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.

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.

We consider a two-way relay channel in which two transmitters want to exchange information through a central relay. The relay observes a superposition of the trans- mitted signals from which a function of the transmitted messages is computed for broadcast. We consider the design of codebooks which permit the recovery of a function at the relay and derive information-theoretic bounds on the rates for reliable decoding at the relay. In the spirit of compute-and-forward, we present a multilevel coding scheme that permits reliable computation (or, decoding) of a class of functions at the relay. The function to be decoded is chosen at the relay depending on the channel realization. We define such a class of reliably computable functions for the proposed coding scheme and derive rates that are universally achievable over a set of channel gains when this class of functions is used at the relay. We develop our framework with general modulation formats in mind, but numerical results are presented for the case where each node transmits using 4-ary and 8-ary modulation schemes. Numerical results demonstrate that the flexibility afforded by our proposed scheme permits substantially higher rates than those achievable by always using a fixed function or considering only linear functions over higher order fields. Our numerical results indicate that it is favorable to allow the relay to attempt both compute-and-forward and decode-and-forward decoding. Indeed, either method considered separately is suboptimal for computation over general channels. However, we obtain a converse result when the transmitters are restricted to using identical binary linear codebooks generated uniformly at random. We show that it is impossible for this code ensemble to achieve any rate higher than the maximum of the rates achieved using compute-and-forward and decode-and-forward decoding. Finally, we turn our attention to the design of low density parity check (LDPC) ensembles which can practically achieve these information rates with joint-compute- and-forward message passing decoding. To this end, we construct a class of two-way erasure multiple access channels for which we can exactly characterize the performance of joint-compute-and-forward message passing decoding. We derive the processing rules and a density evolution like analysis for several classes of LDPC ensembles. Utilizing the universally optimal performance of spatially coupled LDPC ensembles with message passing decoding, we show that a single encoder and de- coder with puncturing can achieve the optimal rate region for a range of channel parameters.

Most coding schemes used in today's communication systems are designed for memoryless channels. These codes break down when they are transmitted over channels with memory, which is in fact what real-world channels look like since errors often occur in bursts. Therefore, these systems employ interleaving to spread the errors so that the channel looks more or less memoryless (for the decoder) at the cost of added delay and complexity. In addition, they fail to exploit the memory of the channel which increases the capacity for a wide class of channels. On the other hand, most channels with memory do not have simple and mathematically tractable models, making the design of suitable channel codes more challenging and possibly not practical. Recently, a new model has been proposed known as the queue-based channel (QBC) which is simple enough for mathematical analysis and complex enough for modeling wireless fading channels. In this work, we examine the performance of linear block codes when transmitted over this channel. We break down our focus into two parts. First, we investigate the maximum likelihood decoding of binary linear block codes over the QBC. Since it is well known that for binary symmetric memoryless channels, maximum likelihood decoding reduces to minimum Hamming distance decoding, our objective here is to explore whether there exists a similar relation between these two decoding schemes when the channel does have memory. We give a partial answer for the case of perfect and quasi perfect codes. Next, we study Reed-Solomon (RS) codes and analyze their performance when transmitted over the QBC under the assumption of bounded distance decoding. In particular, we examine the two interleaving strategies encountered when dealing with non-binary codes over a binary input channel; namely, symbol interleaving and bit interleaving. We compare these two interleaving schemes analytically and show that symbol interleaving always outperforms bit interleaving. Non-interleaved Reed-Solomon codes are also covered. We derive some useful expressions pertaining to the calculation of the probability of codeword error. The performance of non-interleaved RS codes are compared to that of interleaved ones for the simplest scenario of the QBC which is the additive (first-order) Markov noise channel with non-negative noise correlation. / Thesis (Master, Mathematics & Statistics) -- Queen's University, 2007-08-20 18:13:29.737

