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Simulation results: A simplied asynchronous DS-CDMA system
with BPSK spreading (ideal code, carrier and symbol synchronisation) was simulated using the SPW” software. The channel model
consisted of inter-user interference and AWGN. The short spreading codes corresponding to spreading ratios (processing gains) of
127 and 255 were Gold and Kasami (the large set) sequences,
respectively. Gold sequences of period 2w-1 were used as long
codes. Relative code delays and carrier phases were selected randomly, and they were the same in the simulation of both short and
long codes, i.e. just the codes were changed. Long simulation
times limited the simulation of small BER and large Eb/Nnvalues.
The BER results are shown in Figs. 2 and 3. It can be seen that
the system performance using long codes is 4 . 5 - 1.OdB worse,
when the Eb/Nois -10dB (IOdB i s a typical value in digital cellular
telephone applications). The worse BER performance results from
uncontrolled partial crosscorrelation properties.
10‘’
MER, A.: ‘Multi-rate DS-CDMA A promising m s s technique for
third-generation mobile radio systems’. Proc. PIMRC ’93, 1993,
(Yokohama), pp. 114-1 18
BEKIR, N.E.: ‘Bounds on the distribution of partial correlation for
PN and Gold sequences’, PhD Dissertation, Univ. of Southern
California, Los Angeles CA, 1978, p. 74
Pseudo-syndrome method for supervising
Viterbi decoders at any coding rate
C. Berrou and C. Douillard
Indexing terms. Viterbi decoding, Codes and coding
t
0
2
A new technique for the supervision and synchronisation of
Viterbi decoders, using the novel concept of the pseudo-syndrome,
is presented. This technique is applicable with slight additional
complexity, whatever the coding rate, to all decoders which
contain the function of search for the maximum likelihood path.
Simulation results are presented in the particular case of a K = 7
enoxleddecoder for different rates.
............. j ............................
;.......
...........................
.- . . .
4
signal-to-noise
Node synchronisation: Various ambiguities in the input symbols of
6
8
ratio Eb/NO, dB
Fig. 3 BER of DS-CDMA system when spreading ratio is 255
_ _ _ _ Kasami sequences (the large set) of length 255
__ Gold sequences of length 1073741823
. . . . . Theoretical single user BPSK curve
Spreading ratio: 255, number of simultaneous usen: 20
Conclusion: The loss in the BER performance is tolerable, because
long codes provide several benefits that are desirable in the design
a Viterbi decoder may have to be removed, for instance the relative positions of the symbols after depuncturing and/or demultiplexing. This problem is referred to as node synchronisation;
solving it generally consists in scanning all the possible cases of
synchronisation by relying on a supervision algorithm, able to discriminate between the in-sync (good synchronisation) and the outof-sync (bad synchronisation) behaviour of the decoder.
Among other techniques, node synchronisation based on the
computation of a syndrome has been proposed. The syndrome is a
Boolean [1,2] or possibly a soft [3] value which is representative of
the validity of the decoder input samples as symbols compatible
with convolutional generation. The syndrome is easily identified
for an R = 1/2 coding rate; for instance, with constraint length K
= 7 and encoding polynomials 133 and 171, it is formed (as a
Boolean) by the exclusive-OR of ten symbols considered in hard
decision. For higher rates, a larger number of s);snbols is necessary
to build the syndrome, and its reliability becomes very sensitive to
the channel noise. The pseudo-syndrome method is inspired by
this, but with reduced complexity and improved performance.
state
00
of a large cellular CDMA network. The benefits are [3]: the
number of available individual codes is extremely large, the flexibility with respect to multiple bit rates and variable spreading
ratios is high, there is no need for inter-user or inter-cell synchronisation, and the code does not change when the mobile station
crosses the cell boundary (the handover situation). Slightly worse
BER performance can be improved with powerful error correction
coding as in [2].
IEE 1994
27 April 1994
Electronics Letters Online No: 19940706
K. H. A. KLrkkPinen (University of Oulu. Department of Electrical
Engineering, Telecommunication Lubaratory, Linnanmaa SI, 90570
Oulu. Finland)
M. J. Laukkanen (Nokia Cellular Systems, Teknologiantie 4. 90570
Ouh. Finland)
H. K. Tarnanen (University of Turku, Department of Mathematical
Sciences, 20500 Turku, Finland)
References
on the maximum cross correlation of
(3), pp. 397-399
signals’, IEEE Trans., 1974, IT-U),
2 GILHOUSEN, K.S., JACOBS, I.M., PADOVANI, R., WEAVER, L.A., WHEATLEY,
C.E. and VITERBI, AI.: ‘System and method for generating signal
waveforms in a CDMA cellular telephone system’. Patent No. WO
9200639, 1992
1
WELCH, L.R.: ‘Lower bounds
1036
~~
.
