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Error control in mobile-radio data communication

R. C. French and P. J. Mabey

172 Philips tech. Rev. 39,172-182,1980, No. 6/7

Mobile radio - an essential for police, fire brigades, ambulances, taxis and public transport -can transmit far more than simple spoken messages. Selective calling, fast and automatictransfer of standard messages, transmission of printed text to and from the vehicle and even ofpictures are allpossible with the use of digital transmission. However, the mobile-radio channelis plagued with fading and interference, and quantitative information relating to this has beencollected in measurement runs in central London. Despite the channel imperfections, reliabledata transmission ispossible, but it is necessary to use carefully selected codes in which sufficient'redundant' bits have been added to the information bits to enable errors to be detected andcorrected.

Digital signals in mobile radio

Applications

In mobile radio spoken messages are transmitted toand from vehicles. For a long time this was the onlyfunction of mobile radio, and it still is in many cases.However, with the increasing use of data processingin binary digital form, it is a natural development toapply the same methods to mobile radio. The pos-sibilities are many and varied.

intended for others. In addition, the mobile stationalways gives its own identity code automatically at thestart of every transmission; this ensures that the trans-mitting vehicle is identified at the base station. Similarsystems, but working with combinations of audiotones, are on the market [1].

Digital signalling can also be used to report thestatus of the vehicle. The mobile operator can do thisby setting a selector switch on his equipment to the

Fig. 1. Pye MOU 1000 mobile data unit, for operation with the OS 1000 vehicle-availabilitysystem. A hundred pre-numbered messages can be sent (SEND) and received (MESSA GE). Thestatus of the vehicle can be reported by using ten other pushbuttons - 'busy', 'free', 'on watch',etc.; these messages are sent automatically in response to a call from the base station. An identity-code card is inserted in the slot al lower left.

One example is a selective calling system. When avehicle is called, the base station first transmits thedigital code for that vehicle. The receiver in thevehicle reacts by switching on the audio circuits, sothat the call can be heard. The other receivers remainquiescent and no-one is distracted by messages

R. C. French, Ph.D., and P. J. Mabey, B.Sc. (Eng.), are withPhilips Research Laboratories (PRL), Redhill, Surrey, England.

appropriate position - e.g. 'busy', 'free', 'on watch','off watch' - and the base station periodicallyrequests the status of all vehicles, which then replyautomatically. Such a system is also on the market [2].

In addition, this system can send a hundred precodedand numbered messages; the operator chooses theappropriate number and presses the SEND button(fig· 1).

Philips tech. Rev. 39, No. 6/7 DATA COMMUNICATION BY MOBILE RADIO 173

Data transmission is also used for vehicle locationby radio [3]. Moreover, it can increase the inforrna-tion flow to the vehicle. The vehicle can be providedwith a printer unit that will reproduce maps, pictures,etc.; matrix printers are very suitable here (jig. 2).A computer terminal can be fitted in the vehicle fordirect interrogation of a data base; police in Canadaare already using such methods in detective work.Finally, we should mention here the application ofdigital transmission in larger systems for calling indi-vidual persons by radio (e.g. digital radio pagingschemes in London and Chicago) [4] and for diallingtelephone connections between a vehicle and thepublic telephone system.

Reception conditions and interference

In the United Kingdom, the mobile-radio frequen-cies are about 173 MHz in the VHF band and about462 MHz in the UHF band, i.e. wavelengths of about1.7 m and 65 cm. Narrow-band frequency modulationis used (the channel spacing is 25 kHz at UHF and12.5 kHz in the VHF band).One of the problems in mobile radio is the economic

use of the frequency spectrum. In the Philips researchorganization and elsewhere efforts are being made tofind digital modulation systems that give a minimumbandwidth [5]. The methods so far used in digitalmobile-radio transmission include frequency-shiftkeying (FSK) of a subcarrier [6].

Another problem is the corruption of the digitalsignal by noise of various origins, and we shall con-sider this here. Mobile radio has to operate underextremely unfavourable conditions. The transmitterpowers are low, e.g. 20 W from a base station (5 Wfrom a mobile unit), and the transmitting antennasare not very high, e.g. 30 m above the ground. Thismeans that the field-strength is small and the meansignal voltage at the receiver antenna input may oftenbe only a few microvolts. Multiple reflections of thesignals by hills and buildings set up a standing-wavepattern, so that there are rapid variations in signalstrength ('fading') as the vehicle moves through thepattern; the signal level of ten changes by more than20 dB in less than a metre. In addition to the reflec-tions there is the shadowing effect of hills and tallbuildings, which lowers the mean signal level locally.