Most of the conventional communication systems use channel interleaving as well as hard decision decoding in their designs, which lead to discarding channel memory and soft-decision information. This simplification is usually done since the complexity of handling the memory or soft-decision information is rather high. In this work, we design two lossy joint source-channel coding (JSCC) schemes that do not use explicit algebraic channel coding for a recently introduced channel model, in order to take advantage of both channel memory and soft-decision information. The channel model, called the non-binary noise discrete channel with queue based noise (NBNDC-QB), obtains closed form expressions for the channel transition distribution, correlation coefficient, and many other channel properties. The channel has binary input and $2^q$-ary output and the noise is a $2^q$-ary Markovian stationary ergodic process, based on a finite queue, where $q$ is the output's soft-decision resolution. We also numerically show that the NBNDC-QB model can effectively approximate correlated Rayleigh fading channels without losing its analytical tractability. The first JSCC scheme is the so called channel optimized vector quantizer (COVQ) and the second scheme consists of a scalar quantizer, a proper index assignment, and a sequence maximum a posteriori (MAP) decoder, designed to harness the redundancy left in the quantizer's indices, the channel's soft-decision output, and noise time correlation. We also find necessary and sufficient condition when the sequence MAP decoder is reduced to an instantaneous symbol-by-symbol decoder, i.e., a simple instantaneous mapping. / Thesis (Master, Electrical & Computer Engineering) -- Queen's University, 2011-09-25 19:43:28.785

The efficient and reliable communication of data from multiple sources to a single receiver plays an important role in emerging applications such as wireless sensor networks. The correlation among observations picked-up by spatially distributed sensors in such a network can be exploited to enhance the efficiency and reliability of communication. In particular, information theory shows that optimal communication of information from correlated sources requires distributed joint source-channel (DJSC) coding. This dissertation develops new approaches to designing DJSC codes based on low density parity check (LDPC) codes. The existence of low complexity code optimization algorithms and decoding algorithms make these codes ideal for joint optimization and decoding of multiple codes operating on correlated sources. The well known EXIT analysis-based LDPC code optimization method for channel coding in single-user point-to-point systems is extended to the optimization of two-user LDPC codes for DJSC coding in multi-access channels (MACs) with correlated users. Considering an orthogonal MAC with two correlated binary sources, an asymptotically optimal DJSC code construction capable of achieving any rate-pair in the theoretically-achievable two-user rate-region is presented. A practical approach to realizing this scheme using irregular LDPC codes is then developed. Experimental results are presented which demonstrate that the proposed codes can approach theoretical bounds when the codeword length is increased. For short codeword length and high inter-source correlation, these DJSC codes are shown to significantly outperform separate source and channel codes. Next, the DJSC code design for the transmission of a pair of correlated binary sources over a Gaussian MAC (GMAC) is investigated. The separate source and channel coding is known to be sub-optimal in this case. For the optimization of a pair of irregular LDPC codes, the EXIT analysis for message passing in a joint factor-graph decoder is analyzed, and an approach to modeling the probability density functions of messages associated with graph nodes which represent the inter-source dependence is proposed. Simulation results show that, for sufficiently large codeword lengths and high inter-source correlation, the proposed DJSC codes for GMAC can achieve rates higher than the theoretical upper bound for separate source and channel coding.

Radio spectrum has become a scarce and priced resource due to the rapid growth of wireless networks. However, recent surveys conducted by the FCC indicate that a large part of the allotted frequency spectrum lies unused. Cognitive radio systems, built on the software defined radios, allow the efficient usage of these unused frequency spectrum. Cognitive radio systems can be modeled as a multiple access channel in which certain users have the priority (primary users) while others (cognitive or secondary users) are allowed to access the channels without causing any interference to the primary users. However a secondary user’s transmissions not only encounter high levels of uncertainty and variability in the number of channels available to them, but they also suffer data losses if a primary user activity occurs. Under such rigid constraints, the reliable transmission of real time multimedia of a secondary user with an acceptable quality of service becomes challenging. Multimedia transmission in a cognitive system requires channel adaptive source and channel coding schemes. In order to address this problem, this thesis investigates and develops a novel joint source-channel coding (JSCC) approach. The proposed JSCC allows the dynamic generation of codes, which minimizes the end-to-end distortion. This JSCC is based on quantized frame expansions to introduce redundancy into transmitted data. An algorithm has been developed to determine the optimal trade-off between redundancy and quantization rate, under a constraint on channel capacity. The proposed approach does not require the communication of any overhead data between the transmitter and receiver. When compared to codes commonly used to deal with packet losses, simulation results indicate that the proposed JSCC can achieve lower distortion for secondary user’s transmissions in cognitive radio systems.

