Rate-compatible convolutional codes for multirate DS-CDMA systems

828 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 47, NO. 6, JUNE 1999

Transactions Papers

zRate-Compatible Convolutional Codesfor Multirate DS-CDMA Systems

Pal K. Frenger, Pal Orten, Tony Ottosson, and Arne B. Svensson,Senior Member, IEEE

Abstract— New rate-compatible convolutional (RCC) codeswith high constraint lengths and a wide range of code ratesare presented. These new codes originate from rate 1/4 optimumdistance spectrum (ODS) convolutional parent encoders with con-straint lengths 7–10. Low rate encoders (rates 1/5 down to 1/10)are found by a nested search, and high rate encoders (rates above1/4) are found by rate-compatible puncturing. The new codesform rate-compatible code families more powerful and flexiblethan those previously presented. It is shown that these codes arealmost as good as the existing optimum convolutional codes of thesame rates. The effects of varying the design parameters of therate-compatible punctured convolutional (RCPC) codes, i.e., theparent encoder rate, the puncturing period, and the constraintlength, are also examined. The new codes are then applied toa multicode direct-sequence code-division multiple-access (DS-CDMA) system and are shown to provide good performance andrate-matching capabilities. The results, which are evaluated interms of the efficiency for Gaussian and Rayleigh fading channels,show that the system efficiency increases with decreasing coderate.

Index Terms— Multicode direct-sequence code-divisionmultiple-access (DS-CDMA), multichannel systems, nestedconvolutional codes, optimum distance spectrum (ODS), rate-compatible punctured convolutional codes (RCPC codes), ratematching.

I. INTRODUCTION

COMMON for all first- and second-generation cellularcommunication systems is that they are dominated by

speech communication. There are however, indications that theincrease in traffic in the future will mainly be in other typesof services. Services that are believed to be important are,for instance, fax and image transmission, video conferencing,

Paper approved by S. B. Wicker, the Editor for Coding Theory andTechniques of the IEEE Communications Society. Manuscript receivedSeptember 1, 1997; revised May 5, 1998. This work was supported inpart by the project ACTS AC090 FRAMES which is funded by theEuropean community. This paper was presented in part at the IEEE VehicularTechnology Conference, Arizona, 1997, at the 3rd ACTS Mobile Summit,Rhodes, Greece, June 1998, and at the Nordic Radio Symposium, Saltsjobade,Sweden, October, 1998.

P. K. Frenger is with Ericsson Research, Ericsson Radio Systems AB,SE-16480 Stockholm, Sweden (e-mail: [email protected]).

P. Orten, T. Ottosson, and A. B. Svensson are with the Communi-cation Systems Group, Department of Signals and Systems, ChalmersUniversity of Technology, SE-412 96, Goteborg, Sweden (e-mail: [email protected]; [email protected]; [email protected]).

Publisher Item Identifier S 0090-6778(99)05009-6.

electronic billing, positioning, audio, Internet access, and puredata transmission. It is already clear, judging from evolvingstandards (see e.g., [1]–[3]), that these services will requiredifferent data rates, quality of service (bit error rate), and datarate variability. Furthermore, some services are delay sensitiveand some are not. Hence, a communication system shouldbe designed with a high amount of flexibility regarding thedata rate and its variability, the provided quality of service,and the delay. One of the requirements on the radio layeris thus to provide a modular data rate system so that a usercan allocate the data rate needed with a reasonable resolutionfor the time needed. This division of the channel resourcesinto subchannels can be done in the time, frequency, orcode domain. It is also possible to design hybrid systems,for example, allowing users to allocate several codes andseveral carriers. Common for all these solutions is that manysubchannels exist, and a user is allowed to allocate severalof these subchannels. We will refer to such a system as amultichannelsystem.