Besides poor propagation the received signal is con-taminated by ignition noise from nearby vehicles andwith 'co-channel interference' resulting from re-use ofthe same radio channel in another part of the country.The ignition noise results in a significant number oferrors in the received data signal, particularly athigher bit rates in the lower-frequency mobile-radiobands. Co-channel interference resulting from chan-

nel re-use is significant because of the great variabilityin both the wanted and the unwanted signals causedby multipath propagation, which makes it necessaryto use large re-use distances [7]. However, a shortageof radio channels encourages the use of the minimumre-use distance possible.

Fig. 2. As shown by this picture of Marilyn Monroe, a generallyuseful identity portrait can be obtained by printing out the image,transmitted in digital form by the mobile-radio system, on a matrixprimer. Maps, etc., can also be rapidly made available to thevehicle crew in [he same way.

[1] An example is the UED 6 universal encoder-decoder unit madeby Pye Telecommunications Ltd, Cambridge, England.

[2] Pye DS 1000 vehicle availability system.[3] R. W. Gibson, PINPOINT - a radio system for locating and

monitoring vehicles, Philips tech. Rev. 35, 15-22, 1975.[4] R. H. Tridgell, The application of coding techniques to radio-

paging, in: 1980 Int. Zurich Seminar on Digital Comm.,pp. C 9.1-9.5.

[5] L. E. Zegers and C. B. Dekker, A comparison of digital trans-mission techniques for standard FM mobile radio sets, IEEETrans. COM-25, 364-368, 1977.F. de Jager and C. B. Dekker, Tamed frequency modulation, anovel method to achieve spectrum economy in digital transmis-sion, IEEE Trans. COM-26, 534-542, 1978.

[6] H. C. van den Elzen and P. van der Wurf, A simple method ofcalculating the characteristics of FSK signals with modulationindex 0.5, IEEE Trans. COM-20, 139-147, 1972.An explanation of FSK is given in F. W. de Vrijer, Modula-tion, Philips tech. Rev. 36, 305-362, 1976.

[7] R. C. French, The effect of fading and shadowing on channelreuse in mobile radio, IEEE Trans. VT-28, 171-181,1979.

174 R. C. FRENCH and P. J. MABEY Philips tech. Rev. 39, No. 6/7

These poor reception conditions cause a high bit-error rate (e.g. 10/0)with digital signals. To permit anaccurate estimate of the transmission quality to beobtained a good statistical description of the errors isrequired. We therefore made measurements in avehicle, both in London and near the laboratories atRedhill [8]. Tape recordings were made of the errorpatterns in real conditions to investigate various error-detecting and error-correcting codes. It was foundthat when a code with sufficient added 'redundant'bits was used, satisfactory data transmission was pos-sible even on the difficult mobile-radio channel. Weshall look at this in more detail later. Before that,however, we shall give an account of the measure-ments in a moving vehicle and we shall discuss theerror rates at various signal levels and various bitrates.

Measurements in London

The measurements in London enabled us to collectstatistical data about the field-strength distributionand the bit errors introduced in digital transmission.The measurements were made at 17 locations (fig. 3).The transmitter was located on the roof of MullardHouse, a ten-storey office building in central London,and had a power of 3.5 watts; the transmissions weremade in the UHF band at a frequency of 462.425 MHz.The continuously transmitted data signal was apseudo-random sequence consisting of a repeatedcycle of 127 bits.The test vehicle carried equipment for recording the

signal level at the antenna and the errors in thereceived data signal. The signal level was sampledperiodically during the test runs and the dB valuesobtained with the aid of a logarithmic amplifier wererecorded on a cassette tape. This data was used laterfor calculating mean values and statistical distribu-tions on a minicomputer. Fig. 4 shows a number ofmean values, each relating to a test run of 7 minutes ata certain distance from the transmitter. For compari-son we have included a curve showing the signallevelto be expected for propagation in free space. Themeasured values were 30 to 50 dB below this curve!Similar results have been found elsewhere [9].

The errors in the received data signal were detectedby synchronously generating the same 127-bit pseudo-random sequence locally in the vehicle and comparingthe local and received sequences. The outcome of thiscomparison was recorded bit by bit on a digital cas-sette tape. Besides single isolated bit errors, mainlydue to ignition noise, there are short periods (typicallyten milliseconds) during which many of the bits are inerror. These are known as bursts of errors and are the

result of passing through a fade. If it is assumed thatthe fades are half a wavelength apart and that thevehicle travels at 30 krn/h in town traffic, this meansthat it passes through about 26 fades per second.

• ·Comden• Town

Fig. 3. The map of central London, showing the 17 locations (.)where the field-strength and bit-error measurements were made in amoving vehicle for mobile-radio studies. The transmitter (Basestation) was located on the roof of Mullard House, a ten-storeyoffice building near Tottenham Court Road.

