Detta arbete börjar med att presentera en kodningssats gällande linjärkodning över ändliga ringar för kodning av korrelerade diskretaminneslösa källor. Denna sats inkluderar som specialfall motsvarandeuppnåbarhetssatser från Elias och Csiszár gällande linjär kodning överändliga kroppar. Dessutom visas det att för varje uppsättning av ändligakorrelerade diskreta minneslösa källor, så finns alltid en sekvens avlinjära kodare över vissa ändliga icke-kropp-ringar som uppnårdatakompressionsgränsen bestämd av Slepian-Wolf-regionen. Därmed slutervi problemet med linjär kodning över ändlig icke-kropps-ringar föri.i.d. datakomprimering med positiv bekräftelse gällande existens. Vi studerar också kodning av funktioner, där avkodaren är intresseradav att återskapa en diskret mappning av data som genererats av flerakorrelerade i.i.d. källor och som kodats individuellt. Vi föreslårlinjär kodning över ändliga ringar som en alternativ lösning på dettaproblem. Vi visar att linjär kodning över ändliga ringar presterarbättre än sin ändliga-kropp-motsvarighet, liksom dessutomSlepian-Wolf-kodning, i termer av att uppnå bättre kodningshastigheterför kodning av flera diskreta funktioner. För att generalisera ovannämnda genomförbarhetssatser, både gällandedatakompression och funktionskodningsproblemet, till Markov-källor(homogena irreducerbara Markov-källor), så introducerar vi ett nyttkoncept gällande klassificering av typiska sekvenser, benämndSupremus-typiska sekvenser. Den asymptotiska likafördelningsprincipensamt en generaliserad version av typiskhets-hjälpsatsen förSupremus-typiska sekvenser bevisas. Jämfört med traditionell (stark ochsvag) typiskhet, så tillåter Supremus-typiskhet oss att härleda bättretillgängliga verktyg och resultat, som låter oss bevisa att linjärkodning över ringar är överlägsen andra metoder. I motsats härtillmisslyckas argument baserade på den traditionella versionen antingen medatt nå liknande resultat eller så är de härledda resultaten svåra attanalysera på grund av en utmanande utvärdering av entropitakt. För att ytterligare undersöka den grundläggande skillnaden mellantraditionell typiskhet och Supremus-typiskhet och dessutom göra våraresultat än mer allmänt gällande, så betraktar vi ävenasymptotiskt medelvärdesstationära ergodiska källor. Våra resultat visaratt en inducerad transformation med avseende på en ändligt mätbar mängdöver ett rekurrent asymptotiskt medelvärdesstationärt dynamiskt systemmed ett sigma-ändlig sannolikhetsmått är asymptotisktmedelvärdesstationär. Följaktligen så gällerShannon-McMillan-Breiman-teoremet, liksom Shannon-McMillan-teoremet, föralla reducerade processer härledda ur rekurrenta asymptotisktmedelvärdesstationära stokastisk processer. Alltså ser vi att dettraditionella typiskhetkonceptet endast realiserarShannon-McMillan-Breiman-teoremet i ett globalt hänseende, medanSupremus-typiskhet leder till att resultatet håller samtidigt även föralla härledda reducerade sekvenser. / This work first presents a coding theorem on linear coding over finite rings for encoding correlated discrete memoryless sources. This theorem covers corresponding achievability theorems from Elias and Csiszár on linear coding over finite fields as special cases. In addition, it is shown that, for any set of finite correlated discrete memoryless sources, there always exists a sequence of linear encoders over some finite non-field rings which achieves the data compression limit, the Slepian--Wolf region. Hence, the optimality problem regarding linear coding over finite non-field rings for i.i.d. data compression is closed with positive confirmation with respect to existence. We also address the function encoding problem, where the decoder is interested in recovering a discrete function of the data generated and independently encoded by several correlated i.i.d. sources. We propose linear coding over finite rings as an alternative solution to this problem. It is demonstrated that linear coding over finite rings strictly outperforms its field counterpart, as well as the Slepian--Wolf scheme, in terms of achieving better coding rates for encoding many discrete functions. In order to generalise the above achievability theorems, on both the data compression and the function encoding problems, to the Markovian settings (homogeneous irreducible Markov sources), a new concept of typicality for sequences, termed Supremus typical sequences, is introduced. The Asymptotically Equipartition Property and a generalised typicality lemma of Supremus typical sequences are proved. Compared to traditional (strong and weak) typicality, Supremus typicality allows us to derive more accessible tools and results, based on which it is once again proved that linear technique over rings is superior to others. In contrast, corresponding arguments based on the traditional versions either fail to draw similar conclusions or the derived results are often hard to analyse because it is complicated to evaluate entropy rates. To further investigate the fundamental difference between traditional typicality and Supremus typicality and to bring our results to a more universal setting, asymptotically mean stationary ergodic sources, we look into the ergodic properties featured in these two concepts.Our studies prove that an induced transformation with respect to a finite measure set of a recurrent asymptotically mean stationary dynamical system with a sigma-finite measure is asymptotically mean stationary. Consequently, the Shannon-McMillan-Breiman Theorem, as well as the Shannon-McMillan Theorem, holds simultaneously for all reduced processes of any finite-state recurrent asymptotically mean stationary random process.From this, we see that the traditional typicality concept only realises the Shannon-McMillan-Breiman Theorem in the global sequence, while Supremus typicality engraves the simultaneous effects claimed in the previous statement into all reduced sequences as well. / <p>QC 20150225</p>

