Convolutional Coding Schemes for Variable Rate ... - Semantic Scholar

Convolutional Coding Schemes for Variable Rate, Unequal Error Protection, and Packet Data Services Sorour Falahati, Pal Frenger, Pal Orten, Tony Ottosson and Arne Svensson

Communication Systems Group, Dept. of Signals and Systems Chalmers University of Technology, SE-412 96 Goteborg, Sweden fSorour.Falahati, Pal.Frenger, Pal.Orten, Tony.Ottosson, and [email protected]

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 rst generation analog systems were replaced by the second generation digital systems. These systems have higher capacity due to source (speech) 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 trac 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 (see e.g. [1, 2]), that these services will require dierent data rates, quality of service (bit error rate) 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 exibility regarding the data rate and its variability, the provided quality of service, and the delay. The quality of service (bit error rate) requirements imply an adaptive error control coding scheme making it possible to change code rate from one connection (or data packet) to another. Also within one transmission there may be needs for dierent quality classes in for example speech communication (unequal error protection (UEP)), or to adapt to the channel condition thus achieving a higher spectral eciency. Other applications of variable code rate channel codes are packet transmission based on hybrid automatic repeat request (HARQ) [3,4], and rate matching where a speci c source data rate is mapped onto the allocated channel data rate. Due to the reasons presented, we would 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 a main diculty in the complexity needed to perform soft-decision decoding which is vital for any bandwidth ecient 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 (or a few decoders) to decode all code rates. For block codes, however, the decoders must usually be designed for a speci c code. For convolutional codes, soft-decision decoding comes naturally using a soft metric in the Viterbi decoder, and the use of rate-compatible convolutional (RCC) 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 dicult to use turbo codes for delay sensitive

services. Furthermore, the high complexity in decoding turbo codes may be prohibitive. Another possible coding/decoding scheme is long constraint length convolutional codes together with sequential decoding [5]. In this paper, which is a summary of research performed on channel coding within FRAMES by Chalmers during the last year [5{11], we discuss applications of the newly found powerful families of rate-compatible convolutional codes with 533 code rates in the range 1 512 { 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: (1) rate matching in a multicode DS-CDMA system; (2) combined coding and spreading in a DS-CDMA system; and (3) Hybrid ARQ type II schemes for fading channels. Furthermore, we treat sequential decoding and its applicability for fading channels. =

=

2 Optimum Distance Spectrum (ODS) 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 rst attempts to nd good codes were therefore restricted to nding maximum free distance (MFD) 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 [12]. To guarantee maximum free distance, a full search was performed only in the few cases where no code ful lling 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 [7], Frenger, Orten and Ottosson introduced the concept of optimum distance spectrum (ODS) 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 and 1 4 are given in [7,8]. =

=

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3 Rate-Compatible Convolutional (RCC) 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 [4]. Thus we present a exible 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 (RCPC) Codes

Rate-compatible punctured convolutional (RCPC) 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 speci ed 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 bit(s). The bits to be punctured are described by a puncturing matrix of size n  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 code of rate 1=n, we obtain a family of (n , 1)p dierent codes with the rates R = p=(np); p=(np , 1); : : : ; p=(p + 1). 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 [13]. The problem with the existing RCPC codes [13, 14] is the limited number of code rates (and thus also a limited range of code rates). Furthermore, because only codes with constraint

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 [8,9] 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 [15].

3.2 Nested Convolutional Codes

Nested convolutional codes [16,17] are obtained by extending a code of rate 1=n to a rate 1=(n+1) code by searching for the \best" 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 search for low-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 [10] Frenger, Orten and Ottosson present nested codes with rates 1=512{1=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 (parent code of rate 1 4 and puncturing period = 8) for rate matching, we constructed a multicode DS-CDMA system [18] with the basic data rate 0 = 15 kbit/s (the data rate on one spreading code). As seen in Figure 1, the 24 RCPC codes and the 6 nested codes (down to rate 1 10) give a very ne resolution in the source data rate. =

p

R

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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 (DS-CDMA), where spreading is achieved by multiplication of the signal by a pseudo-random spreading sequence. In order to achieve suciently 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 to errors in the channel parameter estimates [19]. 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 [20, 21]. 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 of good low-rate codes. Current proposals use either orthogonal, biorthogonal or superorthogonal convolutional codes [22]. We have in [10] 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

automatic repeat request (ARQ) 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 [3]. In simple ARQ unprotected (no channel coding) 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 (the channel coding) 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 (incremental redundancy). Thus, the throughput for this scheme will be better than a simple ARQ scheme for bad channel conditions. In [11] some new hybrid schemes based on RCPC codes are proposed and compare with previously studied schemes. Four hybrid type-II ARQ schemes (schemes 2-5) are compared to a simple ARQ scheme (scheme 1). The type-II schemes use RCPC encoders (can be found in [9]) 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 Lp 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 [11]. 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 (found in [11]) for dierent 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 [5] 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. A well 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 dierent path (see for instance [23]). As a consequence of this searching strategy, the computational complexity is a random variable. This means that occasionally there will be over ows in the input buer 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 [23], and it is thus possible to nd the mean and variance of the computational complexity. By using the requirement that the variance of the computational complexity should be nite, we can obtain theoretically for which b 0 sequential decoding is possible. Such results for a number of dierent modulation methods and code rates for a Rayleigh fading channel are presented in [5]. Table 1 shows these theoretical limits for BPSK modulation and soft decision decoding. We can see from Table 1 that for rate = 1 2 coding with BPSK modulation and soft decision sequential decoding is possible when b 0 is above 8 dB. This limit has been veri ed by simulations in [5]. As long as we operate above the theoretical limit we can achieve as low error rate as wanted simply by choosing a suciently 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 over ow rate in the input buer (given by hardware speed and delay requirements) and the probability of choosing the wrong trellis path (set by the constraint length). It has also been shown in [5] that the loss due to nite 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 over ows. Multiple rate and variable rate is also possible when using sequential decoding. It has been indicated though that puncturing might have a more severe eect when using sequential decoding compared to using Viterbi decoding. More detailed results on sequential decoding on Rayleigh fading channels can be found in [5]. E =N

R

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E =N

Acknowledgments The work presented in this paper has been partly nanced by the project ACTS AC090 FRAMES which is partly funded by the European community.

