Secure, reliable, and efficient communication over the wiretap channel

Secure wireless communication between devices is essential for modern communication systems. Physical-layer security over the wiretap channel may provide an additional level of secrecy beyond the current cryptographic approaches. Given a sender Alice, a legitimate receiver Bob, and a malicious eavesdropper Eve, the wiretap channel occurs when Eve experiences a worse signal-to-noise ratio than Bob. Previous study of the wiretap channel has tended to make assumptions that ignore the reality of wireless communication. This thesis presents a study of short block length codes with the aim of both reliability for Bob and confusion for Eve. The standard approach to wiretap coding is shown to be very inefficient for reliability. Quantifying Eve's confusion in terms of entropy is not solved in many cases, though it is possible for codes with a moderate complexity trellis representation. Using error rate arguments, error correcting codes with steep performance curves turn out to be desirable both for reliability and confusion.Masteroppgave i informatikkINF399MAMN-INFMAMN-PRO

The Error-Pattern-Correcting Turbo Equalizer

The error-pattern correcting code (EPCC) is incorporated in the design of a turbo equalizer (TE) with aim to correct dominant error events of the inter-symbol interference (ISI) channel at the output of its matching Viterbi detector. By targeting the low Hamming-weight interleaved errors of the outer convolutional code, which are responsible for low Euclidean-weight errors in the Viterbi trellis, the turbo equalizer with an error-pattern correcting code (TE-EPCC) exhibits a much lower bit-error rate (BER) floor compared to the conventional non-precoded TE, especially for high rate applications. A maximum-likelihood upper bound is developed on the BER floor of the TE-EPCC for a generalized two-tap ISI channel, in order to study TE-EPCC's signal-to-noise ratio (SNR) gain for various channel conditions and design parameters. In addition, the SNR gain of the TE-EPCC relative to an existing precoded TE is compared to demonstrate the present TE's superiority for short interleaver lengths and high coding rates.Comment: This work has been submitted to the special issue of the IEEE Transactions on Information Theory titled: "Facets of Coding Theory: from Algorithms to Networks". This work was supported in part by the NSF Theoretical Foundation Grant 0728676

Underwater acoustic communications and adaptive signal processing

This dissertation proposes three new algorithms for underwater acoustic wireless communications. One is a new tail-biting circular MAP decoder for full tail-biting convolution (FTBC) codes for very short data blocks intended for Internet of Underwater Things (IoUT). The proposed algorithm was evaluated by ocean experiments and computer simulations on both Physical (PHY) and Media access control (MAC) layers. The ocean experimental results show that without channel equalization, the full tail-biting convolution (FTBC) codes with short packet lengths not only can perform similarly to zero-tailing convolution (ZTC) codes in terms of bit error rate (BER) in the PHY layer. Computer simulation results show that the FTBC codes outperform the ZTC codes in terms of MAC layer metrics, such as collision rate and bandwidth utilization, in a massive network of battery powered IoUT devices. Second, this dissertation also proposes a new approach to utilizing the underwater acoustic (UWA) wireless communication signals acquired in a real-world experiment as a tool for evaluating new coding and modulation schemes in realistic doubly spread UWA channels. This new approach, called passband data reuse, provides detailed procedures for testing the signals under test (SUT) that change or add error correction coding, change bit to symbol mapping (baseband modulation) schemes from a set of original experimental data --Abstract, page iv

