With the enormous growing applications of mobile communications, how to reduce the power dissipation of wireless communication has become an important issue that attracts much attention. One of the key techniques to achieve low power transmission is to develop a powerful channel coding scheme which can perform good error correcting capability even at low signal-to-noise ratio. In recent years, the trend of the error control code development is based on the iterative decoding algorithm which can lead to higher coding gain. Especially, the rediscovery of the low-density parity-check code ¡]LDPC¡^has become the most famous code after the introduction of Turbo code since it is the code closest to the well-know Shannon limit. However, since the block size used in LDPC is usually very large, and the parity matrix used in LDPC is quite random, the hardware implementation of LDPC has become very difficult. It may require a significant number of arithmetic units as well as very complex routing topology. Therefore, this thesis will address several design issues of LDPC decoder. First, under no SNR estimation condition, some simulation results of several LDPC architectures are provided and have shown that some architectures can achieve close performance to those with SNR estimation. Secondly, a novel message quantization method is proposed and applied in the design LDPC to reduce to the memory and table sizes as well as routing complexity. Finally, several early termination schemes for LDPC are considered, and it is found that up to 42% of bit node operation can be saved.

Compressed video bitstream transmissions over wireless networks are addressed in this work. We first consider error control and power allocation for transmitting wireless video over CDMA networks in conjunction with multiuser detection. We map a layered video bitstream to several CDMA fading channels and inject multiple source/parity layers into each of these channels at the transmitter. We formulate a combined optimization problem and give the optimal joint rate and power allocation for each of linear minimum mean-square error (MMSE) multiuser detector in the uplink and two types of blind linear MMSE detectors, i.e., the direct-matrix-inversion (DMI) blind detector and the subspace blind detector, in the downlink. We then present a multiple-channel video transmission scheme in wireless CDMA networks over multipath fading channels. For a given budget on the available bandwidth and total transmit power, the transmitter determines the optimal power allocations and the optimal transmission rates among multiple CDMA channels, as well as the optimal product channel code rate allocation. We also make use of results on the large-system CDMA performance for various multiuser receivers in multipath fading channels. We employ a fast joint source-channel coding algorithm to obtain the optimal product channel code structure. Finally, we propose an end-to-end architecture for multi-layer progressive video delivery over space-time differentially coded orthogonal frequency division multiplexing (STDC-OFDM) systems. We propose to use progressive joint source-channel coding to generate operational transmission distortion-power-rate (TD-PR) surfaces. By extending the rate-distortion function in source coding to the TD-PR surface in joint source-channel coding, our work can use the ??equal slope?? argument to effectively solve the transmission rate allocation problem as well as the transmission power allocation problem for multi-layer video transmission. It is demonstrated through simulations that as the wireless channel conditions change, these proposed schemes can scale the video streams and transport the scaled video streams to receivers with a smooth change of perceptual quality.

In this thesis, bit-by-bit power allocation in order to minimize mean-squared error (MSE) distortion of a basic communication system is studied. This communication system consists of a quantizer. There may or may not be a channel encoder and a Binary Phase Shift Keying (BPSK) modulator. In the quantizer, natural binary mapping is made. First, the case where there is no channel coding is considered. In the uncoded case, hard decision decoding is done at the receiver. It is seen that errors that occur in the more significant information bits contribute more to the distortion than less significant bits. For the uncoded case, the optimum power profile for each bit is determined analytically and through computer-based optimization methods like differential evolution. For low signal-to-noise ratio (SNR), the less significant bits are allocated negligible power compared to the more significant bits. For high SNRs, it is seen that the optimum bit-by-bit power allocation gives constant MSE gain in dB over the uniform power allocation. Second, the coded case is considered. Linear block codes like (3,2), (4,3) and (5,4) single parity check codes and (7,4) Hamming codes are used and soft-decision decoding is done at the receiver. Approximate expressions for the MSE are considered in order to find a near-optimum power profile for the coded case. The optimization is done through a computer-based optimization method (differential evolution). For a simple code like (7,4) Hamming code simulations show that up to 3 dB MSE gain can be obtained by changing the power allocation on the information and parity bits. A systematic method to find the power profile for linear block codes is also introduced given the knowledge of input-output weight enumerating function of the code. The information bits have the same power, and parity bits have the same power, and the two power levels can be different.