In dividing the resources into multiple channels, there isusually a tradeoff (due to intersymbol interference, channelvariability, and implementation costs) between a low datarate on each subchannel for efficient support of, e.g., speechservices, and a high spectral efficiency for the system. It istherefore reasonable to assume a resolution in data rate onthe order of 10–50 kbit/s. However, the variability in, forexample, speech, is in steps in the order of a few kilobits persecond, requiring a rate matching system as an interface to theallocated subchannels. Two obvious ways of rate matchingexist; a) repetition of some of the data bits so that the datarate after repetition matches the channel rate; and b) channelcoding which introduces the extra redundancy bits needed.Repetition is, in fact, a very simple channel code, which ingeneral has a low performance gain compared to other codingschemes. It has, though, the advantage that all source datarates can be matched to the existing channel rates by repeatingsome or all of the data bits one time or more. Using channelcoding for rate matching, on the other hand, implies a needfor many code rates so that a high resolution of source datarates can be supported. It would, of course, also be possibleto switch periodically between a few different code rates andthus achieve a perfect rate matching using channel coding.

0090–6778/99$10.00 1999 IEEE

FRENGERet al.: RATE-COMPATIBLE CONVOLUTIONAL CODES FOR MULTIRATE DS-CDMA SYSTEMS 829

The requirement for different bit error rates implies an adap-tive error control coding scheme making it possible to changecode rate from one connection or data packet to another.Also within one transmission there may be needs for dif-ferent quality classes in, for example, speech communication[unequal error protection (UEP)], or to adapt to the channelcondition, thus achieving a higher spectral efficiency. Also,packet transmission based on hybrid automatic repeat request(HARQ) uses variable rate channel codes [4]–[7]. Based onthe different arguments presented, we claim that there is aneed for a channel coding scheme with many code rates.The question that remains is what type of coding scheme touse. Two main categories exist: block codes and convolutionalcodes. Block codes have a main difficulty in the complexityneeded to perform soft-decision decoding which is vital for anybandwidth efficient cellular communication system because ofthe multipath fading nature of the mobile radio channel [8, p.813]. Also, due to implementation costs, it is advantageousto be able to use the same decoder (or a few decoders) todecode all code rates. For block codes, the decoders mustusually be designed for a specific code. With convolutionalcodes, soft-decision decoding comes naturally using a softmetric in the Viterbi decoder, and the use ofrate-compatibleconvolutional (RCC) codes makes it possible to apply thesame decoder for all code rates within the code family. Othercoding schemes such as turbo coding [9] exist. However, forturbo codes to perform well, a large interleaver is needed.It is therefore difficult to use turbo codes for delay sensitiveservices. Furthermore, the high complexity in decoding turbocodes may be prohibitive. Another possible coding/decodingscheme is long constraint length convolutional codes togetherwith sequential decoding [10]. However, the fractional rateloss due to the many tail bits may be large, and thereare indications that the loss in performance using puncturedconvolutional codes together with sequential decoding is moredetrimental than for Viterbi decoding [11].

In this paper we present new flexible rate-compatible con-volutional codes suitable for rate matching and error controlin wireless multichannel systems. To illustrate the applicabilityof these new codes, we evaluate the use of these codes in amulticode DS-CDMA system [12]. The organization of thepaper is as follows. Section II introduces the concept of rate-compatible codes and describes how the higher code ratesare obtained by puncturing, and the lower code rates areobtained by nesting the parent encoder. The procedure forfinding new codes is given in Section III, where two differentsearch criteria, optimum distance spectrum and a channeloptimized, are presented. Section IV contains a short reviewon how to calculate the performance of convolutionally codedsystems. Then a thorough evaluation of parameter choicesfollows in Section V. The effects of different parent encoderrates and constraint lengths are examined, as well as theperformance obtained by different puncturing periods. Theapplicability of the proposed codes in a multicode DS-CDMAsystem is presented in Section VI. The achievable efficiencyon Gaussian and Rayleigh fading channels is used to evaluatethe system. Conclusions are given in Section VII, and finallythe new codes are given in the Appendix.

II. RATE-COMPATIBLE CONVOLUTIONAL CODES

RCC codes are constructed such that lower code rates makeuse of the same code symbols as the higher code rates plussome extra redundancy symbols. This can easily be obtainedby repeating symbols. However, repetition usually results inworse performance than nesting or puncturing [5]. Thus, inthis paper we present a flexible and powerful family of RCCcodes obtained by combining these two techniques such thatpuncturing is used for the higher code rates while nesting isused to achieve very-low rate, low-complexity coding.

