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According to this equation the delay splitting differential
mode due to the slightest core ellipticity
seems to be intimately related to the chromatic dispersion of
the fundamental mode. For small ellipticities a proportional
relationship between the measured difference kx — ).y and the
ellipticity may be assumed. Thus, knowledge of the scaling
factor enables the ellipticity to be determined.
Finally, one concludes from Fig- 2 the existence of specific
wavelengths A=JC and A=y giving equal delays for L P l l x or
L P l l y , respectively, and the LP 1 0 mode. In the case of circularly symmetric fibres the wavelength A= may be used for low
mode dispersion transmission. However, it has turned out that
the wavelength / = is strongly dip-dependent.
(dXg)xy of the
Conclusions: The measurement of spectral time delays in the
two-mode region of elliptical-core single-mode fibres proved
to be a conceptually simple method to determine effective
cutoff wavelengths and cutoff wavelength splittings due to different orientations. The stability of the LPn-mode orientation
states in elliptical fibres may possibly be exploited for mode
division multiplex systems.
Acknowledgments: Financial support from the Deutsche Forschungsgemeinschaft is gratefully acknowledged. Thanks are
due to H. Karstensen (Technical University Braunschweig) for
fibres.
K.-F. KLEIN
W. E. HEINLEIN
22nd September 1982
employed being called modems. In both cases the objective is
to match the characteristics of the signal to those of the transmission path, and to introduce modifications into the signal to
facilitate synchronisation, error detection etc. Introduction of
these modifications must involve transmission of additional
information, and to accommodate this redundancy must be
introduced. The design of transmission codes involves the effective use of this redundancy. Up to the present time the
coding techniques used have been relatively simple (see
Appendix A of Reference 1), but now that LSI digital circuits
are available it is reasonable to consider more complex operations. In this letter we describe a coding scheme based on the
use of the class of mathematical operations known as transforms. We describe a specific example based on the use of the
Fourier transform but the technique is general, and other
transforms, such as Bessel transforms and number theoretic
transforms, may be employed. The use of Fourier transforms in
data transmission has received a little attention in the past,2
but, as far as we are aware, earlier work has concentrated on
the use of the transform as a substitute for modulation, and as
a result the more general implications of using transforms as a
means of processing digital signals, and, in particular, the effects of applying a transform to a signal containing redundancy, seem to have been ignored.
General principle: This is shown in Fig. 1. A block of the
incoming digital signal (data) is collected in a register, and
then transferred into a second larger register through a redundant mapping process (referred to as the first mapping).
Lehrstuhlfur Theoretische Elektrotechnik
Universitat Kaiserslautern
D-6750 Kaiserslautern, W. Germany
input
set to complex
conjugate values
References
1
2
GLOGE, D.: 'Weakly guiding fibers', Appl. Opt., 1971, 10, pp. 22522258
YEH, c.: 'Modes in weakly guiding elliptical fibres', Opt. & Quantum Electron., 1976, 8, pp. 43-47
3
KLEIN, K.-F., and HEINLEIN, W. E.: 'Orientation- and polarisation-
4
dependent cutoff wavelengths in elliptical-core single-mode fibres',
Electron. Lett., 1982, 18, pp. 640-641
COHEN, L. G., and LIN, C : 'A universal fiber-optic (UFO) measurement system based on a near IR-fiber Raman laser', IEEE J.
Quantum Electron., 1978, QE-14, pp. 855-859
5
2nd register
(256 x 8 digits)
3rd register
(128 x 8 digits)
BUCKLER, M. J., SHIEVERS, J. w., and PARTUS, F. P. : 'Optimization of
multimode fiber bandwidth via differential group delay analysis'.
Proc. 6th European Conference on optical communications, York,
1980, pp. 33-36
6
input
register
KATO, Y., KITAYAMA, K., SEIKAI, s., and UCHIDA, N.: 'Effective cutoff
wavelength of the L P n mode in single-mode fiber cables', IEEE J.
Quantum Electron., 1981, QE-17, pp. 35-38
0013-5194/82/220947-03$!. 50/0
APPLICATION OF TRANSFORM
TECHNIQUES TO DIGITAL LINE
CODES AND DATA TRANSMISSION
Indexing terms: Data transmission, Codes, Transforms
A method for processing digital signals prior to transmission
through the use of transforms is described. This provides
means for control of the signal spectrum, for improving immunity to interference, and for including adaptive equalisation.
