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cated a persistent increase in the loss coefficient as a functionof frequency along the extraordinary direction but not alongthe ordinary direction. This indicates that although the loss inLiNbO, is small, it is not negligible.8................. .........I6$ 6 - 5E 4 - 4 x

- 3 $2 - I.................. .4a -i;fJi10.......................... 5 E

& 2 - 43

0 ............ .*.*..-*.:. 2-2 10 20 40 0 80 100 120 140 160

bfrequency, GH zFig. 2 Mic rowav e refractive index and electric field absorption co efl-cient for L iNbO,

a Ordinary rayb Extraordinary rayFor the results presented so far, the samples were alignedwith the optic axis parallel or perpendicular to the electricfield of the transient radiation. Rotating the sample away fromthese positions leads to a transmission function of the typeshown in Fig. 3.The circles (amplitude) and squares (phase) inFig. 3 were taken for the 5.98 sample oriented with

B =45. The lines in Fig. 3 are theoretical predictionsobtained with a transmission-line analog of plane-wave pro-pagation through uniform stratified media.5*6The measuredvalues of no and n, were used in the calculation. Also, themodel included a small loss tangent (0904 at lOOGHz andlinearly proportional to frequency) for the E-field directedalong the extraordinary axis. The addition of this loss,although smaller than the experimental resolution, improvedthe fit between the model and the data, accounting for thedecreasing values of the amplitude peaks seen in Fig. 3.Theagreement between theory and experiment is excellent. Themeasured transmission function shows that the orientedLiNbO, demonstrates filter-like properties for the freely pro-pagating microwave radiation.6no4 1 a160frequency, GH z 1114iljFig. 3 Amplitude and phase of transmission function of 5 98 mmLiNbO , slab oriented

e = 450Predictionsof theoretical calculations using measured valuesof noandne0 Amplitude0 Phase

In summary, the measured anisotropic dielectric propertiesof LiNbO,, in the 15-140GHz frequency range, were present-ed. In addition, frequency-dependent transmission functions ofan oriented LiNbO, crystal were measured and compared totheoretical models.W.M. ROBERTSONG. ARJAVALINGAMG. V. KOPCSAYIBM Research Division, T . . Watso n Research CenterPO Box 218, Yorktown Heights, N Y 10598,U S A

References

IZth November 1990

DOL^, D. w., NAZARATHY,., and IUNGERMAN, R. L.: 40GHzelectro-optic modulator with 7. 5V drive voltage, Electron. Lett.,1988,24, pp.528-529KLEIN,. B.: Dielectric waveguide phase shifters at 95GHz usingthe electro-optic effect in LiNbO,, Ferroelectrics, 1983, So, pp.307-312BRIDGES, w. B., KLEIN, M. E., and s c m ~.: Measurement of thedielectric constant and loss tangent of thallium mixed halide crys-tals KRS-5 and KRS-6 at 95GHz, IEEE Trans., 1982, MIT-30,pp. 2 8 6 2 9 2 (and references herein)AHN, B. H.: Measurement of the indices of refraction and theabsorption coefficients of dielectric materials in the millimeterwave region, J. Appl. Phys., 1983.54. pp.212?-2124PASTOL,.,ARJAVALINGAM,G., HALBOUT,.-M., and KOPCSAY,. v.:Coherent broadband microwave spectroscopy using picosecondoptoelectronic antennas, Appl. Phys. Lett., 1989, 54 , pp. 307-309;ARJAVALINGAM, G., PAsmL, Y., HALBOUT, I.-M., and KOPCSAY, G. v.:Broad-band microwave measurements with transient radiationfrom optoelectronically pulsed antennas, IEEE Trans., 1990,MIT-38, pp. 611-621PAsmL, Y., ARIAVALINGAM, G., KOPCSAV,. v., and HALBOUT, I.-M.:Dielectric properties of uniaxial crystals measured withoptoelectronically-generatedmicrowave transient radiation, Appl.Phys. Lett., 1990,55, pp.,2277-2279KLEIN, M. E.: Phase shiftmg at 9 4 G H z using the electro-optic effectin bulk crystals,Int. J. Infrared and Millimeter Waves, 1981, 2, pp.239-246Microwave nonlinear susceptibilities due to electronic and ionicanharmonicities in acentric crystals,Phys. Rev. Lett., 1971,26, pp.387-390BOYD, G . O., BRIDGES, I. ., POLLACK M. A., and TURNER, . H.:

SOFT RS CODES FOR HALF RATE GSMCHANNELIndexina term: Codes and Coding

~~~~ ~After the adoption in 1987 of the RPE-LTP coder as the22.8 KBPS Pan European Mobile Speech Communicationstandard (full rate GSMt or F-GSM), the next stage in theproject is the development of a CODEC (source and channel)operating at 11.4KBPS (half rate GSM or H-GSM). Manyspeech coding algorithms under evaluation are expected tomeet the stringent quality specifications of H-GSM.However, during operation the channel perturbations areexpected to be twice as bad for H-GSM as for F-GSM.Despite this, an error control scheme which uses lessredundancy and provides performance which for the mostpart is superior to the scheme for F-GSM is expected.A highperformance FEC scheme is presented which employs softdecoded Reed-Solomon (RS) codes on the H-GSM channel.

Introduction: In land-mobile communication systems, thechannel is predominantly perturbed by bursty errors , resultingfrom fading and shadowing effects. These effects depend onthe speed and location of the receiver. It is therefore expectedthat dur ing periods of extreme fading and/or shadowing, error* Regular pulse excitation with long term predictiont Groupe Speciale Mobile

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correction codes will fail and data will be lost. Speechdecoders, with appropriate strategies, have been shown tomaintain speech intelligibility in moderate (5 0%) frame losssituation^.^ For this, the synthesiser needs a fairly certain lostframe indicator from the channel decoder.To combat the bursty channel, one approach is to use inter-frame interleaving (used in F-GSM) to achieve time separa-tion of the code bits. This effectively randomises and shareserror bursts between code frames, facilitating the use ofrandom error correcting codes. In the H-GSM contexthowever, delay constraints make this approach undesirable.Interframe interleaving possesses an inherent algorithmicdelay which ultimately imposes undesirable delay constraintson the source coder. The balance is therefore shifted in favourof burst error correcting codes.Reed-Solomon codes are burst error correcting and give afairly certain indication when they fail. Their main disadvan-tage has been the difficulty of incorporating soft decoding.The H-GSM communication equipment is expected toprovide channel state information for use by the channeldecoder. We report on the use of this information as an aid toerasure decoding of RS codes. For vital frame information, thescheme performs at less than 9% frame loss. This performanceis achieved during channel conditions thought to represent apessimistic evaluation of typical operating conditions forH-GSM.H - G S M ch an n e l : H-GSM and F-GSM will operate on thesame system and physical channel. However, in H-GSM oper-ation, a single speech frame is shared only between twoTDMA slots, frames from the the transmit channel alternatingslots with frames from the receive channel. The channel condi-tions are fully specified and s imulated in a variety of realoperating conditions. These simulations are available to mostEuropean PTTs. The set of channel conditions for which thisFEC scheme was optimised include: C /I = 7dB, frequencyhopping, independent Rayleigh fading with receiver station-ary. As indicated above, these represent a pessimistic evalu-ation of normal operating conditions.S peech coder : The 6.8Kbit/s speech coder, developed in acombined source and channel coding approach is a CELP-like algorithm, using orthogonal vectors to generate the exci-tation. Compromise strategies were adopted at each designstage to match the performances of the speech and channelcoders? A lost frame reconstruction strategy was also devel-oped interactively with both the speech and channel coders.This strategy maintains intelligible speech at up to 20%random frame loss.Ch an n e l en coder : The bit map from each source frame is clas-sified according to parameter importance and bit sensitivity toerrors into three classes. Class I (4 3 source and 2 CRC bits)holds the most sensitive bits corresponding to the mostimportant parameters. Class I1 (3 5 bits) holds the bit mapfrom the moderately sensitive line spectrum pairs (LSP). Class111 is transmitted unprotected and Class I is protected withRSI, a (21, 9) and Class I1 with RS2, a (13, 7) RS code over

The choice of G F (25- 1)was motivated by the fact that,with a guard space of 6 bits during representative channelconditions, about 97% of the bursts are of length < 15 bitsand so are possibly correctable by RS2, the lower redundancycode. The CRC was computed on the 4 3 Class I data bitsusing x6 + x + 1= 0 as the generator polynomial. This FECscheme operates at 4. 6 Kbit/s.Ch an n e l decoder : In error decoding, the inverse transform ofthe recursively extended error spectrum' is subtracted fromthe received vector. RSI is expected to correct six symbols(possibly, a burst of 5 3 0 bits), and RS2 should correct threesymbols (15 bit bursts). In erasure decoding, a t-symbol errorcorrecting (n, k) RS code over G F (q - 1) is expected tocorrect an extra v errors after filling p erased symbols if

GF (25 - 1.x

2t 2 2v + p (1)1Galois field

0

0c

" 4 0 0 -I$-

Therefore, by maximising p (p = 2t - , v = I) , 2t -symbol errors can ultimately be corrected. To achieve thisperformance, we must ensure that in a frame with symbolerror count (SEC) 1 2 t- 1, after erasing 2t - symbols, onlyone symbol error remains. However, as a penalty for suchhigh performance, the probability of decoder error for framesin which more than one symbol error is left after erasuresincreases from pdb.eqn. 2, in nonerasure (hard) decoding to pd,,eqn. 3, in erasure (soft)decoding.

1 - ( P i 2 )1 "-P'CLq - )(3 )

The CRC in RSl and an LSP stability test3 after decodingRS2 are used in detecting such decoder errors.Soft decoding is used in an attempt to achieve the per-formance predicted by eqn. 1. By converting the log-likelihoodratios (LLR) of each transmitted bit in to probabilities of biterror, and combining the probabilities for all bits of a symbolan indication of demodulator certainty about the symbolvalue is obtained. Using the statistics of LLR in a receivedcode block and a given symbol, an algorithm for calculatingan erasure metric for each received symbol was devised. The2t - symbols with the highest metrics are then erased. Fig. 1shows the cumulative distributions of symbol error count(SEC) per code frame over 2000 transmitted frames. Ideally,the distributions should have cutoffs at SEC = t (or 2t - 1 inerasure decoding). However, given that some frames will belost, it is suffcient t o decrease the proportion of frames withSEC 2t - 1 while increasing the proportion forSEC 5 2t - 1by decreasing the proportion with SEC = 0.