A. RCPC Codes

Rate-compatible punctured convolutional(RCPC) codes[13] are constructed by puncturing a convolutional code ofrate and constraint length , called the parent code.This code is completely specified by the generator polynomials

, whereand [4]. The puncturing is done accordingto a rate compatibility criterion, which requires that lowerrate codes use the same coded bits as the higher rate codesplus one or more additional bit(s). The bits to be puncturedare described by an puncturing matrix consistingof zeros and ones. The output from the generator iscompared to the appropriate element in the puncturing matrix

At time instant , the output from each generatoris transmitted if and punctured otherwise.Here, denotes the element on row and columnin the matrix The number of columns, or the puncturingperiod , determines the number of code rates and the rateresolution that can be obtained. Generally, from a parent codeof rate , we obtain a family of different codeswith the rates

(1)

Due to the rate compatibility criterion, the code rate of RCPCcodes can be changed during transmission, and thus unequalerror protection can be obtained [13], [14].

The problem with the existing RCPC codes [13], [15] is thelimited number of code rates (and thus also a limited rangeof code rates). Because only codes with constraint lengthsseven or lower have been found, these codes are of limitedapplicability in cellular systems. The bandwidth efficiency is ofmajor importance, and therefore the most powerful codes thatcan be implemented in an efficient way should be used. Withpresent technology it is possible to implement Viterbi decodersfor constraint lengths up to at least ten. For example, the NorthAmerican CDMA standard (IS-95) uses constraint length ninecodes [16, p. 114]. The RCPC coding scheme presented here isconsidered to be a strong candidate for both the TDMA- andCDMA-based modes in the personal communication systemcurrently being studied within the European FRAMES project[17].

B. Nested Convolutional Codes

Nested convolutional codes[18], [19] are obtained by ex-tending a code of rate to a rate code by searching


for the best1 additional generator polynomial It isobvious that this type of code family is rate-compatible andthe big advantage is the modular code design that reduces thecomplexity of the search for low-rate codes.

III. SEARCHING FOR RCC CODES

Code searching is done by repeatedly puncturing (in steps ofone bit) or nesting (in steps of one generator polynomial) therate parent encoder. At each puncturing or nestingstep, the best encoder according to some criterion is chosen andis used for additional puncturing or nesting in the followingstep. Furthermore, we eliminate all catastrophic encoders [4].Two possible search criteria are described below; thesuperiordistance spectrumand thechannel optimizedcriterion.

A. Optimum Distance Spectrum (ODS) RCC Codes

Important parameters for the performance of convolutionalcodes are thefree distance , and thedistance spectrum

, where is the total number of informationbit errors for all error events of length In [20] we showedthat encoders with superior distance spectrum perform well onboth AWGN and Rayleigh fading channels. Superior distancespectrum is defined as follows.

Definition 1 (Superior Distance Spectrum):A feedforwardencoder with error weights giving a code with free distance

has a distance spectrum superior to a feedforward encoderwith error weights giving a code with free distance ifone of the following conditions is fulfilled: 1) or 2)

and there exists an integer such thatfor and for

We define anoptimum distance spectrum(ODS) RCC codeas a code generated by a feedforward encoder satisfying therate compatibility criterion and giving superior distance spec-trum compared to all other feedforward encoders of the samerate and constraint length still satisfying the rate compatibilitycriterion.2

B. Channel Optimized RCC Codes

The performance of a convolutional code is not directlyreflected by its distance spectrum, and hence, a more appro-priate design criterion may be to minimize the upper boundon the bit error probability (see Section IV). This approachhas been taken in, e.g., [18] and [21], and coding gains in thearea of 0.1–0.4 dB were reported. However, optimum distancespectrum codes perform well for both AWGN and fadingchannels [20], while channel optimized codes are designedfor a specific channel and signal-to-noise ratio. Tests indicatethat the additional coding gain obtained by minimizing the biterror rate, compared to optimizing the distance spectrum, ison the order of 0.1 dB and in a rather small interval.Hence, we do not pursue a channel optimized approach here.