Introduction: It is common practice in digital transmission to
introduce a recoding operation between the primary digital
signal and the output to the transmission path. In high-speed
systems used for digital transmission of telephony and television this operation is called transmission coding. 1 In lowspeed data-transmission systems an analogous process, based
on the digital modulation of a carrier signal, is used, the units
ELECTRONICS LETTERS 28th October 1982
output
Fig. 1 Arrangements for a transform encoder
This redundant block is subjected to a transform operation to
produce a third block of similar size, but with modified
characteristics. In particular, the way in which the redundancy
appears has been altered. In the case of binary transmission
this block could form the transmitted signal, but more generally it is interpreted as a sequence of transmission waveforms
or symbols through a second mapping. The receiver carries
out the reverse sequence of operations, namely a third input
mapping, inverse transformation and a final fourth mapping
to extract the original signal. Note that, although we describe
the input as a binary signal, similar operations could be performed on ternary or other multilevel signals.
Example: We now describe as an example a scheme for recoding 9-6 kbit/s binary data for transmission over a telephony
channel. This involves modifying the spectrum of the signal to
match the bandpass characteristics of the channel, inclusion of
facilities for adaptive equalisation, and various provisions for
improving noise suppression characteristics of the signal.
The first register collects a block of 250 digits of the incoming signal. This block is considered to be arranged as 70
3-digit words followed by 20 2-digit words. It is then mapped
into the first 128 words of a 256 8-digit word register as follows. The first 16 words are set to zero. Following this, 7
blocks of 12 words are formed, with words 31 and 32 passed
over. In each block the first word is set to 64 (for 8 digits the
range is 128 to -127) the second set to 0, and 10 of the 3-digit
words mapped into uniformly spaced levels in the remaining
10 words. Following this the remaining 20 2-digit words are
mapped into words 103 to 128 in a similar manner, with
words 111 and 112 passed over. These 128 words are then
Vol. 18 No. 22
949
taken to represent the real and imaginary components of 64
complex numbers. The remaining 128 words in the second
register are set to the complex conjugates of these values. We
now take this array to represent the discrete frequency spectrum of a signal, so application of an inverse discrete Fourier
transform will produce a third array, of 128 8-digit words,
representing the corresponding time-domain signal. This
signal can be produced by feeding these words into a digital/
analogue convertor (the second mapping). It can now be seen
that by setting the first 8 frequency elements (16 words) to
zero we have ensured that the signal has little energy below
about 300 Hz. The highest harmonic component is about 2500
Hz. The fixed pairs of words in each block represent a set of
constant sinusoidal tones in the output that may be used to
identify frequency and phase distortion in the transmission
path, and can be employed for adaptive equalisation, and for
synchronisation in the receiver. The change from 3 to 2 digit
mapping in the upper part of the spectrum provides greater
noise immunity at high frequencies, where noise levels may be
expected to be higher. The two gaps, which correspond to
250
150
50
-50
Simulation: We have set up a computer simulation to verify
that the characteristics described are obtained. An example is
shown in Fig. 2. Fig. 2a shows the multilevel signal after the
first mapping, and Fig. 2b the signal after the transform operation. This has an RMS level of 63 (arbitrary voltage units).
To this we add Gaussian noise (RMS level 8), an impulse
(peak level 100) and a tone at 576 Hz (RMS level 35) to give
the resulting interference shown in Fig. 2c (RMS level 38).
After the receiving operations this level of interference produces 6 errors in the block of 250 digits. In the absence of the
mapping and transform operation nearly 50% of the digits are
in error when similar interference is added. In this example a
high level of interference was used to obtain a significant
number of errors in a short sample. Further work is in
progress to establish optimum parameter sets for various conditions, and to check performance by physical implementation.