i = 0P d, = q ' " - P - x '

0 0 10 0 20 0SEC, /frame

Fig. 1 SEC distribution on channel with no burst sharingWe experimented with various schemes for pushing thecutoffs towards SEC 1 2 t- 1. As expected, interframe inter-leaving schemes gave the best performance, but as explainedabove, they increase the delay. By interleaving the Class 111bits with the other two classes and then interleaving the tworesulting bit maps double-symbol-wise, we were able toimprove the distribution for RS1 significantly and for RS2only moderately (Fig. 2). This scheme constitutes a bit stuffing

and code frame burst sharing approach.As more than 50% of all correctable code frames (Fig. 2)have SEC 5 , erasure decoding for such frames constitutes acomputational overhead. In general, hard decoding isattempted for every code frame and soft decoding is only usedwhen hard decoding fails. Decoding (hard or soft) is said tohave failed when we fail to detect bandwidth folding of theerror spectrum.ELECTRONICS LETTERS 17th January 1991 Vol.27 No. 2 177

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The performance of the implemented scheme is shown inTable 1. Theoretically, soft decoding is expected to augmentdecoding to 92% for RS1 and 76.4% for RS2. However, ascan he seen, the actual performance in both cases is below thistheoretical limit. This is due to limitations in the erasuremetric computation algorithm, especially in RS2 because ofthe small t . Nevertheless, the difference in performance ascompared to hard decoding is quite substantial, especially forRSl which protects the most important class.

40 008N

0 0 100 20 0SEC, /frame 1561121

Fig. 2 SEC distribution on channel with burst sharingFor RS1, say, eqns. 2 and 3 imply a 33% increase in pd.Because only 8% of the frames are nondecodable in the firstplace (Table I), only about 3% of all frames will result indecoder errors. These are for the most part, picked out by theCRC. Decoder, CRC, and LSP test failures are all sent as lostTable 1 THEORETICAL AND ACTUALPERFORMANCE O F CODES

Performance (% frames in 2000)Hard decode Soft decode Actual

RS 1 61.8 92.0 91.3RS2 71.5 76.4 73.4

frame indicators to the speech decoder. The codes were alsotested with random errors (hard decoding only) and no framelosses were recorded for either code up to 3.5 x lo- BERover 2000 speech frames.Conclusions: A soft-decoded multiple RS solution has beenpresented for the H-GSM channel. Its performance has beenshown to be within the bounds of our lost frame reconstruc-tion strategy. With a total bit rate of 11,4Kbit/s , source andchannel coding, the H-GSM bit rate is achieved. It has beenshown that the probability of passing erroneous data to thespeech decoder is very low. A more complete report on thecombined source/channel coding approach of the project willbe published in the near future. Compromise decisions had tobe taken at various stages of this project to adapt the source/channel coders to the channel and to each other. In informallistening tests of the whole simulated speech and channelcoder with lost frame reconstruction, the subjective quality ofthe output speech was comparable to F-GSM under equiva-lent channel conditions.Work on better erasure metric computations to achieve per-formance closer to the theoretical limit is in progress. Realtime implementation work for both source and channel codersis also in progress. To enable efficient computation, the RSdecoder algorithm has been extensively modified. It has beenshown that by knowing and indicating data loss to the speechdecoder, reasonable recovery strategies can be used to mini-mise the degradation caused by burst errors.S . A. ATUNGSIRIP. SWEENEY 12th November 1990R. SOHEILIA. M. KONDOZB.G. EVANSDept . of Electronic and Electrical EngineeringUniuersity of SurreyGuildford, Surrey GU2 SX H, U nited KingdomReferermes

HELLING,K., VARY, P., M A S A ~ U X , D., PETIT, I., GALAND, c., andROW, M.: Speech coder for the European mobile radio system.Proc. of ICASSP-89, Glasgow,UK , pp. 1065-1069KITTLE, L.: Analogue and discrete channel models for signal trans-mission in mobile radio,Frequenz, 1982,36, pp. 153-160ATUNGSIRI, s. A., KONWZ, A. M., and EVANS, B. G.: Error detectionand control for the parametric information in CELP coders. Proc.of ICASSP-90, 1, Albuquerque, NM , USA, April 1990, pp.229-232LEE, K. Y.: Analysis-by-synthesis inear predictive coding. PhDthesis, University of Surrey, Guildford,UK, October 1990BLAHUT, R. E.: Theory and practice of error control codes(Addison-WesleyPublishing Company, Inc., 1983)

DEMONSTRATION OF SOLITONTRANSMISSION AT 2*4Gbit/s OVER12000kmand to show that the long-range soliton-solitoninteraction discovered earlier4 in high dispersion fibre doesindeed become insignificant in low D fibre. In those experi-ments, however, the pulse source was a mode-locked colourcentre laser, producing essentially transform limited, nearlysechz-shaped pulses, at the relatively low repetition rate of200MHz. We show here that nearly identical results can beobtained at GHz bit rates, using a mode-locked diode laser as

Indexing terms: Opt icalfi bres, Optical transmissionThe transmission of 60ps solitons at 2 ,4Ghit/s over paths asmeat as l2OOOkm in a recirculating loot, of dispersion CnllrPPI--_--.ihifted fibre and erbium fibre amplifiers is reported.With amode-locked diode laser as signal source,at each distance, a The recirculating loop (Fig. 1) used the same 25 km lengthsmeaSurements madeof the effectiveulse that is very Of AT&T dispersion fibre ( D = 138p/nm/km, =close to that predicted from jitter in pulse arrival times from 35pmZ, 0.25d~/ kmoss at A = 1532 nm) as in Reference 1.the Gordon-Haus effect. With a gain-switched optical lyfiltered laser as source. however. moss excess Dulse broaden- This time, however, each erbium fibre amplifier was pumpeddirectly, with pump light always propagating counter to the