1The optimum distance spectrum criterion [20] will be used for selectingthe best code. Further details of this criterion is given in following section.

2The ODS convolutional codes given in [20] are defined in a similar waybut without the rate compatibility criterion. These codes will be used as parentencoders for the RCC codes.

C. Searching for Rate-Compatible Puncturing Patterns

Clearly, puncturing of a low-rate convolutional code toobtain a specific higher code rate is generally a suboptimumway of obtaining that code rate. The loss due to this subopti-mality is, however, in general limited. Optimum puncturingpatterns have been obtained by computer search, see, e.g.,[5], [22]–[24]. Furthermore, specific codes in an RCPC codefamily are suboptimum punctured codes since all puncturingpatterns cannot be allowed due to the rate-compatibility cri-terion. The puncturings done at one rate are maintained forall higher rate codes, and small steps in the puncturing areadvantageous only for a high resolution of code rates.

The search procedure is as follows. a) Start with a parentcode of rate and an by puncturing matrix of all ones.b) Given the puncturing matrix, find the position where a zerowould result in a superior distance spectrum encoder. Thisis the best puncturing pattern for this rate. Observe that allpositions (except some equivalents) need to be tested. Also,observe that the distance spectrum in most cases only needsto be calculated with a few terms to decide which of theencoders have superior distance spectrum. For this purposewe use the FAST algorithm [25]. In the few cases when thedistance spectra for two puncturing patterns are equal, we needto calculate some extra terms in the spectrum. For these cases,a Viterbi-like breadth-first algorithm is more efficient and thusused. c) Keep the best puncturing pattern as a starting pointto find the best pattern for the next (higher) rate according tob). The procedure is stopped when only ones remain inthe puncturing matrix.

For each new puncturing during the search, the number ofremaining puncturing patterns is reduced. For the higher coderates we should therefore expect to have a larger loss than forthe lower rates. If the higher rates are critical, the search couldinstead be started from the highest rate, adding ones in thepuncturing matrix. The main problem with this is a tremendousinitial search problem since we then have to find the optimum

bits among bits that should not be deleted,being the number of elements in the matrix. The initial searchproblem could be alleviated by starting with an extension ofthe optimum high-rate puncturing similar to that of [5].

IV. PERFORMANCE ANALYSIS

The bit error rate performance of convolutional codes maybe found by extensive simulations or approximately by calcu-lating error bounds. If the distance spectrum, i.e., the numberof bit errors associated with a given distance, of the code isknown, it is rather straightforward to calculate a union upperbound on bit error probability. This bound can be generalizedto apply also to punctured convolutional codes and is givenby [13]

(2)

where is the total number of bit errors for all differentstarting points of error events of distance, relative to thepuncturing period. Since is obtained by summing over


Fig. 1. Upper bounds and simulated results of the bit error probability on aRayleigh fading channel for RCPC codes and ODS codes with rateR = 1=3and 1/2. Constraint lengthK = 9:

all starting points, averaging by the puncturing periodisnecessary in (2) to have a correct bound. Furthermore,is the probability that an error path of distanceis choseninstead of the all zeros path. This pairwise error probability

depends on the channel. For coherent BPSK on an AWGNchannel we have [8, p. 487]

(3)

where denotes the received energy per information bit,the double-sided power spectrum density of the noise

process, and For BPSKmodulation on an uncorrelated Rayleigh fading channel withperfect channel estimates and soft-decision decoding,eval-uates to [8, p. 781]

(4)

with where is the averageAs we will see, the bounds are rather tight, especially

for the lower bit error rates.

V. EVALUATION OF NEW CODES

In the Appendix we present RCPC codes with constraintlengths using rate ODS parent encoders.Furthermore, these code sets are extended using nested codesfrom rate to rate Note that all presentednested codes are maximum free distance codes (i.e., fulfillsthe Heller bound [26]). Using (2)–(4) we can evaluate anupper bound on the bit error probability for the RCPC codespresented in this paper. In all results presented we use 12terms of the distance spectrum. Fig. 1 shows simulation resultsand upper bounds on a Rayleigh fading channel for rate 1/2and rate 1/3 constraint length nine codes. The RCPC codes

Fig. 2. RequiredEb=N0 in dB to obtain the bit error probability 10�6

on Rayleigh fading and Gaussian channels versus the code rateR: Resultsare shown for constraint lengthK = 9; n = 4 and puncturing periodsp = 2; 4; 8, and 16.

are specified in Table III and the ODS codes are taken from[20] and [24]. As we can see in Fig. 1, the upper boundsand the simulated results correspond closely for BER of 10and lower. We will therefore use these bounds for evaluation,instead of performing time-consuming simulations.