D. G. W. INGRAM*
-150
-250
27th September 1982
University Engineering Department
Cambridge University
Cambridge CB2 1PZ, England
200
100
0
-100
T. T. TJHUNG
-200
100
60
20
-20
-60 :
-100Fig. 2
a Representation of contents of first half of second register as 128
8-digit words (range + 128 to — 127)
b Contents of third register as 128 8-digit words
c Added noise and interference
FAULT COVERAGE OF PATTERNSENSITIVE FAULT-DETECTION
ALGORITHMS FOR SEMICONDUCTOR
MEMORIES
Indexing terms: Computers, Semiconductor memories, Fault
coverage
Experimental studies have been made on the fault coverage
of pattern-sensitive fault-detection algorithms proposed for
semiconductor memories. The experiment is carried out on a
microprocessor-based system. A comparative study has been
made based on the experimental results.
Introduction: Semiconductor memory devices, because of their
regularity, lend themselves to more density than other LSI
devices. Because of this density they have their unique testing
problems. Test procedures for semiconductor random access
memories (RAM) can be divided into three categories: 1 " 8 (a)
functional testing, (b) pattern sensitivity testing and (c) DC
parametric testing. The interaction between the memory cells
due to increased density results in the type of fault known as
pattern-sensitivity faults. We are considering only the coupling
fault as pattern-sensitive fault as defined in References 1-5, not
the timing sensitivity fault as defined by Thatte and Abraham. 6 Thatte and Abraham 6 consider the pattern-sensitivity
fault under the category of functional faults.
Background: Semiconductor memories are available in sizes of
N words with 1 bit/word or N words with m bits/word
(N = 2r, r = 1, 2, 3, ...). For an (N words x 1 bit) memory
there are 2* possible states or patterns. A cell may fail because
of certain bit patterns stored in any other cell in the whole
950
frequencies of 576 Hz and 2112 Hz, ensure that any singlefrequency interference at these points will be eliminated in the
receiver. We will not discuss the receiver operations, since
these follow directly from those in the transmitter, but we note
that any impulsive interference in the transmission path will
be converted into an extended low-level interference by the
receiver transform, and will thus be largely suppressed.
Department of Electrical Engineering
National University of Singapore
Kent Ridge Campus, Singapore 0511
* D. G. W. Ingram is currently a Visiting Professor in the Department of Electrical Engineering, National University of Singapore,
Kent Ridge, Singapore 0511
References
1
BYLANSKI, p., and INGRAM, D. G. w.: 'Digital transmission systems'
(Peter Peregrinus, 1980), Chap. II
2 WEINSTEIN, s. B., and EBERT, p. M.: 'Data transmission by frequency
multiplexing using the discrete Fourier transform', IEEE Trans.,
1971, COM-19, pp. 628-634
0013-5194/82/220949-02S1.50/0
memory (all 2N patterns), and it may be fault-free for other
patterns. Hayes 1 has defined this as an unrestricted neighbourhood, and it is physically infeasible1-3-8 to test a memory
for unrestricted neighbourhood patterns. It is also very unlikely that such interactions will exist in a two-dimensional
memory layout. In practice, one would expect pattern sensitivity to be much more localised, i.e. only a few cells in close
physical proximity of a cell C, can affect operations addressed
to C ; . These cells are called neighbourhoods N(Cf) of C, (it is
customary to include C, in its own neighbourhood). 2 ' 4 - 8 If the
base cell C, is deleted from the set of cells in a neighbourhood,
the resulting set of cells is called the deleted neighbourhood. 4
Based on this neighbourhood concept, several patternsensitive fault models have been suggested and test algorithms
proposed for each of these models by Hayes,2 Srini,3 Suk and
Reddy4 and Thatte and Abraham. 6 So far, no experimental
verification has been made on the fault coverage of these
models. We selected the models and algorithms proposed by
Hayes, Srini and Suk and Reddy to check their fault coverage
experimentally by simulating pattern-sensitive faults. We decided not to include Thatte and Abraham's model because it
has considered only limited patterns. We proposed to check
these test algorithms on an 8085-based microprocessor system
with 3 kbyte of user program memory, 1 kbyte of test memory
and 1 kbyte of result memory. It also contains 2 kbyte ROM
for the resident monitor. The microprocessor system is connected to a P D P 11/34 system for program development and
print-out of results. There is provision for down-loading and
up-loading between the PDP 11/36 and the microprocessor
system. The result memory is needed for storing the results of
the test so that the results can be up-loaded by P D P 11/34
and printed.
The algorithms suggested in References 2, 3, 4 and 6, though
ELECTRONICS LETTERS 28th October 1982 Vol. 18 No. 22
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