60dBr---~-------------------,

t40

20

o

o 2 4 6 8 10km-d

Fig. 4. Measured points: level Lav of the received signal, averagedover a run of seven minutes at a distance d from the transmitter.o dB corresponds to 1 IlV at the antenna terminals. Curve: thesignallevel as it would be for propagation in free space.


The number of errors due to noise and fadingwould be expected to depend on the bit rate. Measure-ments were therefore made at various bit rates:37.5 bits/s, 1200 bits/s and 4800 bits/so The low bitrate of 37.5 bits/s was included in the experimentsbecause it is used in selective calling and pagingsystems. However, if more data has to be transmittedthis bit rate is too low; the Pye DS 1000 system men-tioned earlier operates with a bit rate of 1200 bits/soThe number of bit errors is found to increase

markedly when the duration of a single bit becomesshorter than the time taken to go through a fade. Thiswas demonstrated most clearly in experiments madein the immediate neighbourhood of our laboratoriesat a field-strength high enough for the effects ofignition noise to be negligible. In these suburban sur-roundings the vehicle can travel faster - at about45 krn/h (28 mph) - i.e. about 40 fades per second.It can be seen from fig. 5 that the bit-error ratebecomes about three orders larger when the bit rateincreases from 37.5 to 150 bits/s, with very littlefurther increase above 150 bits/soThe same trend was found in the measurements

made in London. A comparison of the three bit ratesmentioned above can be made from fig. 6 [10], buthere the error rate has been plotted against the meansignal level. Besides fading and shadowing, ignitionnoise also played a part here. The curves shown arebased on means for a seven-minute run. The curvesfor 1200 bits/s and 4800 bits/s have a slope that cor-responds approximately to a decrease in the bit-errorrate by a factor of ten for a 10 dB increase in the meansignal level (i.e. a tenfold increase in power). Thecurve for 37.5 bits/s is much steeper. Even at a signallevel of less than 10 dB (with respect to 1 f.LV) the bit-error rate has fallen to less than 10-5• This means thatsystems that operate with this low bit rate, such asthose for selective calling, simple position reportingand other short messages, can be sufficiently reliablewithout the use of error-control codes.This is not the case at higher bit rates. To reduce the

error rate to an acceptable value (l0-5 to 10-6) error-detecting or error-correcting codes will have to beused here. For these codes it is necessary to group the

[s] R. C. French, Radio propagation in London at 462 MHzRadio and electronic Engr. 46, 333-336, 1976. 'R. C. French, Mobile radio data transmission in the urban en-vironment, in: IEEE 1976 Int. Conf. on Communications(ICC 76), Philadelphia, pp. 27.15-27.20.

[9] E.g. in Tokyo: Y. Okumura, E. Ohmori, T. Kawano andK. Fukuda, Field strength and its variability in VHF and UHFland-mobile radio service, Rev. Electr. Comm. Lab. 16,825-873, 1968.

[10] R. C. French, Error performance in mobile radio data trans-mission in the urban environment, NTG-Fachber. 61, 83-881977. '

bits in words or 'blocks'. It is then important to knowhow many errors might be expected in a single block,since this number is the critical factor in the choice ofa code. For blocks of 64 bits this number can be read

t ---L---/»;

I37.5 600 2400 bits/s150

Fig. 5. Bit-error rate Pbo measured as a function of bit rate. Pboincreases rapidly as the bit period becomes shorter than theduration of a fade. The vehicle speed was 45 km/h; there wereabout 40 fades per second. SignalieveilO dB (with respect to 1 IlV),no ignition noise.

10-1r---------------------------------~

-Lav

Fig. 6. The bit-error rate Pbo as a function of the mean signallevelLav, measured in London. At higher bit rates the error ratedecreases by a factor of about 10 for an increase in level of 10 dB.At 37.5 bits/s the duration of a single bit is longer than the timetaken to pass through a fade; as soon as the signal is strong enoughto override the ignition noise a very reliable transmission isobtained.


off from the cumulative error distribution in fig. 7,which is calculated from the measured results at a bitrate of 4800 bits/so It can be seen from this figure, forexample, that at a mean signal level of 11 dB (withrespect to 1 J.1V)1% of the blocks have eight or moreerrors. At 0 dB 1% of the blocks have 21 or moreerrors and one block in a thousand has as many as32 errors, the same number that would occur if nosignals at all were received.