The efficient and reliable communication of data from multiple sources to a single receiver plays an important role in emerging applications such as wireless sensor networks. The correlation among observations picked-up by spatially distributed sensors in such a network can be exploited to enhance the efficiency and reliability of communication. In particular, information theory shows that optimal communication of information from correlated sources requires distributed joint source-channel (DJSC) coding. This dissertation develops new approaches to designing DJSC codes based on low density parity check (LDPC) codes. The existence of low complexity code optimization algorithms and decoding algorithms make these codes ideal for joint optimization and decoding of multiple codes operating on correlated sources. The well known EXIT analysis-based LDPC code optimization method for channel coding in single-user point-to-point systems is extended to the optimization of two-user LDPC codes for DJSC coding in multi-access channels (MACs) with correlated users. Considering an orthogonal MAC with two correlated binary sources, an asymptotically optimal DJSC code construction capable of achieving any rate-pair in the theoretically-achievable two-user rate-region is presented. A practical approach to realizing this scheme using irregular LDPC codes is then developed. Experimental results are presented which demonstrate that the proposed codes can approach theoretical bounds when the codeword length is increased. For short codeword length and high inter-source correlation, these DJSC codes are shown to significantly outperform separate source and channel codes. Next, the DJSC code design for the transmission of a pair of correlated binary sources over a Gaussian MAC (GMAC) is investigated. The separate source and channel coding is known to be sub-optimal in this case. For the optimization of a pair of irregular LDPC codes, the EXIT analysis for message passing in a joint factor-graph decoder is analyzed, and an approach to modeling the probability density functions of messages associated with graph nodes which represent the inter-source dependence is proposed. Simulation results show that, for sufficiently large codeword lengths and high inter-source correlation, the proposed DJSC codes for GMAC can achieve rates higher than the theoretical upper bound for separate source and channel coding.

Communication networks are an integral part of the Internet of Things (IoT) era. They enable endless opportunities for connectivity in a wide range of applications, leading to advances in efficiency of day-to-day life. While creating opportunities, they also incur several new challenges. In general, we wish to design a system that performs optimally well in all aspects. However, there usually exist competing objectives which lead to tradeoffs. In this thesis, driven by several applications, new features and objectives are included into the system model, making it closer to reality and needs. The results presented in this thesis aim at providing insight into the fundamental tradeoff of the system performance which can serve as a guideline for the optimal design of real-world communication systems. The thesis is divided into two parts. The first part considers the aspect of signal reconstruction requirement as a new objective in the source and channel coding problems. In this part, we consider the framework where the quality and/or availability of the side information can be influenced by a cost-constrained action sequence. In the source coding problem, we impose a constraint on the reconstruction sequence at the receiver that it should be reproduced at the sender, and characterize the fundamental tradeoff in the form of the rate-distortion-cost region, revealing the optimal relation between compression rate, distortion, and action cost. The channel coding counterpart is then studied where a reconstruction constraint is imposed on the channel input sequence such that it should be reconstructed at the receiver. An extension to the multi-stage channel coding problem is also considered where inner and outer bounds to the capacity region are given. The result on the channel capacity reveals interesting consequence of imposing an additional reconstruction requirement on the system model which has a causal processing structure. In the second part, we consider the aspect of information security and privacy in lossy source coding problems. The sender wishes to compress the source sequence in order to satisfy a distortion criterion at the receiver, while revealing only limited knowledge about the source to an unintended user. We consider three different aspects of information privacy. First, we consider privacy of the source sequence against the eavesdropper in the problem of source coding with action-dependent side information. Next, we study privacy of the source sequence due to the presence of a public helper in distributed lossy source coding problems. The public helper is assumed to be either a user who provides side information over a public link which can be eavesdropped, or a legitimate user in the network who helps to relay information to the receiver, but may not ignore the information that is not intended for it. Lastly, we take on a new perspective of information privacy in the source coding problem. That is, instead of protecting the source sequence, we are interested in the privacy of the reconstruction sequence with respect to a user in the system. For above settings, we provide the complete characterization of the rate-distortion(-cost)-leakage/equivocation region or corresponding inner and outer bounds for discrete memoryless systems. / <p>QC 20140514</p>