Durağan olmayan kanallarda uyarlamalı hata kontrol yöntemleri
Adaptive coding schemes for time-varying channels
- Tez No: 39482
- Danışmanlar: DOÇ.DR. H. ÜMİT AYGÖLÜ
- Tez Türü: Yüksek Lisans
- Konular: Elektrik ve Elektronik Mühendisliği, Electrical and Electronics Engineering
- Anahtar Kelimeler: Belirtilmemiş.
- Yıl: 1994
- Dil: Türkçe
- Üniversite: İstanbul Teknik Üniversitesi
- Enstitü: Fen Bilimleri Enstitüsü
- Ana Bilim Dalı: Belirtilmemiş.
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: 83
Özet
along that path, the better the code will perform even though dfree does not achieve its optimum value over the additive white Gauss noise (AWGN). As K increases, the significance of these primary and secondary considerations shift relative to one another until K reaches infinity (AWGN) in which case optimum performance is once again achieved by a trellis code designed to maximise dfree. When properties cited above are used as a motivation for good code design, it was showed in [6] that multiple trellis coded modulation (MTCM), wherein more than one channel symbol is assigned to each trellis branch, is a natural choice in this situation. In fact, it was shown in [5] that MTCM allows us to achieve a performance on the fading channel superior to that achievable by a conventional TCM of the same throughput and number of trellis states. Biglieri [3] described a technique for analyzing bounds on the bit-error and error-event probabilities. His method (the method of pairwise states [3]) involves a generalized generating function which enumerates all possible incorrect paths. The generalized generating function can be obtained as the transfer function of a state diagram regarded as a signal flow graph. The state diagram is defined over an expanded set of states, namely 22v, where 2V is the number of states in the trellis and v is the memory of the code. Since the number of states now grows exponentially with 2v rather than v, this method is only useful for very simple codes. Zehavi and Wolf [4] defined a new method which will be applied to a special class of trellis codes. For this class the error weight distribution, the error event probability, and the bit-error probability can be bounded by a generating function which is obtained as the transfer function of a state diagram containing 2V states. This approach can be applied to a broad class of trellis codes with some symmetry properties, namely,“uniform error properties”[17]. Since our aim in this thesis is to obtain high efficient and reliable systems for nonstationary channels, the approach has been to use an adaptive coding scheme that responds to the actual channel error condition by selecting the optimum code rate. Thesis describes an adaptive error control scheme based on FEC by multiple trellis coded modulation technique instead of ARQ. We concentrate on FEC coding because the system throughput deteriorates considerably when the error rate increases since retransmissions are often needed. ARQ design also requires a much more specific system design [18]. Two different coded-modulators with different rates are proposed for a nonstationary channel model with two states, one good and the other bad. While for the good state, which is Gaussian, uncoded 4PSK is used for the bad channel state, which is Rayleigh, a 2 states, 2/4 code rate multiple trellis code modulation system (MTCM) employed. MTCM is preferred due to its high performance on fading channels. The performance of the proposed scheme is analysed both analytically and by a computer simulation. Several comparisons with related error control schemes are also given. vrn
Özet (Çeviri)
SUMMARY ADAPTIVE CODING SCHEMES FOR TİME- VARYING CHANNELS in digital communication system design, the main aim is to improve the error performance. Since the errors occur due to the channel impairments like noise, fading, the channel model should be vvell defined and the error control system should be property chosen. Error statistics on most real channels are time varying. Though statistical characteristics of most real channels can significantly vary with time, propagation experiments for various types of channels indicate that the basic system parameters remain constant över short time intervals. Error statistics for most real channels can thus be obtained by using a quasistationary model, in this model it is assumed that the channel is“stationary”över certain short time intervals, i.e. channel parameters remain constant. A time varying channel is thus represented by M stationary channel models. The most general quasistationary model for representing real channel is the finite- state Markov chain model. Classically, error control techniques have been classified in two ways those that depend on feedback from the receiver on the state of a received message, also knovvn as automatic repeat request (ARQ) systems and those that do not require feedback informatiön, i.e. forvvard error correction (FEC) systems. in any ARQ error control system, a high rate error detecting code incorporated with a certain retransmission protocol, is.used. VVhen a message of k informatiön bits is ready for transmission, n-k parity-check bits are appended to it to form a codevvord. These n-k parity-check bits are formed based on the code used by the system. The codevvord is then transmitted to the receiving end. The transmitted codevvord is contaminated by the channel noise, and the received word may contain transmission errors. When a word is received, the receiver (ör decoder) computes its syndrom. If the syndrom is zero, the received word is a codevvord in the code