~~~1~~~ .-~ ~ . . ~ ~ ~~~~~ ~~ ~~ine is observed for distances meater than afew thousand signals. In this way the required pump power to each ampli-kilometres.In a recent paper, we reported transmission of Sops solitonsover paths as great as lO000km through a chain of erbiumfibre amplifiers and 25 km segments of dispersion shif ted fibre.We also reported negligibly small interactions between pulsesseparated by 5 5 or more pulse widths. We were thus able toverify predictionz that such transmission should work well aslong as the amplification period L is much smaller than thecharacteristic dispersion distance (2/n)z0 (zo is the soliton

fier was reduced to less than 20mW, the amplifier gains weremore easily matched to the corresponding segment loss, andthe potential for crossphase modulation of the signals fromamplitude fluctuations in the pump light5 was eliminated.The mode-locked InGaAsP diode laser was embedded in anexternal cavity of 62.5 mm optical length, whose round-triptime (416.66~~)orresponded to just one period of the2.4GHz pulse repetition rate: we thus avoided the periodicpulse-to-pulse amplitude fluctuations typical of a multiple-length cavity. The cavity end mirrors were formed by anuncoated facet of the diode and a 1200groove/mm grating,178 ELECTRONICS LETTERS 17th January 1991 Vol. 27 No. 2