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

Contemporary Coding Theory

Coding Theory naturally lies at the intersection of a large number of disciplines in pure and applied mathematics. A multitude of methods and means has been designed to construct, analyze, and decode the resulting codes for communication. This has suggested to bring together researchers in a variety of disciplines within Mathematics, Computer Science, and Electrical Engineering, in order to cross-fertilize generation of new ideas and force global advancement of the field. Areas to be covered are Network Coding, Subspace Designs, General Algebraic Coding Theory, Distributed Storage and Private Information Retrieval (PIR), as well as Code-Based Cryptography

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

Performance Prediction of a Turbo-coded Link in Fading Channels

Channel coding is the method of adding redundancy to the data in order to reduce the frequency of errors or to increase the capacity of a channel. Turbo codes are the most superior class of codes making achievable channel capacity almost at par with the Shannon limits. In Adaptive Modulation and Coding (AMC) the prediction of error performance of a channel is an important step before choosing one of the Modulation Coding Scheme (MCS). Since in Turbo-coded system we donot have analytical relations to relate error performance with the Signal to Noise Ratio (SNR). Therefore, normally simulation results are stored in the form of the look up tables. In this work we propose an error performance prediction model for a BPSK modulated Turbo-coded link. This model predicts performance addressing the fading phenomena for wireless radio channels. It takes the large variations in the SNR level within a code block into account along with the coding parameters. The SNR dB values profile inside a code block is considered in terms of their mean and variance. The model proposed is UMTS compliant and is continuous for values of the MCS code rate and the mean and variance of SNR dB values. It is an easier way of predicting link level performance as it replaces the discrete look up tables. Unlike the look-up tables it can be used for differentiation based analytical techniques used in system level optimization

Automatický systém docházky na bázi rozpoznávání tváře

In colleges, universities, organizations, schools, and offices, taking attendance is one of the most important tasks that must be done on a timely or daily basis. Most of the time, it is done manually, for example, by calling names, passing around sheets of papers or checking respective identification cards. These methods are time consuming and sometimes the records are lost. Hence, there is a need for a computer-based attendance management system which can assist with this process of taking attendances automatically and saving them such that the record can be accessible at any time. The main goal of this project is to create a face recognition-based attendance system that will turn the manual process of taking attendance into an automated one. This project meets the requirements for bringing modernization to the way attendance is being taken, as well as the criteria for time management. It can be implemented in classrooms, offices or anywhere an attendance system is required. Users must be registered into the face recognition attendance system. Registration involves taking a picture of each user’s face, building a model from their facial characteristics, and then saving this model into a database. The camera is tasked with taking pictures of users faces and their facial characteristics are extracted using Python OpenCV. Moreover, the face recognition process comes in when users want to take their attendances. Their facial characteristics are compared to those stored in the database and up on a successful face recognition, the system automatically register the attendance and saves it to another database. An Excel sheet showing all recorded attendances can be generated at any time.Na vysokých školách, univerzitách, organizacích, školách a úřadech je docházka jedním z nejdůležitějších úkolů, které je třeba provádět včas nebo denně. To se obvykle provádí ručně, například vyvoláváním jmen, procházením papírů nebo kontrolou příslušných identifikačních karet. Tyto metody jsou časově náročné a někdy dochází ke ztrátě záznamů. Existuje tedy potřeba počítačového systému pro správu docházky, který může tomuto procesu automatického přebírání docházky a jejího ukládání napomáhat, aby byl záznam kdykoli zpřístupněn. Hlavním cílem této práce je vytvořit docházkový systém založený na rozpoznávání obličeje, který změní manuální proces přebírání docházky na automatizovaný. Tento projekt splňuje požadavky na modernizaci docházkové metody i kritéria pro time management. Může být implementován v učebnách, kancelářích nebo kdekoli, kde je vyžadován docházkový systém. Uživatelé musí být registrováni v docházkovém systému rozpoznávání obličejů. Registrace zahrnuje pořízení snímku obličeje každého uživatele, vytvoření modelu z jeho obličejových charakteristik a následné uložení tohoto modelu do databáze. Kamera má za úkol pořizovat snímky tváří uživatelů a jejich obličejové charakteristiky jsou extrahovány pomocí Python OpenCV. Proces rozpoznávání obličeje navíc přichází na řadu, když si uživatelé chtějí vzít docházku. Jejich obličejové charakteristiky jsou porovnávány s těmi uloženými v databázi a po úspěšném rozpoznání obličeje systém automaticky zaregistruje docházku a uloží ji do jiné databáze. List Excel zobrazující veškerou zaznamenanou docházku lze vygenerovat kdykoli.440 - Katedra telekomunikační technikydobř

The Deep Space Network: A Radio Communications Instrument for Deep Space Exploration

The primary purpose of the Deep Space Network (DSN) is to serve as a communications instrument for deep space exploration, providing communications between the spacecraft and the ground facilities. The uplink communications channel provides instructions or commands to the spacecraft. The downlink communications channel provides command verification and spacecraft engineering and science instrument payload data

Iterative receiver design for MIMO-OFDM systems via Sequential Monte Carlo (SMC) techniques

Master'sMASTER OF ENGINEERIN

Multiterminal Source-Channel Coding

Cooperative communication is seen as a key concept to achieve ultra-reliable communication in upcoming fifth-generation mobile networks (5G). A promising cooperative communication concept is multiterminal source-channel coding, which attracted recent attention in the research community. This thesis lays theoretical foundations for understanding the performance of multiterminal source-channel codes in a vast variety of cooperative communication networks. To this end, we decouple the multiterminal source-channel code into a multiterminal source code and multiple point-to-point channel codes. This way, we are able to adjust the multiterminal source code to any cooperative communication network without modification of the channel codes. We analyse the performance in terms of the outage probability in two steps: at first, we evaluate the instantaneous performance of the multiterminal source-channel codes for fixed channel realizations; and secondly, we average the instantaneous performance over the fading process. Based on the performance analysis, we evaluate the performance of multiterminal source-channel codes in three cooperative communication networks, namely relay, wireless sensor, and multi-connectivity networks. For all three networks, we identify the corresponding multiterminal source code and analyse its performance by the rate region for binary memoryless sources. Based on the rate region, we derive the outage probability for additive white Gaussian noise channels with quasi-static Rayleigh fading. We find results for the exact outage probability in integral form and closed-form solutions for the asymptotic outage probability at high signal-to-noise ratio. The importance of our results is fourfold: (i) we give the ultimate performance limits of the cooperative communication networks under investigation; (ii) the optimality of practical schemes can be evaluated with respect to our results, (iii) our results are suitable for link-level abstraction which reduces complexity in network-level simulation; and (iv) our results demonstrate that all three cooperative communication networks are key technologies to enable 5G applications, such as device to device and machine to machine communications, internet of things, and internet of vehicles. In addition, we evaluate the performance improvement of multiterminal source-channel codes over other (non-)cooperative communications concepts in terms of the transmit power reduction given a certain outage probability level. Moreover, we compare our theoretical results to simulated frame-error-rates of practical coding schemes. Our results manifest the superiority of multiterminal source-channel codes over other (non-)cooperative communications concepts