being used. in this case, the received word is assumed to be error free and is delivered (with parity-check bits removed) to the user. If the syndrom of the received word is not zero, the presence of errors is detected. in this case, the receiver discards the erroneously received word, and requests a retransmission continues until the codevvord is successfully received [16]. Hovvever, As the channel error rate increases, an ARQ system maintains high reliability but becomes less and less efficient and this problem is a dravvback of the ARQ systems. in ARQ systems, a request is made whenever a received code block is detected to contain öne ör more errors. The statistic that is normally used to vevaluate its efficiency is P(0,n), the probability of finding no errors in a block of n digits. The probability of detecting a block to be in error is approximately given by 1-P(0,n), vvhich determines the expected number of retransmission and hence the efficiency of the system [8]. in an FEC error control system, an error correcting code is used for combating transmission errors. Again, parity-check bits are added to each transmitted message to form a codevvord (ör a code sequence) based on the code used by the system. When the receiver detects the presence of errors in a received word, it attempts to locate and correct the errors. After the error correction has been performed, the decoded word is then delivered to the user. A decoding error is committed if the receiver either fails to detect the presence of errors ör fails to determine the exact locations of the errors. in either case, an erroneous word is delivered to the user. Since no retransmission is required in an FEC error control system, no feedback channel is needed. The throughput of the system is constant, and is equal to the rate of the code used by the system. The dravvback of FEC systems is high efficiency but less reliability The most frequently used measure to indicate the reliability of a block-coded FEC system is the probability of block error. The channel statistic necessary to evaluate this in the case of random error correction is P(m,n), the probability of exactly m errors occurring in a block of n digits. in the case of burst error correction, the statistic is Q(l,n), the probability of an error burst of length l occurring in a block of length n [8]. The most vvidely used method in design of error control consists of selecting a code with the fixed code rate and error correcting capability for the worst channel state. This procedure provides error rates in each state to be belovv a specified value. Hovvever, the code rate (throughput in ARQ) is smaller with respect to that achievable if the optimum code parameters are selected for the states with lovver error probabilities. Alternatively, if the required high error protection for the vvorst state is achieved by using more complex codes, for example convolutional codes with a high memory order, the price is the complexity of the decoder. A more efficient approach is to use an adaptive coding error control system that responds to the actual channel error condition by selecting the optimum code rate. in classical digital communication system design the function of modulation and error correction coding are separated, Conventional encoders and decoders for error correction operate on binary code symbols transmitted över a discrete channel. VVith a code of rate k/n, n-k redundant check symbols are appended to every k information symbol. Since the decoder receives only discrete code symbols, Hamming distance is the appropriate measure of distance for decoding. The rate loss is occurred by sending redundant check symbols. Generally, there exist two possibilities to compensate for the rate loss; increasing the modulation rate if the channel permits bandvvidth expansion, ör VIenlarging the signal set of the modulation system if the channel is band limited. Hovvever, when modulation and error- correction coding are performed in the classical independent manner, disappointing results are obtained. Trellis coded modulation (TCM) is involved by Ungerboeck [1], [2] as a combined coding and modulation technique for digital transmission över band limited channels. Its main attraction is the achievement of significant coding gains över conventional uncoded multilevel modulation vvithout compromising bandwidth efficiency. TCM schemes employ redundant nonbinary modulation in combination with a finite state encoder that govems the selection of modulation signals to generate coded signal sequences in the receiver. The noisy signals are decoded by a soft decision maximum-likelihood sequence decoder. Simple TCM schemes can improve the robustness of digital transmission against additive noise by 3 dB compared to conventional uncoded modulation. VVith more complex TCM schemes, the coding gains can reach 6 dB ör more. These gains are obtained without bandwidth expansion ör reduction of the effective information rate as required by traditional error-correction schemes. Signal vvaveforms representing information sequences are more impervious to noise-induced detection errors if they are very different from each other. Mathematically, this translates into the requirement that signal sequences should have large distance in Euclidean signal space. The essential new concept of TCM that led to the above mentioned gains was to use signal-set expansion to provide redundancy for coding and to design coding and signal-mapping functions jointly so as to maximise directly the“free distance”(minimum Euclidean distance) betvveen coded sequences. This allovved