Bu çalışmada Bölütlenmiş Hücresel Yapay Sinir Ağları-Hücresel Yapay Sinir Ağları Birleşik Kafes Kodlamalı Kuantalama ve Modülasyon işleminin gerçekleştirildiği yeni bir yapı tanıtılmıştır. Burada gri tonlamalı bir görüntü bizim tarafımızdan önerilen Bölütlemeli Hücresel Yapay Sinir Ağı yaklaşımı kullanılarak 3 bit seviyesine düşürülmüş ve daha sonra CNN tabanlı bir modelden oluşmuş kafes kodlamalı kuantalama ve modülasyon yapısından geçirilmiştir. Son olarak bu önerilen yapının performans analiz işlemleri yapılarak simulasyon ve analitik hata başarım eğrileri elde edilmiştir.In this paper, Segmented Cellular Neural Network-Cellular Neural Network   Combined Trellis Coded Quantization / Modulation (SCNN-CNN CTCQ/TCM) scheme is introduced. Here, a gray scaled image is lowered to 3 bit using our proposed Segmented Cellular Neural Network approach (SCNN) and then passed through a new CNN based structure which models combined trellis coded quantization / modulation. The performance of our combined scheme has been analyzed over Rician fading channel. Computer simulations studies confirm the analytical upper bound curves