Principles of coding for error control

Error-control coding is used to prevent false mes-sages from being accepted, by detecting errors, or toenable messages to be accepted despite the occurrenceof bit errors, by correcting errors. When an error-detecting code is used, code words containing errorsare discarded. This results in some characters beingleft out when the message is printed. The code wordsmay be repeated to complete the message. Error-cor-recting codes, on the other hand, will correct some ofthe errors so that fewer repeats are necessary.Without error-control coding, every. combination

of received bits is a valid message, and bit errorswill transform a transmitted message into a different,false message. With an error-control code, the bitsequences transmitted are restricted so that only cer-tain combinations of bits form valid messages. This issimilar to written language where not all combina-tions of letters form valid words. The bit patterns ofthe code, the code words, are chosen so that when biterrors occur, the resulting bit sequences rarely formvalid code words. Error detection consists in recog-nizing when invalid words have been received. This issimilar to detecting errors in written language bydetermining whether the words are in the dictionary.Error correction consists in estimating which codeword was transmitted when an invalid code word isreceived, which is like locating the most similar wordin the dictionary. Comparison of an invalid word withthe most similar valid word enables the bit errors to belocated and corrected.

In order to restrict the bit patterns which are trans-mitted without restricting the messages which may besent, redundant bits must be transmitted. Check bitsare appended to information bits to form code words.Coding theory provides rules for calculating the checkbits from the information bits, ensuring that theresulting code words are dissimilar bu! withoutadding an excessive number of check bits. The moredissimilar code words are, the less likely it is thatsufficient errors will occur to transform one codeword into another code word, so the less likely falsemessages will be.

For example, if code words differ in at least threebit positions, then at least three bit errors are neces-sary to cause a false message which will pass un-detected. Furthermore, if only one bit error occurs,then the corrupted code word will be more similar tothe transmitted code word than to any other codeword, and so the error can be corrected. If a decodercorrects errors, then, in our example, fewer than threeerrors are sufficient to cause a false message. If two bit

10-'

P(?::m.64).

t 10-2

n=644800bits/s

10-5 '-- ---L ....I..J

1 10-m

100

Fig. 7. The probability P(~ m,64), that the number of errors in acode word of 64 bits is equal to m or more, for various mean signallevels Lav. The probability was calculated from the measurementsmade in London and is of interest for the application of error-detecting or error-correcting codes.

errors occur, then the corrupted code word may bemore similar to a false code word than to the trans-mitted code word.

In coding jargon, the number of bits by-which themost similar code words in a code differ is called the'minimum distance' of the code and is normally de-noted by'd. When fewer than d errors occur we can besure of detecting the errors, when d or more errorsoccur there is a risk that a false message is formed. Ifwe use an error-correcting decoder we can be sure ofsuccessfully correcting (d - 1)/2 or fewer errors. Withmore errors there is a risk of a false message. Thechance of a false message can be calculated [11].

As well as providing rules for calculating the checkbits from the information bits, coding theory alsoprovides simple algorithms for implementing en-


coding. A,simple encoder also means a simple error-detecting decoder. As mentioned above, error detec-tion consists in determining whether the receivedinformation and check bits form a valid code word,i.e. whether the received check bits are the same as areobtained by re-encoding the received informationbits. If there are errors in either the information or thecheck bits, re-encoding results in a different set ofcheck bits from those received. It is not possible withan error-detecting decoder to know whether the errorsare in the information or the check bits.Error correction is more complex to implement

than error detection, but again coding theory providesalgorithms. In 'cyclic block codes', which are the onesconsidered in this article, each check bit is an overallparity check on a different set of the information bitssuch that each information bit is cross-checked. Eachcheck bit is chosen so that the information bits andthe check bit together have an even number of binaryones. By noting which of the parity checks fail, i.e. bynoting which of the recalculated check bits differ fromthe received check bits, it is possible to determinewhich bits of the code word are in error and correctthem [12].

In the following we shall represent the number ofbits in a code word by n, and the number of informa-tion bits in it by k, so that there are n - k check bits ineach code word. An error-detecting code will be de-signated as an (n,k) code for convenience; in a (15,7)-code for example each code word consists of 15 bitsand includes 7 information bits. An error-correctingcode will be designated as an (n,k,t) code, where tindicates the number of bit errors that can be cor-rected per code word.

The simplest example of an error-detectlng code is a code i,nwhich each word of n bits consists of n - 1 information bits andone check bit. The value of the check bit is chosen to ensure that theword contains an even number of binary ones (even parity). Alter-natively odd parity could be used. Now if a single error occurs inthe transmission (in an information bit or in the check bit), the

. parity of the received word will not correspond to the prearrangedparity, showing that there is an error. It is clear that this tn,n - 1)code is only able to detect odd numbers of errors in a code word; itis therefore of no use in mobile radio. An error-detecting code foruse in mobile radio will have to contain more check bits.If it is desired not only to detect an error but to correct it as well,

then it is necessary to find out first if there is an error and thenwhich bit is incorrect. With a single error in a code word of n bitsthis amounts to n + 1 unknowns. The n - k check bits must be ableto supply at least this amount of information, so that for the cor-rection of a single error the condition necessary is

2n-k;:: n + 1.