In Fig. 2 we study the influence of changing the puncturingperiod The required to obtain a BER of 10 isplotted versus the code rate. Results are shown for constraintlength nine RCPC codes with , and for aGaussian as well as for a Rayleigh fading channel. A smallvalue of severely limits the degree of freedom in optimizingthe puncturing pattern, and thus a performance loss results.Choosing a high value of may also cause a loss in perfor-mance since the search procedure is to find a local optimum ateach step given the previous pattern (thus the search space isseverely limited). Fig. 2 indicates that is a good choiceof the puncturing period.

We may also choose to use parent codes of different rates.In Fig. 3, the required to obtain a BER of 10 isplotted versus the code rate for RCPC codes with parentcodes of rate with , and . Results are shownfor Gaussian and Rayleigh fading channels and the constraintlength is nine. We see, as expected, that using a high-rateparent code provides slightly better performance for the high-rate punctured codes. For a smaller values of, the span ofavailable code rates is, however, also smaller. The performanceof the punctured codes obtained with is almost asgood as that of those with Furthermore, we haveobserved that some of the nested codes resulting from parentcodes of rate 1/2 are not maximum free distance codes. Forrate 1/4 parent codes, however, all nested codes presented aremaximum free distance codes. We have thus chosen to presentRCC codes only for (see the Appendix).

In Fig. 4 we evaluate the RCPC codes for , and. All codes use parent codes of rate 1/4 and are given in

Tables I–IV. For code rates lower than 1/4, the nested codesin Table V–VIII are used. We also show in Fig. 4 results for


Fig. 3. RequiredEb=N0 in decibels to obtain the bit error probability 10�6

on Rayleigh fading and Gaussian channels versus the code rateR: Resultsare shown for codes obtained by puncturingR = 1=n parent codes withn = 2; 4; 6, and8. Constraint lengthK = 9 and puncturing periodp = 8:

Fig. 4. RequiredEb=N0 in decibels to obtain the bit error probability 10�6

on Rayleigh fading and Gaussian channels versus the code rateR: Resultsare shown for constraint lengthsK equal to seven, eight, nine, and ten.

ODS codes of rates 1/4, 1/3, and 1/2. The RCPC codes performalmost as well as the ODS codes for all code rates shown.

VI. RATE MATCHING FOR MULTICODE DS-CDMA

For DS-CDMA systems, multiple data rates can efficientlybe achieved by amulticode scheme letting each user usemultiple spreading codes and transmit data on these in parallel[12]. With fixed spreading there will be a number of fixed-ratesubchannels available. If the system is to support any sourcerate, there is a need for matching the source rate to a multipleof the subchannel rate. By using the proposed RCC codes, wehave many different code rates with different levels of errorprotection and a flexible means of matching the source datarate to the rate of the parallel subchannels [27]. However, whenlower rate coding is applied, more subchannels are needed totransmit the channel symbols. This results in more interference

TABLE IRCPC CODES, K = 7; PARENT CODE (117, 127, 155, 171)

to the other users of the system. It is therefore of interestto investigate the performance of the multicode DS-CDMAsystem as the code rate is decreased.