Codes on Graphs and More

Modern communication systems strive to achieve reliable and efficient information transmission and storage with affordable complexity. Hence, efficient low-complexity channel codes providing low probabilities for erroneous receptions are needed. Interpreting codes as graphs and graphs as codes opens new perspectives for constructing such channel codes. Low-density parity-check (LDPC) codes are one of the most recent examples of codes defined on graphs, providing a better bit error probability than other block codes, given the same decoding complexity. After an introduction to coding theory, different graphical representations for channel codes are reviewed. Based on ideas from graph theory, new algorithms are introduced to iteratively search for LDPC block codes with large girth and to determine their minimum distance. In particular, new LDPC block codes of different rates and with girth up to 24 are presented. Woven convolutional codes are introduced as a generalization of graph-based codes and an asymptotic bound on their free distance, namely, the Costello lower bound, is proven. Moreover, promising examples of woven convolutional codes are given, including a rate 5/20 code with overall constraint length 67 and free distance 120. The remaining part of this dissertation focuses on basic properties of convolutional codes. First, a recurrent equation to determine a closed form expression of the exact decoding bit error probability for convolutional codes is presented. The obtained closed form expression is evaluated for various realizations of encoders, including rate 1/2 and 2/3 encoders, of as many as 16 states. Moreover, MacWilliams-type identities are revisited and a recursion for sequences of spectra of truncated as well as tailbitten convolutional codes and their duals is derived. Finally, the dissertation is concluded with exhaustive searches for convolutional codes of various rates with either optimum free distance or optimum distance profile, extending previously published results

Joint Source-Channel Coding Optimized On End-to-End Distortion for Multimedia Source

In order to achieve high efficiency, multimedia source coding usually relies on the use of predictive coding. While more efficient, source coding based on predictive coding has been considered to be more sensitive to errors during communication. With the current volume and importance of multimedia communication, minimizing the overall distortion during communication over an error-prone channel is critical. In addition, for real-time scenarios, it is necessary to consider additional constraints such as fix and small delay for a given bit rate. To comply with these requirements, we seek an efficient joint source-channel coding scheme. In this work, end-to-end distortion is studied for a first order autoregressive synthetic source that represents a general multimedia traffic. This study reveals that predictive coders achieve the same channel-induced distortion performance as memoryless codecs when applying optimal error concealment. We propose a joint source-channel system based on incremental redundancy that satisfies the fixed delay and error-prone channel constraints and combines DPCM as a source encoder and a rate-compatible punctured convolutional (RCPC) error control codec. To calculate the joint source-channel coding rate allocation that minimizes end-to-end distortion, we develop a Markov Decision Process (MDP) approach for delay constrained feedback Hybrid ARQ, and we use a Dynamic Programming (DP) technique. Our simulation results support the improvement in end-to-end distortion compared to a conventional Forward Error Control (FEC) approach with no feedback

Partitions of codes

In this thesis we look at coding theory wherein we introduce the concept of perspective, a generalisation on the minimum distance of a code, which naturally leads to a partition of the code. Subsequently we introduce focused splittings, which shall be shown to be a generalisation of perfect codes. We investigate the existence of such objects, and address questions such as the complexity of finding a focused splittings, which we show to be NPComplete. We analyse the symmetries of focused splittings. We use focused splittings to address the problem of error correction and we construct an encoding method based on them. Finally we test this construction for various classes of focused splittings

Irregular Variable Length Coding

In this thesis, we introduce Irregular Variable Length Coding (IrVLC) and investigate its applications, characteristics and performance in the context of digital multimedia broadcast telecommunications. During IrVLC encoding, the multimedia signal is represented using a sequence of concatenated binary codewords. These are selected from a codebook, comprising a number of codewords, which, in turn, comprise various numbers of bits. However, during IrVLC encoding, the multimedia signal is decomposed into particular fractions, each of which is represented using a different codebook. This is in contrast to regular Variable Length Coding (VLC), in which the entire multimedia signal is encoded using the same codebook. The application of IrVLCs to joint source and channel coding is investigated in the context of a video transmission scheme. Our novel video codec represents the video signal using tessellations of Variable-Dimension Vector Quantisation (VDVQ) tiles. These are selected from a codebook, comprising a number of tiles having various dimensions. The selected tessellation of VDVQ tiles is signalled using a corresponding sequence of concatenated codewords from a Variable Length Error Correction (VLEC) codebook. This VLEC codebook represents a specific joint source and channel coding case of VLCs, which facilitates both compression and error correction. However, during video encoding, only particular combinations of the VDVQ tiles will perfectly tessellate, owing to their various dimensions. As a result, only particular sub-sets of the VDVQ codebook and, hence, of the VLEC codebook may be employed to convey particular fractions of the video signal. Therefore, our novel video codec can be said to employ IrVLCs. The employment of IrVLCs to facilitate Unequal Error Protection (UEP) is also demonstrated. This may be applied when various fractions of the source signal have different error sensitivities, as is typical in audio, speech, image and video signals, for example. Here, different VLEC codebooks having appropriately selected error correction capabilities may be employed to encode the particular fractions of the source signal. This approach may be expected to yield a higher reconstruction quality than equal protection in cases where the various fractions of the source signal have different error sensitivities. Finally, this thesis investigates the application of IrVLCs to near-capacity operation using EXtrinsic Information Transfer (EXIT) chart analysis. Here, a number of component VLEC codebooks having different inverted EXIT functions are employed to encode particular fractions of the source symbol frame. We show that the composite inverted IrVLC EXIT function may be obtained as a weighted average of the inverted component VLC EXIT functions. Additionally, EXIT chart matching is employed to shape the inverted IrVLC EXIT function to match the EXIT function of a serially concatenated inner channel code, creating a narrow but still open EXIT chart tunnel. In this way, iterative decoding convergence to an infinitesimally low probability of error is facilitated at near-capacity channel SNRs