The number of check bits decides the number of check operationsthat have to be made. The check mechanism consists of a set ofequations in which suitably chosen bits from the code word aresummed modulo 2 to check for even parity (or odd parity if

desired). Each check operation provides· one bit; these bits form anumber called the syndrome. If there are n - k check bits, the syn-drome also consists of n - k bits. The value of the syndrome can beused to find the position of the error.

Choosing the optimum code

The choice of a code for any data-transmissionsystem should take into account the characteristics ofthe communications channel. In some cases, the per-formance of a code may be calculated under theassumption that no clustering of errors occurs, butthat all errors are independent. This approach permitsa straightforward mathematical prediction of per-formance but can give very misleading results formobile radio. For example, a code which, accordingto independent error calculations, enables 99.9990/0ofcode words to be received correctly, in fact results inonly 99% of the code words being correct when thecode is used for mobile radio. It is therefore impor-tant to know what the error distribution is, and thisinformation is contained in the error-pattern recor-dings.

One approach used for assessing the performanceof a code is to build an encoder and decoder in hard-ware or software and to transmit data between themin the laboratory, permitting the real error patterns tocorrupt the data before it is decoded. This method hasits limitations, as it leads to lengthy measurements,particularly if very small probabilities are to bemeasured. If, for instance, only one false message in amillion occurs in a coding scheme then many millionsof messages will have to be processed in order tomeasure the false rate. This requires very long error-pattern recordings, far longer than could be collectedconveniently while driving round a city.

We adopted a method of code evaluation whichovercomes the problems described above by analysingthe error pattern statistically. Performance can then

[11] R. W. Lucky, J. Salz and E. J. Weldon, Jr., Principles of datacommunication, McGraw-Hill, New York 1968, pp. 355-360.P. J. Mabey, Mobile radio data transmission - coding forerror control, IEEE Trans. VT-27, 99-109, 1978.

[12] Coding theory and error-correcting algorithms have beenstudied extensively at the Philips research laboratories inBrussels; see for example:J.-M. Goethals, Combinatorial decoding methods for blockcodes, in: Théorie de l'information, Coli. Int. CNRS No. 276,Paris 1977, pp. 223-231;J.-M. Goethals, Single-channel error-correcting convolutionalcodes, Philips J. Res. 33, 248-253, 1978.

[13] Another approach would be to model the error distributionmathematically and use the mathematical model to analyse theperformance of codes. This approach was used at the Philipsresearch laboratories in Brussels to evaluate codes for cor-recting bursts of errors occurring on computer magnetic discs.Results can be found in: Ph. Piret, Structure and errorprobability of burst-correcting convolutional codes, PhilipsRes. Repts. 27, 244-256, 1972.


be simply calculated, different codes can be quicklyassessed, and the effect of changing the code para-meters seen [13].

Error-pattern analysis and code-performance calcula-tionTo assess the performance of a code we need to

know how often a code word is corrupted by errorsand how often the error-detecting or error-correctingability of the code is exceeded. To find this out, wedivided the measured error patterns into blocks of bitsand counted the number of errors in each block. Theresults of this are plotted as the probability P(2:. m,n)of finding m errors or more in a block of n bits, as afunction of m and with n as a parameter. Fig. 11 (dis-cussed more later) illustrates the P(2:. m,n) distribu-tions (solid lines) for a range of block lengths n (from7 to 255 bits) based on error patterns we measured at amean received signallevelof 1.9 dB (with respect to1 !LV).It shows, for example, that at this signallevel2070 of 15-bit blocks will contain three or more errors.

We used the P(2:. m,n) distributions to calculate theperformance of codes in terms of their success ratePc and false rate Pi; Only cyclic block codeswere considered. These codes have also been widelyinvestigated elsewhere, and many powerful codeswith simple encoding and decoding procedures areknown [14].

For error-detecting codes, the following equations are used in thecalculations:

Pc = I-P(";? I,n),

Pe '" z-rp(";? d,n).

Here Pc is simply one minus the probability of any errors P(";? I,n).In eq. (2), r is the number of redundant bits in each code word.Remembering that all code words differ from each other by at leastd bits, we can derive the approximate equation for Pe as follows.An error-detection decoder tests for errors by checking whether areceived block is a code word, Le. if the r check bits are those thatfollow from the k information bits. Now the probability that the 'rcheck bits are right by chance is 2-r, and this is the first factor in(2). Secondly, the error pattern must contain at least d errors to cor-rupt one code word to another, hence the P(";? d,n) factor.For error-correcting codes, the following equations apply. A de-

coder is assumed that corrects all patterns of t or fewer errors, anddetects all other correctable patterns.

Pc = I-P(";? t + I,n),

t

Pe == P(";? d- t,n)z-r Lep.j=O

Here Pc is one minus the probability of t + 1or more errors. Again,the equation for Pe comprises two factors as follows. If all the 2n

possible received bit patterns were corrected to a valid code word,then for each code word there would be 2n/2k = 2r correctableerror patterns. However, only patterns of j :5 t errors are corrected.