TABLE IIRCPC CODES, K = 8; PARENT CODE (231, 273, 327, 375)

TABLE IIIRCPC CODES, K = 9; PARENT CODE (473, 513, 671, 765)


TABLE IVRCPC CODES, K = 10; PARENT CODE (1173, 1325, 1467, 1751)

Fig. 5. Achievable bandwidth efficiency for a multicode DS-CDMA systemusing rate-compatible codes on Gaussian (solid lines) and Rayleigh fadingchannels (dashed lines). The target BER is 10�6 at Eb=N0 = 10 dB, andRs=Rsub = 1:

TABLE VNESTED CODES, K = 7; PARENT CODE (117, 127, 155, 171)

In order to analyze the performance of our system, weapproximate the interference from other users as Gaussian andthen apply the union upper bound on the bit error probabilityfor BPSK on Gaussian and Rayleigh fading channels [see(2)–(4)]. The effective signal-to-noise ratio to be used in thebit error rate calculations is given by [12]

(5)

where is the number of users, is the spreading factor,and is the number of parallel channels that are used.Furthermore, , where is the source datarate, is the subchannel data rate, and the code rateis chosen among available rates such that an integer numberof subchannels is used. The efficiency of the system is givenby , that is, the total data rate of all usersdivided by the chip rate. The efficiencies obtained for a biterror rate of 10 on a Gaussian and Rayleigh fading channel,respectively, are shown in Fig. 5 forand dB. As can be seen, the efficiency isincreased with decreasing code rate. Thus, the extra codinggain obtained by reducing the code rate is larger than thereduction in the effective signal-to-noise ratio. We also see thatthe performance difference between Gaussian and Rayleigh


TABLE VINESTED CODES, K = 8; PARENT CODE (231, 273, 327, 375)

TABLE VIINESTED CODES, K = 9; PARENT CODE (473, 513, 671, 765)

TABLE VIIINESTED CODES, K = 10; PARENT CODE (1173, 1325, 1467, 1751)

fading channels decreases with decreased code rate. This isdue to the increased diversity gain provided by the channelcode as the code rate is reduced. With high diversity order,the performance on the Rayleigh fading channel approachesthat of the Gaussian channel.

VII. CONCLUSIONS

New families of RCPC codes with a high resolution incode rates have been found for constraint lengths ranging fromseven to ten originating from parent codes of rate 1/4 using apuncturing period of eight. Performance evaluations show onlya small loss compared to the existing optimum convolutionalcodes of the same rate. Furthermore, new maximum freedistance codes nested from parent codes of rate 1/4 arepresented for rates down to 1/10.

It has been shown that the choice of parent code rate doesnot affect the performance much. Starting with a low code ratesearching, an RCPC family yields a large span of possible code

rates. This range of code rates makes a communication systemvery flexible and may be used in, for example, rate matchingwhere different source data rates are matched onto the channelrates given by a multichannel communication system. In orderto obtain a finer grid of available code rates, the puncturingperiod may also be increased.

The codes presented in this paper are evaluated for theapplication of rate matching in a multicode DS-CDMA system.The results show that the efficiency of the system is increasedwith decreasing code rate.

APPENDIX

CODE SEARCH RESULTS

The new RCPC codes are given in the Tables I–IV. Thepuncturing is given relative to the previous code rate and theadditional puncturing position (the column “Pos.”) is givenby the row and column number (row, column). The upperleft element is denoted (0,0). Also given in the tables arethe free distance and the first 12 terms of the distancespectra and , where

is the number of error events of length The parentcodes are given in octal form, converting the binary words

into the corresponding octal words. For thenested codes in Tables V–VIII, we only give the additionalgenerator polynomial (in the column “Add. pol.”) and thespectrum is given with 15 terms. Observe that no puncturing isperformed, and hence, must be used in (2). Other RCCcodes with other parent code rates, periods, and constraintlengths can be found in [24].

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Pal K. Frenger was born in Alingss, Sweden,on October 31, 1968. He received the M.S.(civilingenjr) degree in electrical engineering fromChalmers University of Technology, Goteborg,Sweden, in 1994. After that he began workingtoward the Ph.D. degree at the CommunicationSystems Group, Department of Signals and Systems,Chalmers University of Technology. He defendedhis Ph.D. dissertation entitled "Multirate codes andmulticarrier modulation for future communicationsystems" in April 1999.

Between 1995–1999 he was involved in the European FRAMES (FutureRadio wideband Radio Multiple Access System) project. He is presentlyworking at the Access Technologies and Signal Processing Group at EricssonResearch, Ericsson Radio Systems AB in Kista, Sweden. His main area ofresearch interest is in communication systems. In particular, he has beenworking with multicarrier modulation systems and applications, error controlmethods, spread spectrum and CDMA systems, and modulation/demodulationmethods.