Analysis and Error Performances of Convolutional Doubly Orthogonal Codes with Non-Binary Alphabets

RÉSUMÉ Récemment, les codes convolutionnels simple-orthogonaux de Massey ont été adaptés au décodage efficace moderne. Plus spécifiquement, les caractéristiques et propriétés d'simple-orthogonalité de ce groupe de codes ont été étendues aux conditions de double-orthogonalité afin d'accommoder les algorithmes de décodage itératif modernes, donnant lieu aux codes convolutionnels doublement orthogonaux notés codes CDOs. Ainsi À l'écart de l'algorithme de propagation de croyance (Belief Propagation, BP), le décodage itératif à seuil, développé à partir de l'algorithme de décodage à seuil de Massey, peut aussi être appliqué aux codes CDOs. Cet algorithme est particulièrement attrayant car il offre une complexité moins élevée que celle de l'algorithme de décodage à propagation de croyance (en anglais Belief Propagation, noté BP). Les codes convolutionnels doublement orthogonaux peuvent être divisés en deux groupes: les codes CDOs non-récursifs utilisant des structures d’encodage à un seul registre à décalage, et les codes CDOs récursifs (en anglais Recursive CDO, notés RCDO) construits à partir de proto-graphes. À des rapports signal-à-bruit Eb/N0 modérés, les codes non-récursifs CDO présentent des performances d’erreurs comparables à celles des autres technique courantes lorsqu’ils sont utilisés avec l'algorithme de décodage à seuil, présentant ainsi une alternative attrayante aux codes de contrôle de parité à faible densité (en Anglais Low-Density Parity-Check codes, notés LDPC). Par contre, les codes CDOs récursifs RCDO fournissent des performances d'erreur très élevées en utilisant le décodage BP, se rapprochent de la limite de Shannon. De plus, dans l'étude des codes LDPC, l'exploitation des corps finis GF(q) avec q>2 comme alphabets du code contribue à l'amélioration des performances avec l'algorithme de décodage BP. Ces derniers sont appelés alors les codes LDPC q-aires. Inspiré du succès de l'application des alphabets dans un corps de Galois de q éléments GF(q), dans les codes LDPC, nous portons dans cette thèse, notre attention aux codes CDO utilisant les corps GF(q) finis, appelés CDO q-aires. Les codes CDO récursifs et non-récursifs binaires sont ainsi étendus à l'utilisation des corps finis GF(q) avec q>2. Leurs performances d’erreur ont été déterminées par simulation à l’ordinateur en utilisant les deux algorithmes de décodage itératif : à seuil et BP. Bien que l'algorithme de décodage à seuil souffre d'une perte de performance par rapport à l'algorithme BP, sa complexité de décodage est substantiellement réduite grâce à la rapide convergence au message estimé. On montre que les codes CDO q-aires fournissent des performances d'erreur supérieures à celles des codes binaires aussi bien dans le décodage itératif à seuil et dans le décodage BP. Cette supériorité en termes de taux d'erreur est plus prononcée à haut rapport signal-à-bruit Eb/N0. Cependant ces avantages sont obtenus au prix d'une complexité plus élevée, complexité évaluée par le nombre des différentes opérations requises dans le processus de décodage. Afin de faciliter l'implémentation des codes CDO q-aires, nous avons examiné l'effet des alphabets quantifiés dans la procédure de décodage sur les performances d'erreur. Il a été démontré que le processus de décodage nécessite une quantification plus fine que dans le cas des codes binaires.