References

[1] R. V. Cox and P. Kroon, \Low bit-rate speech coders for multimedia communication," IEEE Communications Magazine, vol. 34, no. 12, pp. 34{41, Dec. 1996. [2] K. Rijkse, \H.263: Video coding for low-bit-rate communication," IEEE Communications Magazine, vol. 34, no. 12, pp. 42{45, Dec. 1996. [3] S. Wicker, Error control systems for digital communication and storage, Prentice-Hall, Englewood Clis, NJ, 1995. [4] S. Kallel and D. Haccoun, \Generalized type II hybrid ARQ scheme using punctured convolutional coding," IEEE Transactions on Communications, vol. 38, no. 11, pp. 1938{1946, Nov. 1990. [5] P. Orten and A. Svensson, \Sequential decoding in future mobile communications," in Proc. IEEE International Symposium on Personal, Indoor and Mobile Radio Communications, Helsinki, Finland, 1997. [6] P. Frenger, P. Orten, T. Ottosson, and A. Svensson, \Rate matching in multichannel systems using RCPCcodes," in Proc. IEEE Vehicular Technology Conference, Phoenix, USA, 1997, pp. 354{357. [7] P. Frenger, P. Orten, and T. Ottosson, \Convolutional codes with optimum distance spectrum," Submitted to IEEE Communications Letters, July 1997. [8] P. Frenger, P. Orten, T. Ottosson, and A. Svensson, \Rate compatible convolutional codes for multirate DS-CDMA systems," Submitted to IEEE Transactions on Communications, Aug. 1997. [9] P. Frenger, P. Orten, T. Ottosson, and A. Svensson, \Rate compatible convolutional codes for multichannel systems," Tech. Rep. 19, Department of Information Theory, Chalmers University of Technology, Sweden, Sept. 1997. [10] P. Frenger, P. Orten, and T. Ottosson, \Combined coding and spreading in CDMA systems using maximum free distance convolutional codes," in Proc. IEEE Vehicular Technology Conference, Ottawa, Canada, 1998. [11] S. Falahati and A. Svensson, \Hybrid type II ARQ schemes for rayleigh fading channels," to be presented at International Conference on Telecommunications, 1998. [12] K. J. Larsen, \Short convolutional codes with maximal free distance for rates 1/2, 1/3, and 1/4," IEEE Transactions on Information Theory, vol. IT-19, pp. 371{372, May 1973. [13] J. Hagenauer, \Rate-compatible punctured convolutional codes (RCPC codes) and their applications," IEEE Transactions on Communications, vol. 36, no. 4, pp. 389{400, Apr. 1988. [14] L. H. C. Lee, \New rate-compatible punctured convolutional codes for Viterbi decoding," IEEE Transactions on Communications, vol. 42, no. 12, pp. 3073{3079, Dec. 1994. [15] ACTS Mobile Communication Summit, Rhodes, Greece, 1998, Session A5, Radio Access Techniques II. [16] P. J. Lee, \New 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. 171{177, Feb. 1985. [17] S. Lefrancois and D. Haccoun, \Search procedures for very low rate quasi-optimal convolutional codes," in Proc. IEEE International Symposium on Information Theory, Trondheim, Norway, 1994, p. 278. [18] T. Ottosson and A. Svensson, \Multi-rate schemes in DS/CDMA systems," in Proc. IEEE Vehicular Technology Conference, Chicago, USA, 1995, pp. 1006{1010. [19] P. Orten and T. Ottosson, \Robustness of DS-CDMA multiuser detectors," in Proc. IEEE Communication Theory Mini-Conference, Phoenix, USA, 1997. [20] A. J. Viterbi, \Very 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. 641{649, May 1990. [21] J. Y. N. Hui, \Throughput analysis for code division multiple accessing of the spread spectrum channel," IEEE Journal on Selected Areas in Communications, vol. SAC-2, no. 4, pp. 482{486, July 1984. [22] A. J. Viterbi, CDMA: principles of spread spectrum communication, Addison-Wesley, Reading, MA, 1995. [23] A. J. Viterbi and J. K. Omura, Principles of digital communication and coding, McGraw-Hill, New York, NJ, 1979.

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2L p C2 Table 1: Theoretical limits for sequential decoding on Rayleigh fading channel with soft de- 5. C0 C3 cisions and BPSK modulation. C4 =1 2 3 1 2 2 5 1 3 14 13 12 23 34 C5 5.9 6.5 8.0 10 11.3 0 [dB] b Soft-gain 3.4 4.1 6.0 8.9 11 [dB] Figure 3: Diagram of the ve dierent ARQ schemes. Here p is the channel-block length. First the code word C1 is transmitted. If a repeat request is made the next code word (C2), containing bits that were punctured out in the previous code word, is transmitted. R

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