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Çok-düzeyli kodlama/çok-aşamalı kod çözme tekniğinin incelenmesi ve frekans/faz kaydırmalı anahtarlama modülasyonuna uygulanması

Multilevel coding/multistage decoding and its application to frequency/phase shift keying modulation

  1. Tez No: 21765
  2. Yazar: İBRAHİM ALTUNBAŞ
  3. Danışmanlar: YRD. DOÇ. DR. ÜMİT AYGÖLÜ
  4. Tez Türü: Yüksek Lisans
  5. Konular: Elektrik ve Elektronik Mühendisliği, Electrical and Electronics Engineering
  6. Anahtar Kelimeler: Belirtilmemiş.
  7. Yıl: 1992
  8. Dil: Türkçe
  9. Üniversite: İstanbul Teknik Üniversitesi
  10. Enstitü: Fen Bilimleri Enstitüsü
  11. Ana Bilim Dalı: Belirtilmemiş.
  12. Bilim Dalı: Belirtilmemiş.
  13. Sayfa Sayısı: 185

Özet

ÖZET Bu tezde, çok-düzeyli kafes kodlama ve çok-aşamalı kodçözme tekniğine dayanarak, 8-PSK, 32-CROSS ve 2FSK/4PSK modülasyon türleri için kodlama kazancı yüksek, kodçözme karmaşıklığı düşük sayısal veri iletim sistemleri tasarlanmıştır. Kodlama kazancını artırmak amacıyla her düzey için uygun kodlama oranları belirlenmiş ve bu kodlama oranları için her düzeyin bölmelediği işaret kümesine ilişkin en küçük Oklid uzaklığını maksimum yapan konvolüsyonel kodlar kullanılmıştır. Kod çözme karmaşıklığını azaltmak amacıyla ise, belli bir kodlayıcı serbest Hamming uzaklığı için sınırlı uzunluğu (bellek elemanı sayısı) en küçük olan konvolüsyonel kodlar, kimi düzeylerde de boşluktu konvolüsyonel kodlar kullanılmıştır. Böylece, ele alınan modülasyon türleri için literatürde bulunan klasik Ungerboeck tipi sistemlere göre aynı kodlama hızında ve aynı bandgenişliğinde daha yüksek kodlama kazançlı ve daha düşük kodçözme karmaşıklıktı yeni sistemler elde edilmiştir. -V-

Özet (Çeviri)