<p>Topics in source and channel coding for audiovisual communication systems are studied. The goal of source coding is to represent a source with the lowest possible rate to achieve a particular distortion, or with the lowest possible distortion at a given rate. Channel coding adds redundancy to quantized source information to recover channel errors. This thesis consists of four topics.</p><p>Firstly, based on high-rate theory, we propose Karhunen-Loéve transform (KLT)-based classified vector quantization (VQ) to efficiently utilize optimal VQ advantages over scalar quantization (SQ). Compared with code-excited linear predictive (CELP) speech coding, KLT-based classified VQ provides not only a higher SNR and perceptual quality, but also lower computational complexity. Further improvement is obtained by companding.</p><p>Secondly, we compare various transmitter-based packet-loss recovery techniques from a rate-distortion viewpoint for real-time audiovisual communication systems over the Internet. We conclude that, in most circumstances, multiple description coding (MDC) is the best packet-loss recovery technique. If channel conditions are informed, channel-optimized MDC yields better performance.</p><p>Compared with resolution-constrained quantization (RCQ), entropy-constrained quantization (ECQ) produces a smaller number of distortion outliers but is more sensitive to channel errors. We apply a generalized γ-th power distortion measure to design a new RCQ algorithm that has less distortion outliers and is more robust against source mismatch than conventional RCQ methods.</p><p>Finally, designing quantizers to effectively remove irrelevancy as well as redundancy is considered. Taking into account the just noticeable difference (JND) of human perception, we design a new RCQ method that has improved performance in terms of mean distortion and distortion outliers. Based on high-rate theory, optimal centroid density and its corresponding mean distortion are also accurately predicted.</p><p>The latter two quantization methods can be combined with practical source coding systems such as KLT-based classified VQ and with joint source-channel coding paradigms such as MDC.</p>

<p>With the increasing popularity and relevance of ad-hoc wireless sensor networks, cooperative transmission is more relevant than ever. In this thesis, we consider methods for optimization of cooperative transmission schemes in wireless sensor networks. We are in particular interested in communication schemes that can be used in applications that are critical to low-delays, such as networked control, and propose suitable candidates of joint source-channel coding schemes. We show that, in many cases, there are significant gains if the parts of the system are jointly optimized for the current source and channel. We especially focus on two means of cooperative transmission, namely distributed source coding and relaying.</p><p>In the distributed source coding case, we consider transmission of correlated continuous sources and propose an algorithm for designing simple and energy-efficient sensor nodes. In particular the cases of the binary symmetric channel as well as the additive white Gaussian noise channel are studied. The system works on a sample by sample basis yielding a very low encoding complexity, at an insignificant delay. Due to the source correlation, the resulting quantizers use the same indices for several separated intervals in order to reduce the quantization distortion.</p><p>For the case of relaying, we study the transmission of a continuous Gaussian source and the transmission of an uniformly distributed discrete source. In both situations, we propose design algorithms to design low-delay source-channel and relay mappings. We show that there can be significant power savings if the optimized systems are used instead of more traditional systems. By studying the structure of the optimized source-channel and relay mappings, we provide useful insights on how the optimized systems work. Interestingly, the design algorithm generally produces relay mappings with a structure that resembles Wyner-Ziv compression.</p>

Solutions to the problem of large peak to average power ratio (PAPR) in orthogonal frequency division multiplexing (OFDM) systems are proposed. Although the design of PAPR reduction codewords has been extensively studied and the existence of asymptotically good codes with low PAPR has been proved, still no reduced PAPR capacity achieving code has been constructed. This is the topic of the current thesis.This goal is achieved by implementing a time-frequency turbo block coded OFDM. In this scheme, we design the frequency domain component code to have a PAPR bounded by a small number. The time domain component code is designed to obtain good performance while the decoding algorithm has reasonable complexity. Through comparative numerical evaluation we show that our method achieves considerable improvement in terms of PAPR with slight performance degradation compared to capacity achieving codes with similar block lengths. For the frequency domain component code, we used the realization of Golay sequences as cosets of the fi rst order Reed-Muller code and the modi cation of dual BCH code. A simple MAP decoding algorithm for the modi ed dual BCH code is also provided. Finally, we provide a flexible and practical scheme based on probabilistic approach to a PAPR problem. This approach decreases the PAPR without any signi cant performance loss and without any adverse impact or required change to the system. / Engineering and Applied Sciences