UÇAN, Osman Nuri

ÖZMEN, Atilla

English

DoÄuÅ Ãniversitesi Dergisi

PERFORMANCE OF GRAY SCALED IMAGES USING 
SEGMENTED CELLULAR NEURAL NETWORK­
CELLULAR NEURAL NETWORK COMBINED 
TRELLIS CODED QUANTIZATION / MODULATION 
(SCNN-CNN CTCQ/TCM) APPROACH
OVER RICIAN FADING CHANNEL
Osman Nuri Uçan Atilla Özmen
Department o f Electrical and Electronics Engineering 
Istanbul University, Avcılar 34850, Istanbul, Turkey
Abstract: In this paper, Segmented Cellular Neural Network-Cellular Neural 
Network Combined Trellis Coded Quantization/M odulation (SCNN-CNN 
CTCQ/TCM) scheme is introduced. Here, a gray scaled image is lowered to 3 bit 
using our proposed Segmented Cellular Neural Network approach (SCNN) and then 
passed through a new CNN based structure which models combined trellis coded 
quantization /  modulation. The performance of our combined scheme has been 
analyzed over Rician fading channel. Computer simulations studies confirm the 
analytical upper bound curves.
Keywords: Segm ented cellular neural network, trellis code quantization/ 
modulation, Rician fading channel
Özet : Bu çalışmada Bölütlenmiş Hücresel Yapay Sinir Ağları-Hücresel Yapay Sinir 
Ağları Birleşik Kafes Kodlamalı Kuantalama ve Modülasyon işleminin gerçekleşti­
rildiği yeni bir yapı tanıtılmıştır. Burada gri tonlamalı bir görüntü bizim tarafımızdan 
önerilen Bölütlemeli Hücresel Yapay Sinir Ağı yaklaşımı kullanılarak 3 bit seviyesi­
ne düşürülmüş ve daha sonra CNN tabanlı bir modelden oluşmuş kafes kodlamalı 
kuantalama ve modülasyon yapısından geçirilmiştir. Son olarak bu önerilen yapının 
performans analiz işlemleri yapılarak simulasyon ve analitik hata başarım eğrileri el­
de edilmiştir.
Anahtar kelimeler: Birleşik kaynak / kanal kodlaması, hücresel sinir ağ yapıları
217
L INTRODUCTION
Cellular Neural Network (CNN) (Chua, 1988:1257-1272) with a complex dynamic 
behaviour have found interesting applications in image processing, pattern recogni­
tion. CNN is an analog parallel computing paradigm defined in space, and 
characterized by locally of connections between processing elements.
To minimize the communication or storage rate and hence the bandwidth or storage 
capacity required for a given communication and signal processing system, 
quantization plays a valuable role. If quantization is done before some form of 
digital signal processing, the subsequent signal processing in principal becomes 
simpler because of the reduced number of bits required to represent the input signals. 
In addition, portions of such signal processing can be incorporated into the 
quantization system so as to ease the computational burden. Here the key becomes 
the preservation of the information necessary to the application.
In our study, a new CNN approach is introduced for a quantization problem and 
denoted as ‘Segmented Cellular Neural Network (SCNN)’. SCNN helps us to 
quantize any high levels input images to any order output level. Here since 
classical CNN output has only two output levels, input high level gray scaled images 
have been grouped in sub-gray levels. Then each sub-group has passed through a 
CNN having two different output levels. Thus using SCNN structure, we are able to 
quantize any high level input data to any desired lower level. As an example SCNN 
has been applied to Lenna image with 256 gray levels and it has been decreased to 8 
gray levels.
During the last two decades, trellis coded modulation (Ungerboeck, 1982:55-67) has 
proven to be a very effective modulation scheme for band limited channels. 
Motivated by trellis coded modulation, trellis coded quantization (TCQ) (Marcellin 
and Fischer, 1990:82-93) was developed as a computationally efficient scheme for 
source coding. In (Uysal and Uçan, 1997:906-911), TCQ and TCM trellis structures 
are combined in such a way that the TCQ/TCM system operates on only one 
identical trellis and is denoted as Combined TCQ/TCM. Here the CNN model has 
been introduced for the considered trellis structure of Combined TCQ/TCM.
In this paper, the high level gray scaled input image is segmented using the SCNN 
model and passed through a CNN model of Combined TCQ/TCM structure. The 
performance of SCNN-CNN CTCQ/TCM scheme has been analysed over Rician 
fading channel. Computer simulations studies confirm the analytical upper bound 
curves.
This paper is organised as follows: In Section II, the Cellular Neural Network (CNN) 
model
is given. In section III, the follows Combined TCQ/TCM is explained. In section IV, 
the Segmented Cellular Neural Network-Cellular Neural Network Combined Trellis 
Coded Quantization /  Modulation (SCNN-CNN TCQ/TCM) is introduced. In the last 
section, error performance of SCNN-CNN CTCQ/TCM over Rician Fading channel 
is investigated and as an example Lenna input image is considered.