----------ABSTRACT Recently, the self orthogonal codes due to Massey were adapted in the realm of modern decoding techniques. Specifically, the self orthogonal characteristics of this set of codes are expanded to the doubly orthogonal conditions in order to accommodate the iterative decoding algorithms, giving birth to the convolutional doubly orthogonal (CDO) codes. In addition to the belief propagation (BP) algorithm, the CDO codes also lend themselves to the iterative threshold decoding, which has been developed from the threshold decoding algorithm raised by Massey, offering a lower-complexity alternative for the BP decoding algorithm. The convolutional doubly orthogonal codes are categorized into two subgroups: the non-recursive CDO codes featured by the shift-register structures without feedback, while the recursive CDO (RCDO) codes are constructed based on shift registers with feedback connections from the outputs. The non-recursive CDO codes demonstrate competitive error performances under the iterative threshold decoding algorithm in moderate Eb/N0 region, providing another set of low-density parity-check convolutional (LDPCC) codes with outstanding error performances. On the other hand, the recursive CDO codes enjoy exceptional error performances under BP decoding, enjoying waterfall performances close to the Shannon limit. Additionally, in the study of the LDPC codes, the exploration of the finite fields GF(q) with q>2 as the code alphabets had proved to improve the error performances of the codes under the BP algorithm, giving rise to the q-ary LDPC codes. Inspired by the success of the application of GF(q) alphabets upon the LDPC codes, we focus our attention on the CDO codes with their alphabets generalized with the finite fields; particularly, we investigated the effects of this generalization on the error performances of the CDO codes and investigated their underlying causes. In this thesis, both the recursive and non-recursive CDO codes are extended with the finite fields GF(q) with q>2, referred to as q-ary CDO codes. Their error performances are examined through simulations using both the iterative threshold decoding and the BP decoding algorithms. Whilst the threshold decoding algorithm suffers some performance loss as opposed to the BP algorithm, it phenomenally reduces the complexity in the decoding process mainly due to the fast convergence of the messages. The q-ary CDO codes demonstrated superior error performances as compared to their binary counterparts under both the iterative threshold decoding and the BP decoding algorithms, which is most pronounced in high Eb/N0 region; however, these improvements have been accompanied by an increase in the decoding complexity, which is evaluated through the number of different operations needed in the decoding process. In order to facilitate the implementation of the q-ary CDO codes, we examined the effect of quantized message alphabets in the decoding process on the error performances of the codes

Contribution to the construction of fingerprinting and watermarking schemes to protect mobile agents and multimedia content

