T, two
signals are transmitted simultaneously from the antennas
Tx1 and Tx2. For example, in the first time slot T = 1,
signal x1 is transmitted from antenna Tx1 and signal x2 is
transmitted simultaneously from antenna Tx2. In the next
time slot T = 2, signals 2
x

and 1
x
(the conjugates of
symbols x1 and x2) are simultaneously transmitted from
antennas Tx1 and Tx2, respectively.
Figure 1 shows the base band representation of a sim-
ple two-transmitter STBC, namely, that of the G2 code
seen in Equation (3) using one receiver. We can see from
the Figure 1 that there are two transmitters, namely, Tx1
as well as Tx2 and they transmit two signals simultane-
ously. As it can be seen from the Figure 1, the transmit-
ted symbol x1 and x2 propagates through two different
fading channels, namely, h1 and h2. As mentioned earlier,
Table 1. Encoding and transmission process for the STBC.
Antenna
Time slot, T Tx1 Tx2
1 x1 x2
2 2
x
 1
x

(3) Figure 1. Base band representation of the simple two
transmitters STBC G2 of (3) using one receiver.

390 M. BENAISSA ET AL.
the complex fading envelope is assumed to be constant
across the corresponding two consecutive time slots.



11 11hhT hT2
(4)



22 21hhT hT2
1
(5)
At the receiver, independent noise samples, n1 and n2
are added in each time slot; hence the signals received
over non dispersive or narrow-band channels can be ex-
pressed with the aid of Equation (3) as
11122
yhxhxn (6)
21221
yhxhx 2 n (7)
where y1 is the first received signal and y2 is the second.
Note that the received signal y1 consists of the transmit-
ted signals x1 and x2, while y2 consists of their conjugates.
In order to determine the transmitted symbols, we have
to extract the signals x1 and x2 from the received signals
y1 and y2. Therefore, both signals y1 and y2 are passed to
the combiner, as shown in Figure 1. In the combiner-
aided by the channel estimator, which provides perfect
estimation of the diversity channels in this example sim-
ple signal processing is performed in order to separate
the signals x1 and x2. Both signals x1 and x2 are then
passed to the maximum likelihood detector of Figure 1,
based on the Euclidean distances between the combined
signal x and all possible transmitted symbols. The sim-
plified decisio n rule is based on choosing xi if and only if




ˆˆ dist ,dist ,
ij
x
xxxi j (8)
where dist(A, B) is the Euclidean distance between sig-
nals A and B and the index j spans all possible transmit-
ted signals. From Equation (8), we can see that maxi-
mum likelihood transmitted symbol is the one having the
minimum Euclidean distance from the combined sig-
nal ˆ
x
.
3. Trellis Coded Modulation with
Ungerboeck-Gray Mapping
The TCM scheme, proposed by Ungerboeck, was de-
signed for throughput of m bits/sec/Hz, where m bits are
input to the encoder (among input bits are un-
coded) and m + 1 bits are output and mapped with
2m+1-airy modulation using set partitioning yielding a
coding rate
0m

1
m
Rm 

(9)
In this case the mapping by set partitioning (called
also Ungerboeck mapping) is applied. The Ungerboeck
TCM encoder was chosen by maximizing df. In [5], df is
compute by an algorithm that replaces the search in TCM
trellis for the path that maximizes df. In [7], the
TCM-UGM scheme considered, for a throughput of m
bits/sec/Hz, that the mapper is a 2m+1-airy that uses a
mapping technique combining Ungerboeck mapping and
Gray code mapping. In this case, bits are input to
the encoder, and systematically output and mapped using
Ungerboeck mapping. The Gray mapping is applied on
the remaining
mm


1mm


 uncoded bits and the gener-
ated parity bit. When no uncoded bits are considered
(0m

), this scheme is equivalent to Ungerboeck TCM
scheme with 0m


0m
. In [7], the optimal encoder code-
generator is obtained by searching in the trellis, of two
different paths (with a minimum Euclidean distance) that
begin at state zero and finish to the same state. The op-
timal code-generator is obtained by maximizing df. In
this work, the TCM-UGM encoder, illustrated in Figure
2, considers m = 2 input bits of which no uncoded bits
are considered (

).
4. Proposal System
Figure 3 represents the image transmission system for
which we evaluate the FER and PSNR after decoding.
An input image is compressed by JPEG. The binary
symbols resulting from the JPEG compressing constitute
the sequence of data to be transmitted. The information
data is first encoded by the TCM or TCM-UGM encoder
exposed in section 3. The complex constellation symbols,
generated by mapper, are interleaved and fed into the
space-time block encoder described in section 2 (with nT
transmit and nR receive antennas). At each time slot T,
the output symbols xi are modulated and transmitted si-
multaneously each from a different transmit antenna. At
the receiver end, the received noisy symbol is decoded
using space-time block decoder and deinterr leaved giving
a soft-decision exploited by TCM or TCM-UGM de-
coder and is used for the reconstruction image.
5. Simulation Result
The performance simulation of the associations TCM/
Figure 2. TCM-UGM encoder for 2 bits/s/Hz.