the construction of modulation codes vvhose free distance significantly exceeded the minimum distance betvveen uncoded modulation signals at the same information rate, bandwidth and signal power TCM schemes, the trellis branches are labelled with redundant nonbinary modulation signals rather then with binary code symbols. Nevertheless, the maximisation of free Euclidean distance is an appropriate criterion only for optimum trellis coded modulation design for additive vvhite Gaussian noise. Divsalar and Simon [5]-[7] shovved that when TCM is used on a Rician fading channel with interteaving/deinterleaving, the asymptotic performance of TCM at high signal-to-noise ratio (SNR) is guided by other factors depending on the value of the Rician parameter K, i.e., the ratio of direct plus specular povver (coherent components) to diffuse power (noncoherent component). in particular, for small values of K, the channel tends toward Rayleigh, the primary design criteria for high SNR become: The length of the shortest error event path, and the product of branch distances along that path [5]. Shortest error event path is equal to the number of trellis branches along that path. Equivalently, if we assume that the ali zeros path in the trellis diagram represents the transmitted sequence, then length is the number of branches in the shortest length path to which a nonzero MPSK symbol is associated [6]. At low values of K, the longer is the shortest error event path and the larger is the product of the branch distances VIIalong that path, the better the code will perform even though dfree does not achieve its optimum value over the additive white Gauss noise (AWGN). As K increases, the significance of these primary and secondary considerations shift relative to one another until K reaches infinity (AWGN) in which case optimum performance is once again achieved by a trellis code designed to maximise dfree. When properties cited above are used as a motivation for good code design, it was showed in [6] that multiple trellis coded modulation (MTCM), wherein more than one channel symbol is assigned to each trellis branch, is a natural choice in this situation. In fact, it was shown in [5] that MTCM allows us to achieve a performance on the fading channel superior to that achievable by a conventional TCM of the same throughput and number of trellis states. Biglieri [3] described a technique for analyzing bounds on the bit-error and error-event probabilities. His method (the method of pairwise states [3]) involves a generalized generating function which enumerates all possible incorrect paths. The generalized generating function can be obtained as the transfer function of a state diagram regarded as a signal flow graph. The state diagram is defined over an expanded set of states, namely 22v, where 2V is the number of states in the trellis and v is the memory of the code. Since the number of states now grows exponentially with 2v rather than v, this method is only useful for very simple codes. Zehavi and Wolf [4] defined a new method which will be applied to a special class of trellis codes. For this class the error weight distribution, the error event probability, and the bit-error probability can be bounded by a generating function which is obtained as the transfer function of a state diagram containing 2V states. This approach can be applied to a broad class of trellis codes with some symmetry properties, namely,“uniform error properties”[17]. Since our aim in this thesis is to obtain high efficient and reliable systems for nonstationary channels, the approach has been to use an adaptive coding scheme that responds to the actual channel error condition by selecting the optimum code rate. Thesis describes an adaptive error control scheme based on FEC by multiple trellis coded modulation technique instead of ARQ. We concentrate on FEC coding because the system throughput deteriorates considerably when the error rate increases since retransmissions are often needed. ARQ design also requires a much more specific system design [18]. Two different coded-modulators with different rates are proposed for a nonstationary channel model with two states, one good and the other bad. While for the good state, which is Gaussian, uncoded 4PSK is used for the bad channel state, which is Rayleigh, a 2 states, 2/4 code rate multiple trellis code modulation system (MTCM) employed. MTCM is preferred due to its high performance on fading channels. The performance of the proposed scheme is analysed both analytically and by a computer simulation. Several comparisons with related error control schemes are also given. vrnIn Chapter II, the time-varying channels are considered, corresponding channel models given in the literature are overviewed. Since the available channel bandwidth is limited in a time-varying channel environment, in Chapter III bandwidth efficient modulation technique, trellis coded modulation (TCM), is reviewed, which is the most relevant in recent years, in Chapter III the multiple trellis coded modulation technique is also investigated because of its high performance on fading channels. The adaptive error control techniques are considered in Chapter IV and then the integration of MTCM schemes to adaptive error control is investigated. The performance of the designed adaptive system is analysed analytically, in Chapter V the performance of the proposed scheme is analysed by computer simulations and lot of perfomance comparisions made between related codes used on Rayleigh fading and Gaussian channels. DC
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