Ένα από τα βασικότερα τμήματα ενός συστήματος ψηφιακής μετάδοσης είναι η κωδικοποίηση καναλιού, η οποία στόχο έχει την ανίχνευση και διόρθωση των λαθών που εισάγονται στην πληροφορία μέσα στο κανάλι. Οι Bose, Chaudhuri και Hocquenghem (BCH) κώδικες είναι μία μεγάλη ομάδα ισχυρών κυκλικών κωδίκων διόρθωσης τυχαίων λαθών. Οι BCH κώδικες περιγράφονται με χρήση αλγεβρικών δομών που λέγονται πεπερασμένα πεδία. Για την κατανόηση των λειτουργιών κωδικοποίησης και αποκωδικοποίησης απαιτείται η προσεκτική μελέτη της άλγεβρας πεπερασμένων πεδίων και της αριθμητικής της. Οι BCH κώδικες χρησιμοποιούνται στο δορυφορικό πρότυπο DVB-S2, σε συνδυασμό με LDPC κώδικες. Στην παρούσα εργασία πραγματοποιήθηκε σχεδίαση και υλοποίηση κωδικοποιητών και αποκωδικοποιητών για κώδικες BCH(15,5,3) και BCH(16200,16008,12). Ο δεύτερος αποκωδικοποιητής σχεδιάστηκε με βάση της προδιαγραφές που θέτει το DVB-S2, και καλύπτει μία από τις περιπτώσεις κωδικοποίησης του συστήματος. Τέλος, αποδεικνύεται ότι με ελάχιστες μετατροπές ο ίδιος αποκωδικοποιητής μπορεί να καλύψει όλες τις περιπτώσεις διόρθωσης 12 λαθών ενός DVB-S2 συστήματος. / Channel coding is one of the most important parts of a digital transmission system, and it aims at the detection and correction of errors that might have occurred in a noisy channel. Bose, Chaudhuri and Hocquenghem (BCH) codes form a large class of powerful random error-correcting cyclic codes. BCH codes operate over algebraic structures called finite fields. Understanding the processes of encoding and decoding requires a careful study of finite field algebra and the associated arithmetic. DVB-S2 is a specification for satellite broadcasting that deploys BCH codes combined with LDPC codes. This thesis sets out to account for the design and implementation of encoders and decoders for the BCH(15,5,3) and BCH(16200,16008,12) codes. The BCH(16200,16008,12) encoder/decoder was designed according to the DVB-S2 standard. Proof is provided that the same encoder/decoder, with only some minor changes, can be used for all the 12 error-correcting codes used in DVB-S2.

Among the recent advances in the area of low-density parity-check (LDPC) codes, protograph-based LDPC codes have the advantages of a simple design procedure and highly structured encoders and decoders. These advantages can also be exploited in the design of protograph-based generalized LDPC (G-LDPC) codes. In this dissertation we provide analytical tools which aid the design of protograph-based LDPC and G-LDPC codes. Specifically, we propose a method for computing the codeword-weight enumerators for finite-length protograph-based G-LDPC code ensembles, and then we consider the asymptotic case when the block-length goes to infinity. These results help the designer identify good ensembles of protograph-based G-LDPC codes in the minimum distance sense (i.e., ensembles which have minimum distances grow linearly with code length). Furthermore, good code ensembles can be characterized by good stopping set, trapping set, or pseudocodeword properties, which assist in the design of G-LDPC codes with low floors. We leverage our method for computing codeword-weight enumerators to compute stopping-set, and pseudocodeword enumerators for the finite-length and the asymptotic ensembles of protograph-based G-LDPC codes. Moreover, we introduce a method for computing trapping set enumerators for finite-length (and asymptotic) protograph-based LDPC code ensembles. Trapping set enumerators for G-LDPC codes represents a more complex problem which we do not consider here. Inspired by our method for computing trapping set enumerators for protograph-based LDPC code ensembles, we developed an algorithm for estimating the trapping set enumerators for a specific LDPC code given its parity-check matrix. We used this algorithm to enumerate trapping sets for several LDPC codes from communication standards. Finally, we study coded-modulation schemes with LDPC codes and pulse position modulation (LDPC-PPM) over the free-space optical channel. We present three different decoding schemes and compare their performances. In addition, we developed a new density evolution tool for use in the design of LDPC codes with good performances over this channel.