Dans cette thèse, nous concevons et étudions un système de communication bidirectionnel par lumière visible (VLC) entre une diode électroluminescente (DEL) de couleur, intégrée à un objet connecté, et un smartphone. Le dispositif est ainsi capable d'envoyer et de recevoir des informations à travers sa DEL, tandis que le smartphone utilise sa caméra pour recevoir des données et son flash pour envoyer des informations. Nous mettons en œuvre et évaluons expérimentalement ce système VLC DEL-à-camera conçu spécifiquement pour les DELs de couleur à faible puissance. En nous appuyant sur les résultats d'une vaste étude expérimentale, nous modélisons, pour la première fois dans la littérature, le canal de communication DEL-à-caméra. Nous proposons alors un modèle de processus de Bernoulli modulé par une chaîne de Markov, qui nous permet d'étudier facilement l'efficacité de différentes stratégies de retransmission des messages. Nous exploitons ce modèle afin de concevoir un simulateur pour l'évaluation des performances des communications DEL-à-caméra. Afin d'obtenir un système de communication bidirectionnel, nous étudions ensuite les communications de type flash-vers-DEL entre un smartphone non-modifié et une petite DEL de couleur. Les performances, bien que limitées, sont suffisantes pour établir une voie retour qui permet de mettre en œuvre des mécanismes de fiabilisation. Nous proposons alors un mécanisme de codage linéaire pseudo-aléatoire, spécialement adapté aux conditions et contraintes du système DEL-à-caméra en ligne de visée directe. Notre évaluation expérimentale souligne que ce type d'approche augmente le rendement jusqu'à deux fois par rapport aux stratégies de retransmission classiques. Enfin, la plupart des objets que nous adressons ont des contraintes énergétiques importantes. Par conséquent, nous comparons la consommation d'énergie de notre système avec celle d'un module Bluetooth Low Energy avec une activité similaire. Nos résultats montrent que notre système réduit la consommation d'énergie dans le cadre d'un profil d'utilisation classique. / With the exponential growth of the Internet of Things, people now expect every household appliance to be smart and connected. At the same time, smartphones have become ubiquitous in our daily life. Their continuous performance improvement and their compatibility with a broad range of radio protocols as WiFi, Bluetooth Low Energy (BLE) or NFC make them the most convenient way to interact with these smart objects. However, providing wireless connectivity with BLE or NFC means adding an extra chipset and an antenna, increasing the object size and price. Previous works already have demonstrated the possibility of receiving information through visible light using an unmodified smartphone thanks to its camera. Also, LED-to-LED communication for smart devices like toys has been shown previously. However, past efforts in LED to camera communication for IoT device communication have been limited. In this work, we design LightIoT, a bidirectional visible-light communication (VLC) system between a low-cost, low-power colored LED that is part of an IoT device and an off-the-shelf smartphone. The IoT device is thus able to send and receive information through its LED, while the smartphone uses its camera to receive data and its flashlight to send information. We implement and experimentally evaluate a LED-to-camera VLC system, designed specifically for small LEDs. The proposed solution exploits the rolling shutter effect of unmodified smartphone cameras and an original decoding algorithm, achieving a throughput of nearly 2 kb/s. Based on the insight gained from an extensive experimental study, we model, for the first time in the literature, the LED-to-camera communication channel. We propose a Markov-modulated Bernoulli process model, which allows us to easily study the performance of different message retransmission strategies. We further exploit this model to implement a simulator for LED-to-Camera communications performance evaluation. In order to achieve bi-directional communications, we evaluate flashlight-to-LED communications using non-rooted smartphones and small LEDs. With these constraints, our implementation achieves a throughput of 30 bits/second. While limited, this is enough for a feed-back channel coming to support the required redundancy mechanisms. Some of these redundancy mechanisms are based on random linear coding, never tested previously in VLC. Therefore, we design and implement, for the first time in the literature, a pseudo random linear coding scheme especially fitted for line-of-sight LED-to-camera conditions. Experimental evaluation highlights that this type of approach increases the goodput up to twice compared to classical retransmission strategies. Finally, we compare the energy consumption of LightIoT with the one of a BLE module with similar activity. Our results show that using the LED for communication purposes reduces the energy consumption under a normal usage behavior.