Convolutional Coding Schemes for Variable Rate, Unequal Error Protection, and Packet Data Services Sorour Falahati, Pçal Frenger, Pçal Orten, Tony Ott

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1 Convolutional Coding Schemes for Variable Rate, Unequal Error Protection, and Packet Data Services Sorour Falahati, Pçal Frenger, Pçal Orten, Tony Ottosson and Arne Svensson Communication Systems Group, Dept. of Signals and Systems Chalmers University of Technology, SE Gíoteborg, Sweden fsorour.falahati, Pal.Frenger, Pal.Orten, Tony.Ottosson, and Abstract Flexible and low-complexity variable rate coding schemes based on rate-compatible convolutional codes are presented. The codes have a wide range of code rates and are optimized for good performance on both AWGN and Rayleigh fading channels. Furthermore, the application of these codes for rate matching, combined coding and spreading in a DS-CDMA system and hybrid type-ii ARQ schemes are demonstrated. Very long constraint length convolutional codes with sequential decoding is proposed and shown to be suitable for high performance services in wireless systems. 1 Introduction Since the introduction of cellular telephony in the early 80's, virtually all markets and operators have seen a rapid increase in the number of subscribers. In the early 90's the ærst generation analog systems were replaced by the second generation digital systems. These systems have higher capacity due to source èspeechè coding, channel coding and the inherent robustness of digital transmission. Common for all these systems is that they are dominated by speech communication. However, there are indications that the increase in traæc in the future will mainly be in other types of services. One example of such a service is the nowadays so popular Internet browsing. Other services that are believed to be of some importance in the future are fax and image transmission, video conferencing, electronic billing, positioning, audio, lowresolution video, and pure data transmission. It is already clear, judging from evolving standards èsee e.g. ë1, 2ëè, that these services will require diæerent datarates, quality ofserviceèbit error rateè and data rate variability. Furthermore, some services are delay sensitive and some are not. Hence, a communication system should be designed with a high amount of æexibility regarding the data rate and its variability, the provided quality of service, and the delay. The quality of service èbit error rateè requirements imply an adaptive error control coding scheme making it possible to change code rate from one connection èor data packetè to another. Also within one transmission there may be needs for diæerent quality classes in for example speech communication èunequal error protection èuepèè, or to adapt to the channel condition thus achieving a higher spectral eæciency. Other applications of variable code rate channel codes are packet transmission based on hybrid automatic repeat request èharqè ë3, 4ë, and rate matching where a speciæc source data rate is mapped onto the allocated channel data rate. Due to the reasons presented, wewould argue that there is a need for a channel coding scheme with many code rates. The question that remains is what type of coding scheme to use. Two main categories exist; block codes and convolutional codes. Block codes have amaindiæculty in the complexity needed to perform soft-decision decoding which is vital for any bandwidth eæcient cellular communication system because of the multipath fading nature of the mobile radio channel. Also, due to implementation costs it is advantageous to be able to use the same decoder èor a few decodersè to decode all code rates. For block codes, however, the decoders must usually be designed for a speciæc code. For convolutional codes, soft-decision decoding comes naturally using a soft metric in the Viterbi decoder, and the use of rate-compatible convolutional èrccè codes makes it possible to apply the same decoder for all code rates within the family. Other coding schemes such as turbo coding exist. However, for turbo codes to perform well a large interleaver is needed, and therefore it is diæcult to use turbo codes for delay sensitive