218
D. CELLULAR NEURAL NETWORK (CNN)
CNN is an analog parallel-computing paradigm defined in space, and characterized 
by locally of connections between processing elements. At the CNN information is 
only exchanged between neighboring neurons. This local information characteristic 
doesn't prevent the capability of obtaining global processing. In digital signal 
processing, discrete time cellular neural network (DT-CNN) (Cimagalli, May: 1993) 
is applied to some practical problems and can be written by the following equations
x(n+l) = Ay(n) + Bu(n) + I
xj(n + l) = X  Ajkyk(n) + X  Bjkuk(n)+Ij (1)
k eN r(j) keN r(j)
y(n) =  ^  (x(w) + 1| - 1x(n) - 1|)
Where, A, B, u, y, x, I denote feedback connection weights matrix, input connection 
weights matrix, input, output, state and bias respectively, j and k are cell indices and 
N is the neighborhood function.
m . COMBINED TRELLIS CODED QUANTIZATION/MODULATION 
(CTCQ/TCM)
In a classical joint TCQ/TCM (Marcellin and Fischer, 1991:172-176; Aksu and 
Salehi, 1996: 529-533) system, the source is first encoded by a trellis coded 
quantizer, then modulated by a TCM scheme. The reproduction codebook size (i.e. 
number of quantization levels) is selected as N=2R+CEF . There are totally N1=2r+CEF 
subsets. N is chosen so that it can be properly divided by N 1; so each subset has 
exactly N 2=N /Nl=2R r codewords. Here R ^ l is the encoding rate in bits/sample, r 
and CEF are positive integers satisfying l<r<R and CEF^O. The parameter CEF 
stands for "codebook expansion factor", since the codebook size is 2CEF times that 
of a nominal R bits/sample scalar quantizer.
The setup of the joint TCQ/TCM system in previous studies is unnecessarily comp­
lex. For instance, in the case of the codebook expansion factor is chosen as CEF=1, 
the TCQ encoder simply generates a sequence of quantization levels from a codebo­
ok of size N=2R+1 and these levels are mapped to modulation symbols in the 2R+1- 
point TCM signal constellation. Since there is one-to-one correspondence between 
the quantization level within a TCQ subset and the modulation symbol within a TCM 
subset, the cascade organization of TCQ and TCM blocks may be renounced. In (Uy­
sal and Uçan, 1997: 906-911), TCQ and TCM trellis structures are combined in such 
a way that TCQ/TCM system operates on only one identical trellis.
On the branches of the combined trellis diagram, both quantization levels qk,l which 
denotes the 1th level in the k th quantization subset Qk with k = 0 ,l.. .N l-1 ,1=1,2..,N2 
and signal set Sj with j= 0 ,l.. .N -l are placed using Ungerboeck rules (Ungerbo- 
eck,1982:55-67). Thus a single trellis is sufficient to describe the overall combined
219
scheme under the assumption that identical trellises are used. "Combined Trellis 
Coded Quantization /  Modulation" has advantage over classical joint systems in 
terms of decoding time and complexity (Uysal and Uçan, 1997:906-911).
IV. SEGMENTED CELLULAR NEURAL NETWORK-CELLULAR 
NEURALNETWORK COMBINED TRELLIS CODED QUANTIZATION/ 
MODULATION (SCNN-CNN TCQ/TCM)
In this section, ‘Segmented Cellular Neural Network (SCNN)’ is introduced for 
quantization application. SCNN scheme quantizes any high level input image to any 
order output levels. Here since classical CNN output has only two output levels, 
input high level gray scaled image has been grouped in sub-gray levels. Then each 
sub-group has passed through a CNN having two different output levels. Thus using 
SCNN structure, we are able to quantize any high level input data to any desired 
lower level.
As an example SCNN has been applied to Lenna image with 256 gray levels. At first 
stage Lenna image is grouped in 4 different gray-scaled levels, each including 64 
gray levels. Thus a high level image can be decreased to 8 gray levels by considering 
each subgroup as a CNN structure having different output levels. Decreased level 
image at the output of SCNN is transformed to binary sequences in order to apply 
this information as an input for the CNN model of the combined TCQ/TCM 
structure given at Figure 2. Since the CNN input and output data size should match 
each other, we increase the 2 bit input data sequence to 3-bit by stuffing memory 
information of the trellis scheme (Figure 2). At the CNN equivalent of C TCQ/TCM 
scheme, modulated output 8PSK signals are modeled by their related binary 
correspondences, in order to estimate A, B, I denoting feedback connection weights 
matrix, input connection weights matrix and bias respectively,
V. ERROR PERFORMANCE OF SCNN-CNN CTCQ/TCM OVER RICIAN 
FADING CHANNEL
The basic system under consideration (Fig.1) accepts as input real, continuous 
amplitude, discrete-time source sequence produced by a memoryless Gaussian 