SUMMARY MULTILEVEL CODING/MULTISTAGE DECODING AND ITS APPLICATION TO FREQUENCY/PHASE SHIFT KEYING MODULATION The main purpose in digital communication systems is to transmit most possible data with the minimum number of error from the source to the user in a given time interval. Error probability of the receiver, for a given data rate is considered as a performance criterion. In classical digital communication systems the functions of modulation and coding are considered separetely. Modulators and demodulators convert an analog waveform channel into a discrete channel, whereas encoders and decoders correct errors that occur on the discrete channel. Conventional encoders and decoders for error correction operate code symbols transmitted over the channel. If encoder has the code of rate k/n, n-k redundant check symbols are added to every k information symbols, where k s n. Although, certain number of errors can be corrected by using error-correcting codes, this method causes to rate loss. There are two methods to compansate the rate loss: One of them to increase the modulation rate if the channel permits bandwidth expansion, the other is to enlarge the signal set of the modulation system. But, these methods are not suitable for some band-limited channels such as telephone channels, so that good results couldn't be obtained. In the last of 1970's, Ungerboeck [1],(2],[3] proposed a channel coding technique that achieves remarkable coding gains, without sacrificing the data rate or expanding the bandwidth of the transmitted signal. The basic idea consists of encoding k information bits, by means of a rate R«k/k+1 convolutional encoder, into (k+1) bits which select points from one of the 2k+1 signal constellations according to mapping by set partitioning. That is, coding and modulation are considered as an entity. This technique is known as Trellis-Coded Modulation (TCM) where coding gain is a function of the constraint length of the code and the signal constellation. Maximum likelihood soft decoding of the unquantized demodulator outputs is assumed, thus avoiding loss of information prior to final decoding. This implies that codes can be -VI-designed to achieve minimum free Euclidean distance rather than Hamming distance. Based on this distance measure more powerful codes can be designed. After introducing the TCM, research s increased on this subject. The first method for error and bit error probability upper bounds were given by Biglieri [41 for TCM. Later, Zehavi and Wolf {5J improved a better and easily applicable method for only trellis codes that have a certain symmetry property. In the Zehavi's and Wolf's method, generating function techniques for analyzing error-event and bit-error probabilities for trellis codes are considered. The conventional state diagram approach for linear codes where the number of states is equal to the number of trellis states can not be applied directly to arbitrary trellis codes, and instead, a state diagram where the number of states is equal to the square of the number of trellis states must be used. It is shown that for an interesting class of trellis codes a modified generating function can be defined for which the number of states is equal to the number of trellis states. Furthermore, the complexity of calculating this modified generating function is the same as for the ordinary generating function of a convoiutional code with the same number of trellis states. TCM was rapidly adopted for implementation in high speed telephone-line modems in the mid-1 980's. The most advanced modulation and equalization techniques have often been developed and first implemented in telephone-line modems, because of the applicability of a linear Gaussian model, the commercial importance of the modem industry, the significance of higher data rates or improved signal-to-noise ratio (SNR) margin to the costumer and the relatively low symbol rates (2400 symbols per second) of modems. Many kinds of modems were designed till today. But, neither of these modems was standardized. By the time CCITT began to consider a standart for 9600 bps dial modems in 1983, Ungerboeck's paper had appeared and it was recognized that the 3 or more dB of coding gain that TCM could provide would be essential for reliable 9600 bps operation over the dial network. A variant of Ungerboeck's 8-state 2-dimensional code, due to Wei {6], (7] who introduced nonlinear elements into the convoiutional encoders to prevent phase rotation, was adopted in CCITT Recommendation V.32. with a coding gain of 4 dB [8], [9] and also subsequently in the V.33 standart for 14400 bps private-line modems. The binary partitions of Ungerboeck have been generalized by Calderbank and Sloane via the concept of cosets.This permits -Vil-multidimensional signal sets to be conveniently partitioned. Forney employs the coset code notation to include block codes such as lattice codes in this common framework. While the coset notation encompasses many classes of codes, including binary and Ungerboeck codes, in many cases the algebraic structure implied in the notation has no simple geometric interpretation. Thus it is convenient to apply it to a number of codes related to Ungerboeck's codes, such as those of Padovani and Wolf for phase-shift-keyed (PSK)/ frequency-shift-keyed (FSK) modulations [10] and some codes on irregular signal sets. Another bandwidth efficient coding technique is continuous- phase frequency modulation (CPFSK). The progenitor of CPFSK is the now well-known minimum shift keying (MSK) modulation scheme. Other CPFSK techniques such as multi-h, M-ary CPFSK exploit two advantages of phase continuity. First, these schemes yield transmitted signals whose spectrum falls off more sharply than noncontinuous phase schemes. Second, the requirement of the phase continuity prohibits certain sequences of signals from occuring. This prohibition results in signal sequences with greater minimum Euclidean distance as compared to uncoded modulation. Padovani and Wolf [10] designed the codes which have better coding gains than Ungerboeck's codes by using frequency/phase shift keying (FSK/PSK) modulation. As a result of all these researches, the performance attainable with practical trellis codes is now approaching to the Shannon [11] limit. For example, Ungerboeck's 256-state codes obtain effective coding gains of about 5.5 dB. But, these codes have too high decoding complexity. So, the researches focused on the codes having high coding gains and low decoding cornplexities[12],[13],[14]. The optimal decoding operation for convolutional codes requires a memory that stores a function of the entire past history of the received bit stream. The performance (as measured by error rate) of a convolutional coding system improves as the complexity allowed for the decoder is increased. Several methods of decoding convolutional codes have been developed. The optimal (maximum likelihood ) scheme is generally known as the Viterbi Algorithm. Viterbi decoding for reasonably short lengths (number of memory elements) is feasible to implement and high decoding speeds are achievable. For extremely low error probabilities, a large constraint length is required. This method finds in terms of a defined measure the symbol sequence which is closest to the received symbol sequence. This recursive procedure requires that the shortest path, called the survivor, entering at each state of the trellis be retained at time d. To proceed to time (d+1), all-time-d -VIII-survivors are extended by computing