2 services. Furthermore, the high complexity in decoding turbo codes may be prohibitive. Another possible codingèdecoding scheme is long constraint length convolutional codes together with sequential decoding ë5ë. In this paper, which is a summary of research performed on channel coding within FRAMES by Chalmers during the last year ë5í11ë, we discuss applications of the newly found powerful families of rate-compatible convolutional codes with 533 code rates in the range 1=512 í 8=9 performing well for both the Rayleigh fading and Gaussian channels. These codes can use the same encoder and decoder for all code rates and are thus well suited for low-complexity variablerate channel coding schemes. We present results using these codes for: è1è rate matching in a multicode DS-CDMA system; è2è combined coding and spreading in a DS-CDMA system; and è3è Hybrid ARQ type II schemes for fading channels. Furthermore, we treat sequential decoding and its applicability for fading channels. 2 Optimum Distance Spectrum èodsè Codes Good convolutional codes are normally found by an extensive computer search for the best generator polynomials. The number of possible codes increases exponentially with both the constraint length and the number of generator polynomials, and the ærst attempts to ænd good codes were therefore restricted to ænding maximum free distance èmfdè codes. By employing the Heller upper bound on the free distance of a convolutional code, the search was terminated as soon as a code with free distance equal to the Heller bound was found ë12ë. To guarantee maximum free distance, a full search was performed only in the few cases where no code fulælling the Heller bound was found. The bit error rate of a coded communication system is, however, not only determined by the free distance of the code. For fading channels, but also for AWGN channels the informationweight spectrum is of importance. In ë7ë, Frenger, Orten and Ottosson introduced the concept of optimum distance spectrum èodsè codes as codes that are MFD but also have the lowest possible information-weight spectrum. It is shown that these codes in addition to resulting in low bit error rates for AWGN channels also result in low bit error rates for Rayleigh fading channels. These codes are thus well suited for binary transmission over both AWGN and Rayleigh fading channels. ODS codes for rates 1=2, 1=3 and1=4 are given in ë7, 8ë. 3 Rate-Compatible Convolutional èrccè Codes RCC codes are constructed such that lower code rates make use of the same code symbols as the higher code rate plus some extra redundancy symbols. This can easily be obtained by repeating symbols. However, repetition usually results in worse performance than puncturing or nesting ë4ë. Thus we present a æexible and powerful family of RCC codes obtained by combining these two techniques such that puncturing is used for the higher code rates while nesting is used to achieve very-low rate, low-complexity coding. 3.1 Rate-Compatible Punctured èrcpcè Codes Rate-compatible punctured convolutional èrcpcè codes are constructed by puncturing a convolutional code of rate R = 1=n and constraint length K, called the parent code. This code is completely speciæed by its generator polynomials. The puncturing is done according to a rate compatibility criterion, which requires that lower rate codes use the same coded bits as the higher rate codes plus one or more additional bitèsè. The bits to be punctured are described by a puncturing matrix of size n æ p. The output from the generators is compared to the appropriate element in the puncturing matrix and punctured if the entry is zero. The number of columns, or the puncturing period p, determines the number of code rates and the rate resolution that can be obtained. Generally, from a parent codeofrate1=n, we obtain a family of èn, 1èp diæerent codes with the rates R = p=ènpè;p=ènp, 1è;::: ;p=èp + 1è. Due to the rate-compatibility criterion, the code rate of RCPC codes can be changed at any time during transmission and thus unequal error protection is obtained ë13ë. The problem with the existing RCPC codes ë13, 14ë is the limited number of code rates èand thus also a limited range of code ratesè. Furthermore, because only codes with constraint

3 lengths 7 or lower have been found, these codes are of limited applicability in cellular systems, where constraint lengths of at least 9 are expected. Frenger, Orten, Ottosson, and Svensson have therefore in ë8, 9ë presented new codes with longer constraint lengths, wider range of code rates and high resolution of code rates. The RCPC coding scheme is considered to be a strong candidate for both the TDMA- and CDMA-based modes in the personal communication system currently being studied within the European FRAMES project ë15ë. 3.2 Nested Convolutional Codes Nested convolutional codes ë16,17ë are obtained by extending a code of rate 1=n to a rate 1=èn+1è code by searching for the ëbest" additional generator polynomial. It is obvious that this type of code family is rate-compatible and the big advantage is the modular code design that reduces the complexity of the searchforlow-rate codes. By combining RCPC codes and nested convolutional codes, we get a set of rate-compatible codes with a wide range of code rates. In ë10ë Frenger, Orten and Ottosson present nested codes with rates 1=512í1=4 obtained from parent codes of rates 1=4. Interesting to note is that all these codes have maximum free distance. 