source. Combined TCQ/TCM encoder converts the source sequence of length L, 
x=(xj, x2 ,...,xL) into a sequence of encoder output symbols, which are then block 
interleaved to break up burst errors caused by amplitude fades of duration greater 
than one symbol time. At ith signalling interval, the interleaved symbol is mapped 
into the M-PSK signal where M is given as M=2R+1. Corresponding to the M-PSK 
symbol sequence y=(yj, y2 ,...,yL) , a noisy discrete-time sequence r=(rj, r2 ,...,rL 
appears at the output of the channel. The received signal at ith signalling interval is 
expressed as
ri = P i . yi + ni (2)
where ni is the additive Gaussian noise and is Rician distributed.
At the receiver, first the noise-corrupted sequence is demodulated and deinterleaved, 
later passed through the combined TCQ/TCM decoder which employs theViterbi 
algorithm to determine the most likely coded symbol sequence transmitted and pro­
220
duces the output sequence of quantization levels x=(x1, x2,...,xL) under the assump­
tion that there is one-to-one mapping between quantization levels and modulation 
symbols. The analytical upper bound can be derived as (Divsalar and Simon 
1988:1004-1012).
Pu <
1 dT(D,l)
j^Pp2 1+ KD pp = -— —— r-exp
n dl 1=1
(3)
1 + K  + /fy l l  + K  + (3y
y = exp
4 N,o y
Error performance of SCNN-CNN CTCQ/TCM is investigated and upper bounded 
for Rician Fading channel (Figure 3). At the output of the slowly varying Rician 
channel, total noise variance a , 2can be written as,
2
Here,Cf is the variance of SCNN output and the estimated signal at the receiver. 
0 B2is the Gaussian noise variance. Thus quantization noise is also included both 
analytical and simulation results. As an example, Lenna image was applied to the 
proposed scheme as shown in Figure 1 and the results are also given in Figure 4.
VL CONCLUSION
In this paper, Segmented Celular Neural Network-Cellular Neural Network 
Combined Trellis Coded Quantization /  Modulation (SCNN-CNN CTCQ/TCM) 
scheme is denoted. Segmented Cellular Neural Network approach (SCNN) is 
introduced. A new CNN based structure which models combined trellis coded 
quantization /  modulation is investigated. The performance of our combined scheme 
has been analysed over Rician fading channel. Computer simulations studies confirm 
the analytical upper bound curves.
221
References
AKSU H.A. and SALEHI, M. (May 1996) "Joint Optimization of TCQ /  TCM
Systems", IEEE Trans. Commun., vol. 44, pp. 529-533.
CHUA, L.O. (October 1988), "Cellular Neural Networks: Theory", IEEE Trans. On 
Circuits and Systems, vol.35, pp.1257-1272.
CIMAGALLI, V. (May 12-14, 1993), "Cellular Neural Networks: A Review", 
Proceeedings of Sixth Italian Workshop on Parallel Architectures and Neural 
Networks, Vietri Sul Mare, Italy.
DIVSALAR, D. and SIMON M.K. (September 1988), "The Design of Trellis Coded 
MPSK for Fading Channels: Performance Criteria" IEEE Trans. Commun., 
vol. Com-36, pp. 1004-1012.
MARCELLIN, M.W. and FISCHER, T.R. (Jan.1990), "Trellis Coded Quantization 
of Memoryless and Gauss-Markov Sources", IEEE Trans. Commun., vol. 38, 
pp. 82-93.
MARCELLIN, M.W. and FISCHER, T.R. (Feb.1991), "Joint Trellis Coded Quanti­
zation /  Modulation," IEEE Trans. Commun., vol. 39, pp. 172-176.
UNGERBOECK, G. (Jan.1982) "Channel Coding With Multilevel/Phase Signals", 
IEEE Trans. Inform. Theory, vol. 28, pp. 55-67.
UYSAL, M. and UÇAN, O.N. (1997), "Combined Trellis Quantization/Modulation 
over Fading Mobile Channel " ACTS Mobile Commun. Summit, pp.906-911, 
Denmark.
222
FIGURES
Fig.l. Block diagram of combined SCNN-CNN CTCQ/TCM system.
qoi/so> q o 2 / s 4
Fig.2. The trellis diagram for 4-state 8-PSK SCNN-CNN CTCQ/TCM system.
6
7
7
5
223
Pb
SNRt(dB)
Fig.3. Error performance curves for Rician fading channels (K=5 dB).
(d)
(g) (h) (i)
Fig.4. Gray scaled Lenna images at SCNN-CNN CTCQ/TCM decoder output for 
various SNRt values (a)10.3dB (b) 11.3dB (c) 12.3dB (d) 14.4dB (e) 15.4dB (f) 
16.4dB (g) 17.4dB (h) 18.3dB (i) 19.3dB forK=5dB.
224


Performance of Gray Scaled Images Using Segmented Cellular Neural Network - Cellular Neural Network Combined Trellis Coded Quantization / Modulation (SCNN - CNN CTCQ/TCM) Approach Over Rician Fading Channel

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Performance of Gray Scaled Images Using Segmented Cellular Neural Network - Cellular Neural Network Combined Trellis Coded Quantization / Modulation (SCNN - CNN CTCQ/TCM) Approach Over Rician Fading Channel

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Performance of Gray Scaled Images Using Segmented Cellular Neural Network - Cellular Neural Network Combined Trellis Coded Quantization / Modulation (SCNN - CNN CTCQ/TCM) Approach Over Rician Fading Channel

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