For every integer j there are Cp possible patterns of errors [16]; thefraction of the 2r correctable error patterns which the decoder willactually attempt to correct is therefore

Further, for an erroneous decoding d - t or more errors mustoccur.

Throughput

The value of a code cannot be assessed in terms ofits success and false rates alone. Throughput, i.e. thenumber of information bits transmitted per second, isa very important parameter from a practical point ofview, and will become even more so as the mobile-radio spectrum becomes more crowded and morechannel sharing is introduced. Throughput will sufferif more check bits are added to increase the successrate or lower the false rate or both.

(1)

(2)

Error-detecting codes

Error-detecting codes are of interest because verypowerful codes are available which are easily imple-mented, in both hardware and software. Integratedcircuits are available which perform encoding and de-coding of commonly used error-detecting codes.As an example, the encoding of ASCII characters is

considered. The ASCII code is a seven-bit code foralphanumeric characters; it is identical with the inter-national ISO 7-bit code [16] and it can be used forcommunicating with a mobile printer or visual-dis-play unit and for sending messages from a mobilekeyboard.A single seven-bit ASCII character could be en-

coded in a (15,7) code. Fig. 8 shows the success rateand false rate of this code, calculated using the realerror patterns, for a range of mean received signallevels. At a typical mean signallevelof 10 dB about99% of the code words are received error-free so.about 99% of the characters would be correctlyprinted or displayed. Most of the other code wordshave the errors in them detected so these characterscannot beprinted or displayed. A space could be leftor a special null character substituted. Only one in amillion code words at 10 dB have errors which passundetected and will result in an incorrect character.As the signal level is increased the success rateimproves only gradually, an increase of 14 dB beingrequired to improve the success rate from 99% to99.9%. An increase in level of 14 dB is equivalent to asignal-power increase by a factor of 25. So increasingthe transmitter power is not an efficient way of im-proving the performance.

(3)

(4)


Fig. 8. Success rate Pc (a) and false rate Pe (b) when a (15,7) code for error detection is used (eachcode word consists of 7 information and 8 check bits). The success and false rates have beenplotted against the mean received signal level La. (0 dB ~ I JlV).

Better coding provides a more useful solution. Therepetition of code words, the use of a higher bit rateand the use of an error-correcting code are three waysof getting a better success rate.,

Repetition for improved success

To ensure a very high success rate code words canbe transmitted more than once. A simple schemewould be to send every code word twice. On a burst-error channel, if a code word is corrupted by errorsthen a repeat sent immediately after may be corrupted

0.------------------,

0.9999L..._L0--1-'="0--2'-:-0----:-30'=""d--'B

-LavQ

by the same burst, so for maximum benefit the repeatshould be delayed. A delay of a few code-wordlengths at 1200 bitsis is typically sufficient to makethis burst effect negligible [17].

Automatic repetition of every code word will halvethe throughput on the channel. If a return channel isavailable the error-detection decoder can request re-transmission of just those code words that were cor-rupted by errors so that the throughput is negligiblydegraded under normal conditions.

Higher bit rate

Data-transmission equipment currently being intro-duced for mobile radio commonly uses a data rate of1200 bits/s, However, the mobile-radio channels,which, in the UK, are spaced at 12.5 kHz in the VHFbands and at 25 kHz in the UHF bands are capable ofsupporting data rates of 4800 bitsis or 9600 bitsis ormore respectively, using direct frequency modulationof the radio-frequency carrier, without the intro-

duetion of a subcarrier, which is customary at1200 bits/s. These higher bit rates result in longerbursts of errors than at 1200 bits/s, so an error-de-tecting code will have a poorer performance whenused at these higher bit rates. But it is important toknow whether, by using more redundancy, a systemoperating at a higher bit rate can equal the per-formance of a 1200 bitsis system and in additionachieve a higher throughput.A comparison was made using the UHF measure-

ments at 4800 bitsis and 1200 bits/s, The per-

ur L...J__ _J.__ --l.__ --..L..__J

o 10 20 30dB+-r- t-;

formanee of a (15,7) error-detecting code is plotted infig. 9 for both bit rates. The success rates in each caseare not very different, while the false rates are, at10 dB, almost an order of magnitude worse at thehigher bit rate. This difference in false rate may bemade up for by using three or four additional bits ofredundancy at 4800 bits/s, For example the false rateof a (19,7) code is also shown in fig. 9b and is betterthan the (15,7) code at 1200 bits/s. The throughput is560 information bits per second by sending the (15,7)code at 1200 bits/s, and more than three times this bysending the (19,7) code at 4800 bits/s. Transmittingdata at 4800 bitsis therefore allows a significantly

[14! W. W. Peterson and E. J. Weldon, Jr., Error-correcting codes,MIT Press, Cambridge Mass. 1972.