4 Applications of RCC Codes 4.1 Rate Matching To exemplify the resolution in source data rates obtained using the presented RCPC and nested codes èparent code of rate 1=4 and puncturing period p = 8è for rate matching, we constructed a multicode DS-CDMA system ë18ë with the basic data rate R 0 =15kbitès èthe data rate on one spreading codeè. As seen in Figure 1, the 24 RCPC codes and the 6 nested codes èdown to rate 1=10è give a very æne resolution in the source data rate. 4.2 Combined Coding and Spreading Spread spectrum systems have been used for decades as a way of achieving robustness against interference and jamming. The spread spectrum technique is now also becoming popular in commercial systems because of its inherent robustness in multipath fading channels, and as a promising multiple-access technique. As a multiple-access method, most interest has been given to direct-sequence code-division multiple-access èds-cdmaè, where spreading is achieved by multiplication of the signal by a pseudo-random spreading sequence. In order to achieve suæciently low error rates in such a system, some kind of multiuser detection technique must normally be applied. Recent results though, indicate that compared to the conventional detector, such multiuser detectors are rather sensitive toerrors in the channel parameter estimates ë19ë. This fact indicates that complexity might be better spent on implementation of powerful channel coding schemes. Bandwidth spreading can also be obtained by the redundancy added by error correcting codes. In a conventional narrow-band communication system this bandwidth increase is generally an undesired feature. However, in spread spectrum systems, maximum theoretical performance is achievable by employing low-rate channel codes alone for bandwidth expansion ë20, 21ë. We will refer to spreading using only channel codes as combined coding and spreading or code-spreading. A limiting factor though, has been the lack ofgoodlow-rate codes. Current proposals use either orthogonal, biorthogonal or superorthogonal convolutional codes ë22ë. We have in ë10ë used the low-rate nested convolutional codes for combined coding and spreading. It is shown that the structure of these codes leads to simple encoder and decoder implementation, and due to the rate-compatibility it will also be straightforward to change the spreading factor to achieve multiple rates and variable processing gains. Furthermore, the performance of this code-spread multiple-access system is, as seen in Figure 2, superior to both that of conventionally spread systems with higher rate coding, and that of low-rate orthogonal and superorthogonal convolutional code-spread systems. 4.3 Hybrid Type-II ARQ Schemes In data communications and other non-real time services error free reception is often required. However, since channel coding can not deliver error free transmission, retransmission schemes or

4 automatic repeat request èarqè schemes have to be used. In ARQ a request for retransmission is sent to the transmitter whenever an erroneous packet has been received. This will guarantee error free packages as long as we are able to detect all erroneous packages and wait for retransmissions. Several types of ARQ schemes exist ë3ë. In simple ARQ unprotected èno channel codingè packets are transmitted. This scheme performs remarkably well for good channel conditions. Mobile radio channels, however, are time-varying and for these channels it is advantageous to adapt the protection of packages èthe channel codingè to the channel condition. A hybrid type-ii ARQ scheme starts with a high code rate and if a retransmission is required only the extra redundant symbols are transmitted èincremental redundancyè. Thus, the throughput for this scheme will be better than a simple ARQ scheme for bad channel conditions. In ë11ë some new hybrid schemes based on RCPC codes are proposed and compare with previously studied schemes. Four hybrid type-ii ARQ schemes èschemes 2-5è are compared to a simple ARQ scheme èscheme 1è. The type-ii schemes use RCPC encoders ècan be found in ë9ëè