Pal Orten was born in Molde, Norway, in 1966.He received the M.Sc. (Sivilingeniør) degree inelectrical engineering from the Norwegian Instituteof Technology, Trondheim, Norway, in 1989 and theLic.Eng. (Teknisk Licentiat) degree from ChalmersUniversity of Technology, Goteborg, Sweden, in1997. He is currently working toward the Ph.D.degree and plans to finish within 1999.

From 1990 to 1995, he worked as ResearchScientist at ABB Corporate Research and NeraResearch in Oslo, Norway. His work at ABB and

Nera includes research and development on mobile satellite communications,communication on power lines, and communication on twisted pair cables.His main interests in communication systems are channel coding, CDMAsystems, modulation techniques, and advanced receivers for mobile terrestrialand satellite communications. Since January 1996, he has been involved in theEuropean FRAMES (Future Radio wideband Multiple Access System) project.

Tony Ottossonwas born in Uddevalla, Sweden, in1969. He received the M.Sc., Lic.Eng., and Ph.D.degrees in electrical engineering from ChalmersUniversity of Technology, Goteborg, Sweden, in1993, 1995, and 1997, respectively.

Currently he is an Assistant Professor at the Com-munication Systems Group, Department of Signalsand Systems, Chalmers University of Technology.During 1999, he was also working as a ResearchConsultant at Ericsson Inc., Research Triangle Park,NC, USA. From October 1995 to December 1998,

he participated in the European FRAMES (Future Radio wideband MultipleAccess System) project both as a co-worker and during 1998 as ActivityLeader of the area of coding and modulation. His research interests are in com-munication systems and information theory and are mainly targeted to CDMAsystems. Specific topics are modulation, coding, multirate schemes, multiuserdetection, combined source-channel coding, joint decoding techniques, andsynchronization.

Arne B. Svensson was born in Vedakra, Swe-den, on October 22, 1955. He received the M.S.(Civilingenjor) degree in electrical engineering fromthe University of Lund, Lund, Sweden, in 1979and the Dr.Ing. (Teknisk Licentiat) and Dr.Techn.(Teknisk Doktor) degrees from the Department ofTelecommunication Theory, University of Lund in1982 and 1984, respectively.

Currently, he is with the Department of Sig-nal and Systems at the School of Electrical andComputer Engineering at Chalmers University of

Technology, Gothenburg, Sweden, where he was appointed Professor inCommunication Systems in April 1993. Before 1985 he held various teachingand research positions at the University of Lund. From April 1985 to July1987, he was a Research Professor (Docent) at the Department of Telecommu-nication Theory, University of Lund. In August 1987, he joined the AirborneElectronics Division at Ericsson Radio Systems AB, Mölndal, Sweden. Aftera company reorganization in January 1988, he became employed by EricssonRadar Electronics AB, where he first was a member of the New ProjectsGroup at the Airborne Electronics Division and then from September 1990to December 1994, a member of the Mobile Telephone Systems Group at theMicrowave Communications Division. His consulting company BOCOM, isinvolved in studies of error control methods, modulation and demodulationtechniques, spread spectrum and CDMA systems, and computer simulationmethods for communication systems. His current interest include channelcoding and decoding, digital modulation methods, channel estimation, datadetection, multiuser detection, digital satellite systems, CDMA and spreadspectrum system, and personal communication networks. He has published20 journal papers, four letters and more than 80 conference papers.

Prof. Svensson was recognized in 1986 with the IEEE Vehicular TechnologySociety Paper of the Year Award, and in 1984, he received the YoungScientists Award from the International Union of Radio Science, URSI. Heis a member of the council of SER (Svenska Elektro- och DataingenjörersRiksforening) and a member of the Swedish URSI committee (SNRV, SvenskaNationalkommitten för Radiovetenskap). He is listed inWho’s Who in theWorld and theEuropean Biographical Directory.

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Rate-compatible convolutional codes for multirate DS-CDMA systems

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