M. BENAISSA ET AL.
391
Figure 3. A block diagram of a communication system, nT = 2; nR = 1.
that the system TCM-UGM/STBC presents better resu lts
than the TCM/STBC from a Eb/N0 of 10 dB for BER
curves and 7 dB for FER curves. The TCM-UGM/STBC
system outperforms the performance of the association
TCM/STBC by 0.4 dB at BER = 10–5 and 0.9 dB at FER
= 10–3.
STBC and TCM-UGM/STBC using 8PSK Ungerboeck
mapper (for TCM) and Ungerboeck-Gray mapper (for
TCM-UGM) are investigated for throughput 2 bit/s/Hz
for JPEG image transmission. Rate 2/3 and 16-state
TCM or TCM-UGM encoder is considered. Transmis-
sion over MRF channel, using one receiver antenna, is
simulated employing STBC with G2 as orthogonal code.
The optimal encoders’ code-generator (in sense of df) for
the used TCM and TCM-UGM encoders are illustrated
in Ta ble 2 (the average power per dimensi on in the con-
stellation is normalized to 1/2).
The Peak Signal-to-Noise Ratio (PSNR) is the most
commonly used as a measure of quality of reconstruction
in image compression. The PSNR were identified using
the following formulae:
 

2
2
11
1ˆ
MSE, ,
MxN
jM iN
ij
I
ij Iij
 


 (10)
In simulation, a variety of raw images with high
resolution (512 × 512 pixels) are used (boat image in
Figure 9, goldhill image in Figure 12 and concord aerial
in Figure 15). The images transmitted have different bit
per pixel (bpp) (Table 3) to illustrate the effectiveness of
the proposed system
Mean Square Error (MSE) which requires two MxN
grayscale images
I
and ˆ
I
where one of the images is
considered as a compression of the other is defined as:
The PSNR is defi n ed as:
The performance of the encoding schemes is evaluated
in terms of BER (Bit Error Rate) and FER (Frame Error
Rate) versus bit energy to noise ratio (Eb/N0). The FER
computation considers a frame length of 1024.
2
10 (Dynamicsofimage)
PSNR 10logMSE

 

(11)
Figures 4 and 5 illustrate the performance in sense of
BER and FER, respectively, of TCM/STBC and
TCM-UGM/STBC considering one receiver antenna for
the transmission of this JPEG images. It can be observed
Usually an image is encoded on 8 bits. It is repre-
sented by 256 gray levels, which vary between 0 and 255,
the extent or dynamics of the image is 255.
Table 2. Code-generator for throughput 2bits/s/Hz STBC
encoding and transmission proce ss for the STBC.
Code-generator
2
f
d Memory
order h0 h
1 h 2
TCM 5.172 4 31 14 30
TCM-UGM 5.172 4 23 34 15
Figure 6 to Figure 8 illustrate the performance curves
of the PSNR of the reconstructed image vs Eb/N0. From
these figures, it can be shown clearly that the proposed
system based on TCM-UGM gives better performance.
For an Eb/N0 of 11 dB a PSNR improvement of around 2
dB is obtained for Boat and Goldhill images and around
0.6 dB to the Concord-aerial image.
Table 3. Bit Per Pixel rate for different images.
Image Concord-aerial Boat Goldhill
Bit per pixel 0.5 0.4 0.61
Figures 10 and 11 represent, respectively, the recon-
structed Boat image after transmission using the
TCM-UGM/STBC and TCM/STBC for Eb/N0 equals 11
dB; we can observe a clear visual improvement made by
the proposed system. The same rema rk can be done for the
other images (Figure 13 and Figure 14 for the Goldhill

392 M. BENAISSA ET AL.
Figure 4. BER performance of TCM/STBC and TCM-
UGM/STBC schemes over MRF channel (nR = 1).
Figure 5. FER performance of TCM/STBC and TCM-
UGM/STBC schemes over MRF channel (nR = 1).
Figure 6. Performance PSNR vs Eb/N0 for JPEG boat image
transmission bpp = 0.4.
Figure 7. Performance PSNR vs Eb/N0 for JPEG goldhill
image transmission bpp = 0.61.
Figure 8. Performance PSNR vs Eb/N0 for JPEG concord-
aerial image transmission bpp = 0.5.
Figure 9. Original Boat image.