based on a rate 1=3 constraint length 7 parent code and a puncturing period of p = 2. The possible code rates are 1, 2=3, 1=2, 2=5, and 1=3. The channel block length is L p which in simulations and analysis were assumed to be either 64 or 256 bits. More details on the ARQ schemes may be found in Figure 3 and in ë11ë. In Figure 4 we see the analytical results for a channel block size of 64 bits. The parity-check code is a 16 bit CRC code. As seen scheme 5 performs better than all other schemes and for all signal-to-noise ratios, and simulations èfound in ë11ëè for diæerent fading rates supports this conclusion. Thus at least for delay insensitive services, a hybrid type-ii ARQ scheme with many code rates should be used. 5 Sequential Decoding Due the variety of services which must be provided by wireless systems there will be need for coding schemes that can provide extremely low error rates without the the need for retransmission. In ë5ë Orten and Svensson propose to use long constraint length convolutional codes with constraint lengths in the order of 30 to 50. For such long constraint lengths the Viterbi algorithm can not be used for decoding due to complexity. Awell proven technique, called sequential decoding, is therefore investigated to obtain the performance of this scheme for Rayleigh fading channels. Sequential decoding is based on exploiting only the locally most likely parts of the code tree. If the expanded path turned out to be the wrong path, the algorithm will back up and try a diæerent path èsee for instance ë23ëè. As a consequence of this searching strategy, the computational complexity is a random variable. This means that occasionally there will be overæows in the input buæer due to noisy input causing the search to go back and forth for a long time. An expression for the distribution of computations has been obtained ë23ë, and it is thus possible to ænd the mean and variance of the computational complexity. By using the requirement thatthe variance of the computational complexity should be ænite, we can obtain theoretically for which E b =N 0 sequential decoding is possible. Such results for a number of diæerent modulation methods and code rates for a Rayleigh fading channel are presented in ë5ë. Table 1 shows these theoretical limits for BPSK modulation and soft decision decoding. We can see from Table 1 that for rate R = 1=2 coding with BPSK modulation and soft decision sequential decoding is possible when E b =N 0 is above 8 db. This limit has been veriæed by simulations in ë5ë. As long as we operate above the theoretical limit we canachieve aslow error rate as wanted simply by choosing a suæciently long constraint length code. This is not possible with Viterbi decoding due to the exponential increase in complexity with the constraint length. The total error rate will be given by the overæow rate in the input buæer ègiven by hardware speed and delay requirementsè and the probability of choosing the wrong trellis path èset by the constraint lengthè. It has also been shown in ë5ë that the loss due to ænite interleaving on a correlated channel is moderate. Sequential decoding may also be applied in hybrid ARQ systems utilizing the fact that the decoder will with high probability know when there is a need for retransmission by detecting overæows. Multiple rate and variable rate is also possible when using sequential decoding. It has been indicated though that puncturing might have a more severe eæect when using sequential decoding compared to using Viterbi decoding. More detailed results on sequential decoding on Rayleigh fading channels can be found in ë5ë.

5 Acknowledgments The work presented in this paper has been partly ænanced by the project ACTS A90 FRAMES which is partly funded by the European community. References ë1ë R. V. Cox and P. Kroon, ëlow bit-rate speech coders for multimedia communication," IEEE Communications Magazine, vol. 34, no. 12, pp. 34í41, Dec ë2ë K. Rijkse, ëh.263: Video coding for low-bit-rate communication," IEEE Communications Magazine, vol. 34, no. 12, pp. 42í45, Dec ë3ë S. Wicker, Error control systems for digital communication and storage, Prentice-Hall, Englewood Cliæs, NJ, ë4ë S. Kallel and D. Haccoun, ëgeneralized type II hybrid ARQ scheme using punctured convolutional coding," IEEE Transactions on Communications, vol. 38, no. 11, pp. 1938í1946, Nov ë5ë P. Orten and A. Svensson, ësequential decoding in future mobile communications," in Proc. IEEE International Symposium on Personal, Indoor and Mobile Radio Communications, Helsinki, Finland, ë6ë P. Frenger, P. Orten, T. Ottosson, and