[16! C]' is the binomial coefficient, also denoted by (1).[16! ASCII: American National Standard Code for Information

Interchange. The code conforms to the international standardISO 646 (1973).

[17! R. C. French, The mobile radio data channel, in: 1980 Int.Zurich Seminar on Digital Comm., pp. D1.1-1.9.

180 R. C. FRENCH and P. J. MABEY, Philips tech. Rev. 39, No. 6/7

0 --_ 4800bitsls10-4

--- 4800bitsls-- 1200bitsls \\ 1200bitsls

0.9 10-5 \\ \.\0.99 10-6 \.

! .~. Pe (19,71\

~. t 10-7 \\Pc 0.999

\0.9999 10-8

0 10 20 30dB 0 10 20 30dB-Lay -Layg Q

higher throughput to be obtained for the samereliability as at 1200 bits/s, and the error-detectiondecoder need not be much more complex.

Error-correcting codes

Error-correcting codes provide a means of obtain-ing a high success rate in systems which are restricted

Fig. 9. Success rate Pc (0) and false rate p. (b) when a (15,7) error-correcting code is used at twobit rates. The higher bit rate increases the throughput. The deterioration in p. at the higher bitrate can be counteracted by adding four extra check bits to each code word. Even with the extracheck bits the throughput is still three times greater at the higher bit rate.

0.99

0.999

lFt: 0.9999

••

0.99999 0 20 30dB10-Lay

Q

10-'~------------------~

10-5 I......l __ ~--L. _.J._ _J....__J

o 10 20 30dB-Lay

Fig. 10. Comparison of an error-correcting code (Cor) with an error-detecting code (DeI). Bothcases refer to a (15,7) code; this can be used for correcting two errors per code word. The successrate Pc is increased by the introduetion of error correction (a), but the false rate p. also increases- by a factor of more than 100 (b). The measured points in (0) refer to the error-correcting code;they give an impression of the typical spread in this kind of measurement.

One obstacle which will delay the introduetion of high-bit-ratemobile data systems is the requirement for the data signal to passfrom the base station through a telephone line to the transmittersite. High-bit-rate modems for use on telephone lines are expensivebecause multilevel signals are necessary and amplitude/delayequalizers are usually required. For this reason mobile-dataschemes will be limited to 1200 bits/s until costs drop due to LSI.

to a low bit rate where error-detecting codes withrepeated code words would not give sufficientthroughput. ,

When discussing error detection the (15,7) code wasused to illustrate the, performance of an encodedASCII character. The same code could alternatively

Philips tech. Rev. 39, No. 6/7 DA TA COMMUNICATION BY MOBILE RADIO 181

be used for correcting up to two errors. Its successand false rates are plotted in fig. 10 together with thecurves repeated for error detection. The success rateat 10 dB is improved from 99070 to about 99.8% byusing error correction instead of detection, but thefalse rate has been degraded by more than two ordersof magnitude. For some applications the errorcorrection might be considered superior; for examplewhen transmitting text to a mobile printer the fewwrong characters printed when the error-correctingdecoder produces a false character may be moreacceptable than frequent clusters of characters notprinted because of detected errors.

Error-correcting codes therefore enable a bettersuccess rate to be obtained at the expense of a highfalse rate. The other penalty which may be incurred isa complex decoder. Single-error correcting codes canbe implemented easily, but codes for correcting moreerrors rapidly become more complex. On the otherhand, powerful microcomputers are now availablewhich make the implementation of quite complexerror-correction algorithms feasible. Because thecomplexity of implementation is so sensitive to theparameters of an error-correcting code it is importantto know just how much benefit is gained in per-formance from using long codes capable of correctingmany errors.

The effect of choosing different code parameterscan be seen in the P(~ m,n) distributions. Fig. 11shows the P(~ m,n) distributions for one represen-tative measurement. The points marked on the curvesrefer to a selection of codes. Codes have been selectedhaving code rates R of roughly t tand .t, whichmeans that the number of information bits is thegiven proportion of the total number of bits in aword. To illustrate this consider the (15,7,2) two-errorcorrecting code, whose success rate is l-P(~ 3,15);in fig. 11 the P( ~ 3,15) point has been marked on then = 15 curve, and the value of I-P(~ 3,15) may beread from the right-hand axis, i.e. Pc = 0.98.

The points for the codes at each code rate have beenjoined by a dashed line, e.g. for R = t the dashed linejoins the points for the (7,4,1), (15,7,2), (31,16,3), ...codes. These dashed lines show that increasing thecode-word length (with R constant) produces littlechange in Pc. Changing the code rate (with n constant)causes only a gradual change in Pc. Some improve-ment can be gained by using longer words at a lowcode rate, e.g. t, but using longer words at a high coderate, e.g. t can degrade Pc.