M. BENAISSA ET AL.
393
Figure 10. Reconstructed Boat image for TCM-UGM/STBC,
bpp = 0.4, Eb/N0 = 11dB, PSNR = 24.52 dB.
Figure 11. Reconstructed Boat image for TCM/STBC, bpp
= 0.4, Eb/N0 = 11 dB, PSNR = 22.28 dB.
Figure 12. Original goldhill image.
Figure 13. Reconstructed Goldhill image for TCM-UGM/
STBC bpp = 0.61, Eb/N0 = 11dB, PSNR = 27.92 dB.
Figure 14. Reconstructed Goldhill image for TCM/STBC
bpp = 0.61, Eb/N0 = 11 dB, PSNR = 25.58 dB.
Figure 15. Original concord-aerial image.

M. BENAISSA ET AL.
394
formance in sense of FER and PSNR of the reconstructed
images, compared to TCM/STBC scheme. For a through-
put of 2 bits/s/Hz and an Eb/N0 of 11 dB, TCM-
UGM/STBC permits to obtai n a PSNR gai n of 2 dB.
7. References
[1] V. Tarokh, N. Seshadri and A. R. Calderbank, “Space-
Time Codes for High Data Rate Wireless Communication:
Performance Criterion and Code Construction,” IEEE
Transactions on Information Theory, Vol. 44, No. 2,
1998, pp. 744-765. doi:10.1109/18.661517
[2] S. M. Alamouti, “A Simple Transmit Diversity Tech-
nique for Wireless Communications,” IEEE Journal on
Selected Areas in Communications, Vol. 16, No. 8, 1998,
pp. 1451-1458. doi:10.1109/49.730453
Figure 16. Reconstructed concord-aerial image for TCM-
UGM/STBC bpp = 0.5, Eb/N0 = 11 dB, PSNR = 22.26 dB. [3] V. Tarokh, H. Jafarkhani and A. R. Calderbank, “Space-
Time Block Codes from Orthogonal Designs,” IEEE
Transactions on Information Theory, Vol. 45, No. 5,
1999, pp. 1456-1467. doi:10.1109/18.771146
[4] V. Tarokh, H. Jafarkhani and A. R. Calderbank, “Space-
Time Block Coding for Wireless Communications: Per-
formance Results,” IEEE Journal on Selected Areas in
Communications, Vol. 17, No. 3, 1999, pp. 451-460.
[5] G. Ungerboeck, “Channel Coding with Multilevel/Phase
Signals,” IEEE Transactions on Information Theory, Vol.
28, No. 1, 1982, pp. 55-67.
doi:10.1109/TIT.1982.1056454
[6] L. T. Hanzo, H. Liew and B. L. Yeap, “Turbo Coding,
Turbo Equalisation and Space Time Coding for Trans-
mission over Wireless Channels,” John Willy IEEE Press,
New York, 2002. doi:10.1002/047085474X
[7] A. Bassou and A. Djebbari, “Contribution to the Im-
provement of the Performance of Trellis-Coded Modula-
tion,” WSEAS Transactions on Communications, Vol. 6,
No. 2, 2007, pp. 307-311.
Figure 17. Reconstructed concord-aerial image for TCM/
STBC bpp = 0.5, Eb/N0 = 11 dB, PSNR = 21.58 dB. [8] “Digital Compression and Coding of Continuous tone
Still Images Part 1: Requirements and Guidelines,” In-
ternational Telecommunication Union, 1991.
image and, Figure 16 and Figure 17 for the Concord-
aerial image). [9] “Digital Compression and Coding of Continuous Tone
still Images: Requirements and Guidelines,” International
Standard Organization, 1994.
6. Conclusions [10] G. Lakhani, “DCT Coefficient Prediction for JPEG Image
Coding Image Processing,” IEEE International Confer-
ence on Image Processing, San Antonio, 16 Septem-
ber-19 October 2007, pp. 189-192.
doi:10.1109/ICIP.2007.4379986
In this work, TCM-UGM/STBC encoding scheme has
been used to correct compressed JPEG images trans-
mission errors. The simulatio n results over MRF channel
have shown that the proposed scheme offers better per-