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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