Shannon's classical separation result holds only in the limit of infinite source code dimension and infinite channel code block length. In addition, Shannon theory does not address the design of good source codes when the probability of channel error is nonzero, which is inevitable for finite-length channel codes. Thus, for practical systems, a joint source and channel code design could improve performance for finite dimension source code and finite block length channel code, as well as complexity and delay. Consider a multicast system over a broadcast channel, where different end users typically have different capacities. To support such user or capacity diversity, it is desirable to encode the source to be broadcasted into a scalable bit stream along which multiple resolutions of the source can be reconstructed progressively from left to right. Such source coding technique is called multiresolution source coding. In wireless communications, joint source channel coding (JSCC) has attracted wide attention due to its adaptivity to time-varying channels. However, there are few works on joint source channel coding for network multicast, especially for the optimal source coding over broadcast channels. In this work, we aim at designing and analyzing the optimal multiresolution vector quantization (MRVQ) in conjunction with the subsequent broadcast channel over which the coded scalable bit stream would be transmitted. By adopting random index assignment (RIA) to link MRVQ for the source with superposition coding for the broadcast channel, we establish a closed-form formula of end-to-end distortion for a tandem system of MRVQ and a broadcast channel. From this formula we analyze the intrinsic structure of end-to-end distortion (EED) in a communication system and derive two necessary conditions for optimal multiresolution vector quantization over broadcast channels with random index assignment. According to the two necessary conditions, we propose a greedy iterative algorithm for jointly designed MRVQ with channel conditions, which depends on the channel only through several types of average channel error probabilities rather than the complete knowledge of the channel. Experiments show that MRVQ designed by the proposed algorithm significantly outperforms conventional MRVQ designed without channel information. By building an closed-form formula for the weighted EED with RIA, it also makes the computational complexity incurred during the performance analysis feasible. In comparison with MRVQ design for a fixed index assignment, the computation complexity for quantization design is significantly reduced by using random index assignment. In addition, simulations indicate that our proposed algorithm shows better robustness against channel mismatch than MRVQ design with a fixed index assignment, simply due to the nature of using only the average channel information. Therefore, we conclude that our proposed algorithm is more appropriate in both wireless communications and applications where the complete knowledge of the channel is hard to obtain. Furthermore, we propose two novel algorithms for MRVQ over broadcast channels. One aims to optimize the two corresponding quantizers at two layers alternatively and iteratively, and the other applies under the constraint that each encoding cell is convex and contains the reconstruction point. Finally, we analyze the asymptotic performance of weighted EED for the optimal joint MRVQ. The asymptotic result provides a theoretically achievable quantizer performance level and sheds light on the design of the optimal MRVQ over broadcast channel from a different aspect.

The paradigm of separate source-channel coding is inspired by Shannon's separation result, which implies the asymptotic optimality of designing source and channel coding independently from each other. The result exploits the fact that channel error probabilities can be made arbitrarily small, as long as the block length of the channel code can be made arbitrarily large. However, this is not possible in practice, where the block length is either fixed or restricted to a range of finite values. As a result, the optimality of source and channel coding separation becomes unknown, leading researchers to consider joint source-channel coding (JSCC) to further improve the performance of practical systems that must operate in the finite block length regime. With this motivation, this thesis investigates the application of JSCC principles for multimedia communications over point-to-point, broadcast, and relay channels. All analyses are conducted from the perspective of end-to-end distortion (EED) for results that are applicable to channel codes with finite block lengths in pursuing insights into practical design. The thesis first revisits the fundamental open problem of the separation of source and channel coding in the finite block length regime. Derived formulations and numerical analyses for a source-channel coding system reveal many scenarios where the EED reduction is positive when pairing the channel-optimized source quantizer (COSQ) with an optimal channel code, hence establishing the invalidity of the separation theorem in the finite block length regime. With this, further improvements to JSCC systems are considered by augmenting error detection codes with the COSQ. Closed-form EED expressions for such system are derived, from which necessary optimality conditions are identified and used in proposed algorithms for system design. Results for both the point-to-point and broadcast channels demonstrate significant reductions to the EED without sacrificing bandwidth when considering a tradeoff between quantization and error detection coding rates. Lastly, the JSCC system is considered under relay channels, for which a computable measure of the EED is derived for any relay channel conditions with nonzero channel error probabilities. To emphasize the importance of analyzing JSCC systems under finite block lengths, the large sub-optimality in performance is demonstrated when solving the power allocation configuration problem according to capacity-based formulations that disregard channel errors, as opposed to those based on the EED. Although this thesis only considers one JSCC setup of many, it is concluded that consideration of JSCC systems from a non-asymptotic perspective not only is more meaningful, but also reveals more relevant insight into practical system design. This thesis accomplishes such by maintaining the EED as a measure of system performance in each of the considered point-to-point, broadcast, and relay cases.