the metrics {lengths) of the extended path segments based on the calculated branch metrics, which depend on the branch symbols in the trellis and the value of the received sample. The metric of the extended path into each state are compared, and the shortest of these is isolated. This shortest length path into each state, which represents the time- (d+1) survivor, is retained. The procedure is repeated for iime- (d+2), and so on. Error control techniques using convolutional codes have been dominated by low rate R=»1/n codes. Optimal low rate codes providing large coding gains are available in the literature and practical implementations of powerful decoders such as Viterbi exist for data rates in the range of 10-40 M bits/sec. However, as the trend for ever increasing data transmission and high error performance continues while conserving bandwith, the needs arise for good high-rate R=k/n convolutional codes as well as practical encoding and decoding techniques for these codes. Unfortunately a straightforward application of Viterbi and sequential decoding to high rate codes becomes very rapidly impractical as the coding rate increases. Furthermore, a conspicuous lack of good nonsystematic long memory convolutional codes with rates R larger than 2/3 prevails in the literature. A significant breakthough occured recently with the advent of high rate“punctured”convolutional codes where the inherent difficulties of coding and decoding of high rate codes can be almost entirely circumvented. Viterbi or sequential decoding of rate k/n punctured convolutional codes is hardly more complex than for rate 1/n codes and furthermore, either technique may be easily applicable to adaptive and variable-rate decoding. A punctured code is a high rate code obtained by periodically del eti ng( i.e. puncturing) certain symbols from the output stream of a low rate encoder. The resulting high rate code depends on both the original low rate code and perforation pattern, that is, the number and positions of the punctured symbols. Cain et ai. have defined a class of punctured rate (n-1)/n convolutional codes and clarified the Viterbi decoding procedure for the punctured code. Yasuda et al. have described an optimum soft decision Viterbi decoding scheme and the configuration of a variable-rate Viterbi decoder where the various rates were obtained by deleting bits from a low-rate code in different ways. Hardware experiments and theoretical calculation showed that punctured convolutional coding and soft Viterbi decoding enable reliable communication over band-limited satellite channels. ?IX-Imai and Hirakawa [15] proposed a coded modulation scheme based on a multilevel code which admits a multistage decoder. In this method, the channel signal set is binary partitioned, using the set partitioning rule, where the binary labels of the edges from one level of the partition chain to the next are encoded by independent either block or convolutional codes. In the earliest time of their work due to the use of the block codes and hard-decision decoders, significantly coding gain could not obtained. In a multilevel coded modulation system, there is a tight connection between the Euclidean and Hamming distances. By using this propertly, Yamaguchi and Imai [16] designed systems which contain convolutional codes and soft-decision decoders and showed that these systems have high coding gains and reduced decoding complexity compored to the Ungerboeck's approach. Pottie and Taylor f17] are generalized the multilevel coding technique and showed that most of the trellis codes, in fact, are subclasses of multilevel codes, including Ungerboeck codes. From the coding point of view there are differences between the codes proposed by Pottie-Taylor and the codes proposed by Imai- Hirakawa, although ail the codes are multilevel. Pottie-Taylor and also Calderbank [16] tried to increase the coding gain by using different kinds of encoders in several levels. Error performance of multilevel codes was firstly analysized by Kofman.Zehavi and Shamai {19], [20]. As mentioned before, for the Gaussian channel, Ungerboeck's like codes achieve a remarkable coding gain when compared to uncoded modulation system with the same spectral efficiency and data rate. However, this codes often poor performance when operating over fading channels. The reason is that codes for the Gaussian channel designed to achieve mainly a large minimum Euclidean distance, where as for fading channels, such as Rician and Rayieigh fading channels or channels distributed by jamming and impuls noise, a good error probability performance demands both large Euclidean distances and Hamming distances between channel signal sequences. By using this criterion Zhang, Vucetic [21] and also Kofman et. al. [22] investigated error probability of multilevel systems for fading channels. On the other hand, Kasami et. al. [23] investigated the multilevel technique for combining block coding and modulation. At this investigation, first, a general formulation was presented for multilevel modulation codes in terms of component codes with -X-appropriate distance measures. Then a specific method for constructing multiievet block modulation codes with interdependency among component codes was proposed, in addition a technique was presented for analyzing the error performance of block modulation codes for Gaussian channels based on soft decision maximum likelihood decoding. In this thesis, by using multilevel coding and multistage decoding techniques explained above (Pottie-Taylor coding and Imai-Hirakawa coding) new systems are constructed for 8-PSK, 32- CROSS and 2FSK/4PSK modulations. For the 8-PSK modulation, by using convolutional codes and punctured convolutional codes in the several levels, multilevel systems with rate 2/3 are designed and comparisons are done for the coding gains, decoding complexitiys and error performances with respect to the Ungerboeck's technique. By using a computer simulation model, error probabilities of the Ungerboeck and multilevel systems are compared. On the other hand, the code structure of the V.32 modem using 32-CROSS modulation at rate 9600 bit/s were designed by the multilevel Imai- Hirakawa coding technique and comparisions are given. The FSK/PSK modulation which use several carrier frequencies and phases is very suitable for multilevel coding technique due to the large minimum Euclidean distance at the first partitioning step. So, multilevel coding technique is applied to 2FSK/4PSK modulation and new systems are compared to the Padovani-Wolf systems. It is shown that the new systems have better error performances and reduced decoding complexities. In the second chapter of the thesis, Trellis Coded Modulation technique is explained, error performance and decoding complexity concepts are defined. Chapter 3 is destinated to the presentation of the multilevel coding and multistage decoding. The multilevel Pottie-Taylor coding and Imai-Hirakawa coding approaches are explained and the decoding complexity related to these schemes are defined. Also, the error performance of the Imai-Hirakawa coding technique is analysed. In the fourth chapter, 2FSK/4PSK modulation that uses two different carrier frequencies and four phases is presented. Multilevel systems with rate 2/3 based on several convolutional codes are designed. The analytical error performance calculations are also done and the upper bound curves of several related system are compared..XI-

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