The false rate (not illustrated) is more sensitive tochanges in the word length or code rate. A long codewith a low code rate is necessary to get a combinedhigh success rate and low false rate.

r-------------------~OLav= 1.9dB

0.9

0.99

Plem.n)

t

0.999

10-4 L------_lL_----__J0'99991 10 100

-m

Fig. 11. The probability P('? m,n) of m or more errors in a codeword of n bits. The curves are based on measurements made at amean signallevelof Lav = 1.9 dB. If a code can correct up to m-Ierrors, the success rate Pc is 1- P(?: m,n) (right-hand ordinate).A number of such codes with the same code rate R (ratio of thenumber of information bits to the total number of bits) have beenjoined by dashed lines; increasing the word length is found to haveno great effect on the success rate.

Q

b

Fig. 12. Three code words of n bits (a) are interleaved before trans-mission (b). The bit errors resulting from an error burst EB aredistributed over three code words in the reconstruction (c), so thatthe number of errors does not exceed the correcting capability ofthe code for any of the three words. In practice such an interleavingpattern usually contains several hundred bits.

182 DATA COMMUNICATION BY MOBILE RADIO Philips tech. Rev. 39, No. 6/7

Bit interleavingA very effective way of coping with clustered errors

is to use bit interleaving to disperse the errors so'thatthe errors are less likely to exceed the correctingcapability of the code. Before a message is transmit-ted the bits from several code words are interleaved.Then when an error burst occurs, the errors will beshared among the interleaved codewords (fig. 12) andonly a simple code is required to correct them. Notethat the interleaving process does not involve addingmore redundancy.Interleaving enables errors occurring during the

short-term fades due to multipath reception to be dis-persed into the intervals between these fades. Theshort-term fades are spaced by a minimum of a halfwavelength, 32.5 cm at 462 MHz, and a vehiclemoving at the typical city speed of 30 krn/h(19 mph) will transmit or receive 47 bits (at 1200 bits/s)while travelling this distance. Allowance must then bemade for variation in fade separation, fade depth andvehicle velocity, so a useful interleaving period islikely to be several hundred bits. The longer-termfades due to shadowing lie further apart. It is imprac-tical to combat the errors they cause with bit inter-leaving.The benefit from interleaving is illustrated injig. 13,

which shows the success rate for a (31,16,3) randomerror-correcting code without interleaving, and inter-leaved over 992 bits (32 code words interleaved). Byinterleaving, the success rate at 10 dB mean signallevel has been improved from 99.80/0to 99.998% andthe false rate (not plotted) will be improved by twoorders of magnitude. A considerable improvementhas therefore been obtained from interleaving. Therandom-access memory required to implement an

interleaving period of 992 bits represents a practicalsize and it was found that further improvement in per-formance was only gradual as the interleaving periodwas increased beyond this.

(31.16.3)

0.999

Pc0.9999

0.99999L......J0L.,.._----1...J...0....1..,_----2L...Od__JB-Lav

Fig. 13. Improvement du to bit interleaving. The success rate Pc ofan error-correcting (31,16,3) code is increased considerably byinterleaving over a period of I = 992 bits (32 code words).

Summary. Transmission of digital signals opens up new possibili-ties in the use of mobile radio, such as sending written messages inboth directions or even pictures and maps. The level of the receivedsignal is low, however, and very variable because of shadowing andfading; there is also considerable ignition noise from the sur-rounding traffic. During measurements made in a vehicle travellingin central London and near Philips Research Laboratories (PRL) atRedhilI recordings were made of signal-level fluctuations and bit-error patterns. Bit-error rates were calculated from these recor-dings; the errors are often clustered. For reliable data transmissionit is necessary to use an error-detecting or error-correcting code, inwhich check bits are added to the information bits. The collectedstatistical material has enabled the performance of various codes tobe compared in the laboratory.

Philips tech. Rev. 39, No. 6/7 183

The background of this photograph is part of an enlargement (about200 x) of an aluminium surface machined to be 'optically smooth'; theoriginal was made by means of Nomarski interference contrast. Theconcave or convex tops of the samples shown (maximum diameter4 cm) are optically smooth surfaces, made on a numerically controlledhigh-precision lathe. The turning marks in the background have adepth of about 20 nm and apitch of 10 urn. The black dots are relativ-ely innocuous specks of impurities in the aluminium. The ability toproduce perfectly reflecting curved surfaces, by diamond turning, hasgreatly extended the application of geometrical optics at Phi/ipso Thehigh-precision lathe developed for this type of work at Philips ResearchLaboratories is known as COLA TH; it will shortly be described in thisjournal.

r. c. french and p. j. mabey - philips bound... · errorcontrol in mobile-radio data communication...

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