A. Svensson, ërate matching in multichannel systems using RCPCcodes," in Proc. IEEE Vehicular Technology Conference, Phoenix, USA, 1997, pp. 354í357. ë7ë P. Frenger, P. Orten, and T. Ottosson, ëconvolutional codes with optimum distance spectrum," Submitted to IEEE Communications Letters, July ë8ë P. Frenger, P. Orten, T. Ottosson, and A. Svensson, ërate compatible convolutional codes for multirate DS-CDMA systems," Submitted to IEEE Transactions on Communications, Aug ë9ë P. Frenger, P. Orten, T. Ottosson, and A. Svensson, ërate compatible convolutional codes for multichannel systems," Tech. Rep. 19, Department of Information Theory, Chalmers University of Technology, Sweden, Sept ë10ë P. Frenger, P. Orten, and T. Ottosson, ëcombined coding and spreading in CDMA systems using maximum free distance convolutional codes," in Proc. IEEE Vehicular Technology Conference, Ottawa, Canada, ë11ë S. Falahati and A. Svensson, ëhybrid type II ARQ schemes for rayleigh fading channels," to be presented at International Conference on Telecommunications, ë12ë K. J. Larsen, ëshort convolutional codes with maximal free distance for rates 1è2, 1è3, and 1è4," IEEE Transactions on Information Theory, vol. IT-19, pp. 371í372, May ë13ë J. Hagenauer, ërate-compatible punctured convolutional codes èrcpc codesè and their applications," IEEE Transactions on Communications, vol. 36, no. 4, pp. 389í400, Apr ë14ë L. H. C. Lee, ënew rate-compatible punctured convolutional codes for Viterbi decoding," IEEE Transactions on Communications, vol. 42, no. 12, pp. 3073í3079, Dec ë15ë ACTS Mobile Communication Summit, Rhodes, Greece, 1998, Session A5, Radio Access Techniques II. ë16ë P. J. Lee, ënew short constraint length rate 1=n convolutional codes which minimize the required SNR for given desired bit error rates," IEEE Transactions on Communications, vol. COM-33, no. 2, pp. 171í177, Feb ë17ë S. Lefrançcois and D. Haccoun, ësearch procedures for very low rate quasi-optimal convolutional codes," in Proc. IEEE International Symposium on Information Theory, Trondheim, Norway, 1994, p ë18ë T. Ottosson and A. Svensson, ëmulti-rate schemes in DSèCDMA systems," in Proc. IEEE Vehicular Technology Conference, Chicago, USA, 1995, pp. 1006í1010. ë19ë P. Orten and T. Ottosson, ërobustness of DS-CDMA multiuser detectors," in Proc. IEEE Communication Theory Mini-Conference, Phoenix, USA, ë20ë A. J. Viterbi, ëvery low rate convolutional codes for maximum theoretical performance of spread-spectrum multiple-access channels," IEEE Journal on Selected Areas in Communications, vol. 8, no. 4, pp. 641í649, May ë21ë J. Y. N. Hui, ëthroughput analysis for code division multiple accessing of the spread spectrum channel," IEEE Journal on Selected Areas in Communications, vol. SAC-2, no. 4, pp. 482í486, July ë22ë A. J. Viterbi, CDMA: principles of spread spectrum communication, Addison-Wesley, Reading, MA, ë23ë A. J. Viterbi and J. K. Omura, Principles of digital communication and coding, McGraw-Hill, New York, NJ, 1979.

6 Information block Channel blocks Source data rate [kbit/s] channels 6 channels 5 channels 4 channels 3 channels 2 channels 1 channel R =1 R =2=3; 1=3 R =2=3; 1=3 3= Code rate Figure 1: Possible source data rates using rate matching onto logical channels of rate R 0 =15 kbitès. 4. R =1; 1=2; 1=3 C3 2 Table 1: Theoretical limits for sequential decoding on Rayleigh fading channel with soft decisions and BPSK modulation. R 1=4 1=3 1=2 2=3 3=4 E b =N 0 ëdbë Soft-gain ëdbë R =1; 2=3; 1=2; 2=5; 1=3 C3 C4 C5 Figure 3: Diagram of the æve diæerent ARQ schemes. Here L p is the channel-block length. First the code word is transmitted. If a repeat request is made the next code word èè, containing bits that were punctured out in the previous code word, is transmitted Efficiency Scheme 1 Scheme 2 Scheme 3 Scheme 4 Scheme Nested codes Superorthogonal codes Conventional system Orthogonal codes normalized throughput Total spreading, N tot 0.2 Figure 2: The eæciency of a code-spread system using K = 10 nested encoders, a conventional system using a R = 1=4, K = 10 code, and a system using orthogonal and superorthogonal convolutional codes average Ec/No db Figure 4: Analytical results of normalized throughput for L p = 64 bits.

Convolutional Coding and ARQ Schemes for Wireless Communications Sorour Falahati, Pal Frenger, Pal Orten, Tony Ottosson and Arne Svensson Communicatio

Convolutional Coding and ARQ Schemes for Wireless Communications Sorour Falahati, Pal Frenger, Pal Orten, Tony Ottosson and Arne Svensson Communication Systems Group, Dept. of Signals and Systems Chalmers