- ( ~ . o , . ~ ( ~ k.‘k.l)
+l
/p?i
7
k‘
191.111
0
(0.0)
tl.0
11
Fig. 1 Convolutional code with K = 3, polynomials 5 (symbol X ) and 7
(symbol Y). and associated decoding trellis
Pseudo-syndrome: Consider in Fig. 1 the convolutional code with
K = 3, polynomials 5 (symbol X ) and 7 (symbol Y), and the
decoding trellis. Suppose for instance that, at time k , the maxi-
mum likelihood path is associated with state 00. If this state was
actually the state of the encoder, at the corresponding time, then
the symbols (X,,,,Y,,,) ‘expected‘ by the decoder is not just any
couple. If a hard decision is considered, it must be either (0,O) or
(1,l); these couples are also compatible with state 01. For the
other two states, couples (0,l) and (1,O) are relevant. It is therefore
possible to build a parity relation between the maximum likelihood state at time k and the symbols coming at time k + l .
By denoting v = K-1 (code memory), let S, = (&,
S,-,,
...SnJ,be the maximum likelihood state at time k. Let also, for a
1/2 rate encoder, GX = @xv, gx,.,, ...gxo) and GY = @yv, gyv.,,
...gyri) be the polynomials associated with the generation of sym-
ELECTRONICS LE7TERS 23rd June 1994
Vol. 30
-
No. 13
~~
Pseudo-syndrome method applied Io K = 7 (polynomials 133, 171)
enco&r/&co&r: Psk is calculated as X,+,OY,+@ S,,,Q SI.*. Fig. 2
shows the probability of having PS, equal to 1, as a function of
the signal to noise ratio E J N , for rates R = 1/2, 2/3, 3/4, 5/6 and
8/9. In the out-of-sync situation, PI { P S , = 1) = 0.5; the dashed
line represents the probability minus the standard deviation s of
the measure, when L is 1024, for a large number of measures. In
the in-sync case, the dashed l i e , for the extreme rates, represents
probability plus standard deviation. From these curves, we can see
that very reliable discrimination may be achieved at low E J N , .
Moreover, it happens that the gaps between these curves are close
to the gaps between the curves yielding the binary error rate
(BER). This means it is quite possible to adopt the same threshold
for all coding rates, corresponding roughly to the same BER.
Conclusion: A very simple supervision/synchronsationmethod has
heen proposed for Viterbi decoders which already possess the ability to search for the maximum likelihood path or state. This
method, based on the calculation of the so-called pseudo-syndrome, offers very reliable discrimination between in-sync and
out-of-sync cases. The associated circuit and its parameters can he
independent of the coding rate. It has been implemented successfully in the first turbo encoder/decoder [6lfor supervision needs.
Acknowledgments: The authors thank A. Glavieux for his relevant
remarks on the presentation of this Letter, and COMATLAS for
their support.
0 IEE 1994
27 April 1994
Electronics Letters Online No: 19940737
C. Bemu and C. Douillard (Telecom Bretagne, Integrated Circuits
Lab., BP 832, 29285 BREST Cedex, France)
References
MCELIECE, R. 1..
and
SWANSON. L.:
'Node
synchronisation for the Viterbi decoder', IEEE Trans., 1984,
COM-32,(5) pp. 524-531
SODHA,J., and TArr,D.: 'Node synchronisation for high rate
convolutional codes', Electron. Lett., 1992, 28, pp. 81&812
SODHA.J., and TAIT,D.: 'Soft-decision syndrome based node
synchronisation', Electran. Lett., 1990, 26, pp. 1108-1 109
BERROU, c . , GLAVIEUX. A., and PHITIMAISHIMA, P.: 'Near Shannon
l i t errorcorrecting coding and decoding: Turbo-codes'. Proc.
IEEE Int. Conf. on Communications (ICC'93), Geneva,
Switzerland, 1993, pp. 1064-1070
BERROU. c . , and GLAYIEUX, A.: 'Turbo-codes: General principles and
applications'. 6th Int. Tirrenia Workshop on Digital
Communications, 1993
'CAS5093: Turbo encoder/decoder'. Data sheet, COMATLAS,
Chateaubourg, France,Nov. 1993
1 LORDEN, G.,
2
3
4
5
o.5
--
I
!
!
6
out-of-sync decoder
~=0.016
-R=~e~a__~_,5=0.01q--_
Wideband trapezoidal stri grating for
elimination of specular rJection
T. Mathew, D. S. Stephen, C. K. Aanandan,
P. Mohanan and K. G. Nair
Indexing terms: Grotingfilters. Radar cross-sections,
Electromagnetic wave-diffraction
A trapezoidal strip grating surface that eliminates specular
reflections almost over the entire X-band frequency range for TM
polarisation is reported. This new grating structure ovemmes the
bandwidth limitation of conventional rectangular strip grating
surfaces.
Eb"O
Fig. 2 Pr (PS, = 1 ) in out-of-sync and in-sync conditions o decoder of
K = 7 (133, 171) code for rates R = 1/2, 2/3, 3/4, 5/6 and &&
Quantisation of 4 bits
-mean value
- - _ _mean value minus (out-of-sync) or plus (in-sync, R = 112 and
8/9) standard deviation s for L = 1024
ELECTRONICS LETTERS
23rd June 1994
Vol. 30
Inrroduction: Blazed reflection gratings, capable of scattering plane
electromagnetic waves to first order diffracted waves have been
studied extensively [I, 21. The most common blazed grating consists of rectangular corrugations on a conducting surface. Reflector backed rectangular strip gratings have been reported that can
be used to simulate the effects of cormgated surfaces [3]. They
No. 13
1037
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