The main characteristic of fingerprinting codes is the need of high error-correction capacity due to the fact that they are designed to avoid collusion attacks which will damage many symbols from the codewords. Moreover, the use of fingerprinting schemes depends on the watermarking system that is used to embed the codeword into the content and how it honors the marking assumption. In this sense, even though fingerprinting codes were mainly used to protect multimedia content, using them on software protection systems seems an option to be considered. This thesis, studies how to use codes which have iterative-decoding algorithms, mainly turbo-codes, to solve the fingerprinting problem. Initially, it studies the effectiveness of current approaches based on concatenating tradicioanal fingerprinting schemes with convolutional codes and turbo-codes. It is shown that these kind of constructions ends up generating a high number of false positives. Even though this thesis contains some proposals to improve these schemes, the direct use of turbo-codes without using any concatenation with a fingerprinting code as inner code has also been considered. It is shown that the performance of turbo-codes using the appropiate constituent codes is a valid alternative for environments with hundreds of users and 2 or 3 traitors. As constituent codes, we have chosen low-rate convolutional codes with maximum free distance. As for how to use fingerprinting codes with watermarking schemes, we have studied the option of using watermarking systems based on informed coding and informed embedding. It has been discovered that, due to different encodings available for the same symbol, its applicability to embed fingerprints is very limited. On this sense, some modifications to these systems have been proposed in order to properly adapt them to fingerprinting applications. Moreover the behavior and impact over a video produced as a collusion of 2 users by the YouTube’s s ervice has been s tudied. We have also studied the optimal parameters for viable tracking of users who have used YouTube and conspired to redistribute copies generated by a collusion attack. Finally, we have studied how to implement fingerprinting schemes and software watermarking to fix the problem of malicious hosts on mobile agents platforms. In this regard, four different alternatives have been proposed to protect the agent depending on whether you want only detect the attack or avoid it in real time. Two of these proposals are focused on the protection of intrusion detection systems based on mobile agents. Moreover, each of these solutions has several implications in terms of infrastructure and complexity.Els codis fingerprinting es caracteritzen per proveir una alta capacitat correctora ja que han de fer front a atacs de confabulació que malmetran una part important dels símbols de la paraula codi. D'atra banda, la utilització de codis de fingerprinting en entorns reals està subjecta a que l'esquema de watermarking que gestiona la incrustació sigui respectuosa amb la marking assumption. De la mateixa manera, tot i que el fingerprinting neix de la protecció de contingut multimèdia, utilitzar-lo en la protecció de software comença a ser una aplicació a avaluar. En aquesta tesi s'ha estudiat com aplicar codis amb des codificació iterativa, concretament turbo-codis, al problema del rastreig de traïdors en el context del fingerprinting digital. Inicialment s'ha qüestionat l'eficàcia dels enfocaments actuals en la utilització de codis convolucionals i turbo-codis que plantegen concatenacions amb esquemes habituals de fingerprinting. S'ha demostrat que aquest tipus de concatenacions portaven, de forma implícita, a una elevada probabilitat d'inculpar un usuari innocent. Tot i que s'han proposat algunes millores sobre aquests esquemes , finalment s'ha plantejat l'ús de turbocodis directament, evitant així la concatenació amb altres esquemes de fingerprinting. S'ha demostrat que, si s'utilitzen els codis constituents apropiats, el rendiment del turbo-descodificador és suficient per a ser una alternativa aplicable en entorns amb varis centenars d'usuaris i 2 o 3 confabuladors . Com a codis constituents s'ha optat pels codis convolucionals de baix ràtio amb distància lliure màxima. Pel que fa a com utilitzar els codis de fingerprinting amb esquemes de watermarking, s'ha estudiat l'opció d'utilitzar sistemes de watermarking basats en la codificació i la incrustació informada. S'ha comprovat que, degut a la múltiple codificació del mateix símbol, la seva aplicabilitat per incrustar fingerprints és molt limitada. En aquest sentit s'ha plantejat algunes modificacions d'aquests sistemes per tal d'adaptar-los correctament a aplicacions de fingerprinting. D'altra banda s'ha avaluat el comportament i l'impacte que el servei de YouTube produeix sobre un vídeo amb un fingerprint incrustat. A més , s'ha estudiat els paràmetres òptims per a fer viable el rastreig d'usuaris que han confabulat i han utilitzat YouTube per a redistribuir la copia fruït de la seva confabulació. Finalment, s'ha estudiat com aplicar els esquemes de fingerprinting i watermarking de software per solucionar el problema de l'amfitrió maliciós en agents mòbils . En aquest sentit s'han proposat quatre alternatives diferents per a protegir l'agent en funció de si és vol només detectar l'atac o evitar-lo en temps real. Dues d'aquestes propostes es centren en la protecció de sistemes de detecció d'intrusions basats en agents mòbils. Cadascuna de les solucions té diverses implicacions a nivell d'infrastructura i de complexitat.Postprint (published version